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Microwave drying of particulate foods in a spouted bed

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MICROWAVE DRYING OF PARTICULATE FOODS IN A
SPOUTED BED
By
HAO FENG
A dissertation submitted in partial fulfillment of
the requirements for the degree of
DOCTOR OF PHILOSOPHY
WASHINGTON STATE UNIVERSITY
Program in Engineering Science
MAY 2000
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TO THE FACULTY OF WASHINGTON STATE UNIVERSITY:
The members of the Committee appointed to examine the dissertation of HAO FENG
find it satisfactory and recommend that it be accepted.
Chair
f t
n
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ACKNOWLEDGMENTS
I would like to express my sincere thanks to my major professor. Dr. Juming Tang, for
his guidance, motivation, and encouragement throughout the course of my study and research
at Washington State University. I greatly appreciate my doctoral committee members. Dr.
Ralph Cavalieri. Dr. Ovid Plumb, and Dr. Barry Swanson, for their support, advice, and
direction during the course of my research and in the preparation of this manuscript. It is my
great pleasure to have the opportunity to learn their academic excellence.
I am indebted to Dr. John Fellman and Mr. Dennis Mattinson for assistance in blueberry
flavor determination using GC/MS systems. I would like to extend my thanks to Dr. St. John
Dixon-Warren and Mr. Leonard Henscheid for assistance in the determination of moisture
diffusivity using a thermogravimetric analyzer.
Special thanks go to Mr. Wayne Dewitt and Mr. Vincent Himsl. for their assistance in
developing research apparatus, and Mr. Frank Younce for assistance in using WSU Food
Processing Pilot Plant facilities.
I would thank my fellow students in the Microwave Heating Application Group for
their assistance and friendship during my research, especially Mr. Timothy Wig for his
assistance in building a 2450 MHz microwave and spouted bed drying system.
This work has been supported by Washington State Agricultural Research Center.
Washington State University IMPACT Center and Northwest Center for Small Fruits Research.
Their support has been essential and is greatly appreciated. I acknowledge TreeTop. Selah.
WA. for donating evaporated apples.
Finally, my most sincere thanks go to my parents and my wife, Yingqi. for their
enduring understanding, encouragement, and support.
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MICROWAVE DRYING OF FRUITS AND VEGETABLES IN A SPOUTED BED
Abstract
By Hao Feng, Ph. D.
Washington State University
May 2000
Chair: Juming Tang
Removal of moisture from solids by applying heat energy in drying is important in
many industry sectors. It is also one of the most complex and least understood operations
because of the coupled heat, mass, and momentum transport in multiphase media. When
applied, to food processing, drying provides prolonged shelf life, greatly reduces cost in
transportation and handling, and adds value to the final products. There is an ever-increasing
need for dehydrated food products in the marketplace both domestically and internationally.
For example. S9.5 billion worth of dehydrated vegetables, instant dried soup, and seaweed were
consumed in Japan in 1997. excluding dehydrated vegetables used in restaurants and
institutions. The potential for the US food industry in the global market in dehydrated foods in
is enormous. To produce dehydrated foods with high quality and at a reasonable price is the
key to success for an industrial drying operation. However, traditional drying techniques
degrade the quality of dried products and have a high cost because of low energy efficiency and
lengthy drying time in the falling rate period. Freeze drying can yield a superior quality
dehydrated product but high cost limits this technique to high value products.
In this study, we proposed a new drying process that uses microwave heating to supply
the energy for evaporating moisture and a specific fluidization technique, the spouted bed. to
improve the uniformity in microwave heating. Experimental studies were conducted to validate
this process. In experiments with evaporated diced apples, a particle circulation in the spouted
bed provided uniform heating in the microwave field and resulted in improved quality in heat
sensitive diced apples. The temperature variation during drying was less than 4°C in diced
apples and the discoloration was less than diced apples microwave dried in a stationary bed.
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The diced apples also exhibited lower bulk density and higher reconstitution capacity compared
to diced apples dried to those from traditional drying methods. Blueberries dried with the
combined microwave and spouted bed (MWSB) technique resulted in a lower bulk density and
more reddish and less blue color compared to blueberries dried with conventional methods.
MWSB dried blueberries exhibited a higher rehydration ratio in shorter soaking times. Analysis
of flavor volatiles by GC/MS demonstrated that MWSB drying generated three unique flavor
compounds (2-Butanone. 2-methyl butanal. and 3-methyl butanal). A substantial reduction in
drying time was achieved in both drying experiments. Drying time for diced apples was
reduced by > 80% compared with spouted bed drying. Only 1/19 and 1/24 (with and without
pretreatment) time was used to reach same moisture reduction in MWSB drying of blueberries
when compared to tray drying.
Following the experimental validation of the MWSB technique, a study was conducted
to investigate the fundamentals of MWSB drying. A comprehensive heat and mass transfer
model was developed to describe heat. mass, and momentum transport in hygroscopic porous
media. Special attention was given to internal vapor generation and bound water transport. The
scaling technique was used to simplify the drying equations. The governing equations were
solved using the Crank-Nicolson numerical technique. Experiments with diced apples were
conducted to validate the model. The average moisture content, the pressure increase, and inner
temperature of diced apples were measured and good agreement with model predictions was
achieved. The simulation demonstrated that for medium and low moisture porous media, a
surface moisture accumulation similar to that in high moisture, high power microwave drying
was observed during the beginning of drying. The moisture profile in the diced apples
suggested the importance of capillary flow in microwave drying. A temperature leveling effect
was realized both numerically and experimentally. This unique feature in MWSB drying paves
the road for commercial applications of the technique.
In this study, an effort was made to bridge model analyses to practical applications. All
the parameters used in model were for the product of our concern, diced apples. We designed
three experiments to measure effective diffusivity. permeabilities, and dielectric properties of
apples. The temperature and moisture dependencies of these properties were also determined.
Other needed parameters for diced apples were obtained from literature.
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TABLE OF CONTENTS
Acknowledgments......................................................................................................................in
Abstract.......................................................................................................................................iv
Table of Contents.......................................................................................................................vii
List of Figures...........................................................................................................................xiii
List of Tables................................................................... -..................................................... xviii
Dissertation Outline......................................................................................................................I
Chapter 1. Drying of Biological Materials using Microwave Energy
Introduction..................................................................................................................................3
Interaction between microwave and lossy materials................................................................... 5
Dielectric property as influenced by moisture, temperature, and other factors.....................5
Moisture dependency..................................................................................................... 6
Temperature effect............................................
7
Porosity effect................................................................................................................ 8
Heating Uniformity...............................................................................................................9
Nonuniformity due to geometry..................................................................................... 9
Nonuniformity due to electromagnetic fie ld ............................................
10
Means to overcome nonuniform heating......................................................................10
Heat and mass transfer modeling in microwave drying.............................................................12
The empirical models......................................................................................................... 13
Diffusive theory.................................................................................................................. 14
Heat and mass transfer models............................................................................................15
Stmplffted approaches................................................................................................. 15
Philip and de Vries method......................................................................................... 16
Luikov method............................................................................................................. 17
Whitaker method.......................................................................................................... 17
Two-region model .......
19
Important considerations in the simulation of microwave drying.......................................20
Transport mechanisms________________________________________________20
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Determination o f the heat sourceterm due to microwave heat generation..................20
Model validation...........................................................................................................24
Numerical analysis..............................................................................................................24
Final remarks.......................................................................................... -.................................. 25
References...................................................................................................................................25
Chapter 2. Evaluation of quality attributes for dehydrated biological materials
Introduction.................................................................................................................................31
Factors affecting product quality during drying.........................................................................34
Quality change kinetics...............................................................................................................35
Moisture determination...............................................................................................................40
Physical quality attributes and their determination.....................................................................41
Density................................................................................................................................ 42
Porosity................................................................................................................................48
Shrinkage.............................................................................................................................50
Rehydration capacity...........................................................................................................52
Color................................................................................................................................... 57
Texture.................................................................................................................................57
Final Remarks.............................................................................................................................59
References...................................................................................................................................59
Chapter 3. Heat and Mass Transport Modeling for Microwave Drying of Hygroscopic
Porous Media at Low and Medium Moisture Ranges
Abstract...................................................................................................................................... 70
Introduction.................................................................................................................................70
Moisture Transport mechanism inCellular Materials.................................................................74
Model Development...................................................................................................................77
Assumptions........................................................................................................................77
Transport Relations......................................
78
Mass Fluxes.........................................................................................................................80
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Mass Balance.......................................................................................................................80
Heat Balance........................................................................................................................81
Governing equations............................................................................................................82
Initial and boundary conditions........................................................-.................................. 83
Model reduction..........................................................................................................................85
Physical. Thermal. Thermal-physical, and Transport parameters.............................................. 89
Porosity................................................................................................................................ 89
Vapor pressure.....................................................................................................................90
Surface heat transfer and mass transfer coefficient h and hm.............................................. 90
Other parameters..................................................................................................................9 1
Permeability determination.........................................................................................................93
Theory..................................................................................................................................93
Experimental........................................................................................................................93
Results........................................................................................................
95
Numerical Technique.................................................................................................................. 97
Experimental............................................................................................................................... 98
Model Validation...................................................................................................................... 101
Results and discussion.............................................................................................................. 105
Conclusions............................................................................................................................... 109
Notation.................................................................................................................................... 110
References................................................................................................................................. 113
Chapter 4. Determination of Moisture Diffusivity of Red Delicious Apple Tissues by
Thermogravimetric Analysis
Abstract..................................................................................................................................... 115
Introduction............................................................................................................................... 1 15
Materials and Methods.............................................................................................................. 118
The slope method............................................................................................................... 120
Results and Discussions............................................................................................................ 123
Conclusion................................................................................................................................ 130
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Acknowledgment
131
References..........
131
Chapter 5. Determination of Dielectric properties of Apple Tissues as a Function of
Moisture Content at Two Temperatures
Abstract.....................................................................................................................................137
Introduction............................................................................................................................... 138
Materials and Methods..........................................................................................
140
Apple samples.................................................................................................................... 140
Moisture content control and measurement....................................................................... 140
Temperature control and calibration.................................................................................. 140
Sample size and thickness effect....................................................................................... 141
Dielectric property measurement....................................................................................... 143
Results and Discussions............................................................................................................144
Dielectric relaxation spectra (DRS)................................................................................... 144
Moisture content effect......................................................................................................150
Comparison with literature................................................................................................ 152
Penetration depth...............................................................................................................153
Model prediction of dielectric properties.......................................................................... 154
Conclusions............................................................................................................................... 157
Acknowledgements................................................................................................................... 157
References.................................................................................................................................157
Chapter 6. Microeave Finish Drying of Diced Apples in a Spouted Bed
Abstract.....................................................................................................................................162
Introduction...............................................................................................................................162
Materials and methods..............................................................................................................164
Evaporated diced apples....................................................................................................164
Laboratory drying system..................................................................................................164
Drying tests
...............................................................................................................166
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Heating uniformity.............................................................................................................166
Moisture content................................................................................................................167
Rehydration capacity......................................................................................................... 167
Bulk density.....................................................................................
168
Color.................................................................................................................................. 168
Results and discussions............................................................................
168
Conclusions............................................................................................................................... 179
Acknowledgements................................................................................................................... 180
References................................................................................................................................. 180
Chapter 7. Combined Microwave and Spouted Bed Ddrving of Diced Apples: Effect of
Drying Conditions on Drying Kinetics and Product Temperature
Abstract..................................................................................................................................... 182
Introduction............................................................................................................................... 182
Materials and methods.............................................................................................................. 184
Results and discussion..............................................................................................................187
Temperature variation........................................................................................................187
Color evaluation................................................................................................................189
Drying rate......................................................................................................................... 191
Moisture transport..............................................................................................................192
Conclusions...............................................................................................................................199
Acknowledgements.................................................................................................................. 200
Nomenclature........................................................................................................................... 200
References................................................................................................................................ 201
Chapter 8. Microwave and Spouted Bed Drying of Frozen Blueberries: The Effect of
Drying and Pretreatment Methods on Physical Properties and Retention of Flavor
Abstract.................................................................................................................................... 203
Introduction_________________________________________
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204
Materials and methods..............................................................................................................205
Drying methods................................................................................................................. 205
Flavor Volatile Analysis.................................................................................................... 208
Results and discussion............................................................................ :................................ 209
Drying kinetics.................................................................................................................. 209
Rehydration....................................................................................................................... 2 11
Color.................................................................................................................................. 212
Bulk density....................................................................................................................... 214
Flavor volatile analysis...................................................................................................... 215
Conclusion....................................... ....................................................................................... 2 15
Acknowledgements................................................................................................................... 2 16
References................................................................................................................................. 217
Conclusions.............................................................................................................................. 222
Recommendations for Future Studies................................................................................... 225
Appendix A
1. Phenomenological Relations................................................................................................. 227
2. Equilibrium Relations...........................................................................................................227
3. Mass Balance........................................................................................................................ 228
4. Heat Balance......................................................................................................................... 228
5. Fluxes.................................................................................................................................... 229
6. Moisture Transport Equation................................................................................................232
7. Thermal Transport Equation................................................................................................. 233
8. Total Pressure Equation........................................................................................................236
9. Initial and Boundary Conditions........................................................................................... 238
10. Complementary Conditions................................................................................................240
11. Heat Source Term Estimation............................................................................................. 245
12. Simplification o f Drying Equations....................................................................................246
13. Finite Difference Solution_________________________________________________260
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14. Convergence Study.............................................................................................................272
15. Notation.............................................................................................................................. 274
16. References...........................................................................................................................I l l
Appendix B
Finite difference program.........................................................................................................279
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LIST OF FIGURES
Chapter 1. Drying of Biological Materials using Microwave Energy
Figure I. Moisture content dependency of dielectric properties (Metaxas and Meredith. 1983). 7
Figure 2. Frequency and temperature effects of different dispersion mechanisms on loss factor
(Tangetal.. 1999).................................................................................................................9
Figure 3. Microwave power density distribution inside a material. Arrows indicate incident
microwaves.........................................................................................................................10
Figure 4. Microwave power distribution at different heights in a cavity with (a) and without (b )
a mode stirrer (Zhang and Datta. 1999).............................................................................. 12
Figure 5. Comparison between model predicted and experimentally determined moisture
distribution (Lu et al.. 1998)............................................................................................... 16
Chapter 2. Evaluation of quality attributes for dehydrated biological materials
Figure I. Global food stability map (Labuza. 1970)...................................................................3 1
Figure 2. Drying time and germination of lentils. The dashed lines represent minimum
germination for Canadian No. I and No. 2 lentils. (Tang and Sokhansanj. 1993)............. 35
Figure 3. Optimum operation range for drying lentils (Tang and Sokhansanj. 1993)................36
Figure 4. Quality change vs. history of food product.....................................
36
Figure 5. Volumes (pore structure) can be distinguished in a biomaterial................................ 42
Figure 6. Density reading vs. dipping time for water displacement method (Feng and Tang.
1997).................................................................................................................................. 47
Chapter 3. Heat and Mass Transport Modeling for MicrowaveDryingof Hygroscopic
Porous Media at Low and Medium Moisture Ranges
Figure I. Cell structure (simplified) (Lewicki and Lenart. 1995)...............................................75
Figure 2. Plant material is a capillary-porous medium (Lewicki and Lenart. 1995).................. 76
Figure 3. Setup for permeability determination..........................................................................94
Figure 4. Intrinsic permeability vs. porosity.............................................................................. 96
Figure 5. Gas and liquid relative permeabilities as a function of saturation...............................97
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Figure 6.2450 MHz microwave and spouted bed combined drying system.............................100
Figure 7. Comparison of moisture content for MWSB drying at microwave power level of 4
W/g and hot-air temperature of 70°C................................................................................ 102
Figure 8. Comparison of temperatures for MWSB drying at microwave-power level of 4 W/g
and hot-air temperature of 70°C........................................................................................ 103
Figure 9. Pressure comparison for MWSB drying at microwave power level of 8 W/g and hotair temperature of 70°C..................................................................................................... 104
Figure 10. Moisture profile for MWSB drying at microwave power level of 4 W/g and hot-air
temperature of 70°C...........................................................................................................106
Figure 11. Changes of moisture at different nodes for MWSB drying at microwave power level
of 4 W/g and hot-air temperature of 70°C........................................................................ 107
Figure 12. Temperature profile for MWSB drying at microwave power level of 4 W/g and hotair temperature of 70°C..................................................................................................... 108
Figure 13. Time evolution of temperature for different nodes for MWSB drying at microwave
power level of 4 W/g and hot-air temperature of 70°C......................................................109
Figure 14. Pressure profile for MWSB drying at microwave power level of 4 W/g and hot-air
temperature of 70°C...........................................................................................................110
Chapter 4. Determination of Moisture Diffusivity of Red Delicious Apple Tissues by
Thermogravimetric Analysis
Figure I. Schematic diagram for the ThermogravimetricAnalyzer used in this study..............119
Figure 2. Flow diagram for the convergence analysis of the series solution of the Fick's second
law..................................................................................................................................... 122
Figure 3. The terms needed for a converged moisture diffusivity with a relative error.......... 123
Figure 4. Semi-log drying curves for four temperatures......................................................... 125
Figure 5. Moisture content and drying rate as functions of drying time at 100 °C_________ 125
Figure 6. Moisture diffusivity in Red Delicious apples in the wet zone and dry zone periods of
drying at four temperatures...............................................................................................127
Figure 7. Arrhenius-type temperature dependence of the moisture diffusivity in Red Delicious
apples................................................................................................................................127
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Figure 8. Comparison of the moisture diffusivities from this study with the literature values for
apples. The 95% confidence bands are for the means of all the data shown in the graph 129
Figure 9. Moisture content, drying rates and sample radius in different drying regions
129
Chapter 5. Determination of Dielectric properties of Apple Tissues as a Function of
Moisture Content at Two Temperatures
Figure I. Th open-ended coaxial line probe configuration....................................................... 143
Figure 2. Dielectric dispersion of bound water, free water, and ionic conduction (Tang. 1999).
........................................................................................................................................... 145
Figure 3. Dielectric relaxation spectra of Red Delicious apples at three moisture contents and
two temperatures - comparison between € ande"............................................................147
Figure 4. Dielectric relaxation spectra of Red Delicious apples at three moisture contents and
two temperatures-comparison between two temperatures................................................. 149
Figure 5. Dielectric properties of Red Delicious apples as influenced by moisture content.... 151
Figure 6. Comparison of dielectric properties with literature data............................................154
Figure 7. Penetration depth as a function of moisture content at two temperatures..................154
Chapter 6. Microeave Finish Drying of Diced Apples in a Spouted Bed
Figure I. Schematic diagram of microwave and spouted bed (MWSB) drying system............165
Figure 2. A comparison of center temperature variation among 10 Red Delicious apple dices
randomly taken from the spouted bed after 2.5 minutes of drying with MWSB (6.4 W/g
and hot air of 70°Q and from a stationary bed with MW and flow hot-air drying (hot air of
70°Q.................................................................................................................................. 169
Figure 3. Temperature history and average moisture content of diced Red Delicious apple
during microwave drying at 6.4 W/g (db) and 70°C hot air temperature.......................... 172
Figure 4. Drying curves of three apple cultivars dried with MWSB (6.4 W/g and hot air of
70°C) and SB (70°C hot air).............................................................................................. 173
Figure 5. Drying curve of Red Delicious dried with MWSB method with different microwave
power levels...................
175
Figure 6. Color comparison of apples dried with different methods........................................ 177
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Figure 7. Rehydration capacity of apples dried with different methods
178
Figure 8. Density of apples dried with different methods....................
179
Chapter 7. Combined Microwave and Spouted Bed Ddrying of Diced Apples: Effect of
Drying Conditions on Drying Kinetics and Product Temperature
Figure L Comparison of particle flow patterns in a fluidized bed and a spouted bed.............. 185
Figure 2. Modified Geldart classification chart for particles.....................................................185
Figure 3. Schematic diagram of microwave and spouted bed (MWSB) drying system........... 186
Figure 4. Temperature of diced Red Delicious apples in a MWSB dryer at microwave power
level of 6.4 W/g (dry basis)............................................................................................... 188
Figure 5. Change of moisture content of diced Red Delicious apples during MWSB drying at
(a) microwave power level of 6.4 W/g (dry basis), and (b) air temperature of 70°C........189
Figure 6. Drying rates of diced Red Delicious apples at (a) microwave power level of 6.4 W/g
(dry basis), and (b) air temperature of 70°C...................................................................... 192
Figure 7. Two falling rate periods and the application of the slope method at microwave power
level of 6.4 W/g (dry basis)............................................................................................... 196
Figure 8. (a) Influence of hot air temperature on moisture diffusivity at microwave power level
of 6.4 W/g (dry basis): (b) Influence of microwave power level on moisture diffusivity at
air temperature of 70°C..................................................................................................... 197
Chapter 8. Microwave and Spouted Bed Drying of Frozen Blueberries: The Effect of
Drying and Pretreatment Methods on Physical Properties and Retention of Flavor
Figure I. Schematic diagram of microwave and spouted bed (MW&SB) drying system........207
Figure 2. Drying Kinetics of Elliott Blueberries with Different Drying and Pretreatment
Methods.............................................................................................................................212
Figure 3. Comparison of Rehydration Capacity of Elliott Blueberries Dried with Different
Methods.............................................................................................................................213
Figure 4. Bulk Density of Elliott Blueberries under Different Processing and Pretreatment
Methods............................................................
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216
Figure 5. Chromatogram showing the purgeable flavor volatiles detected by purging our sample
with He onto tenax and then performing purge-and-trap gas chromatography with mass
spectrometry..................................................................................................................... 220
Appendix A
Figure L Change in capillary pressure with respect to moisture( I ) .........................................249
Figure 2. Change in capillary pressure with respect to moisture(2).........................................250
Figure 3. The apple vapor pressure gradient over moisture content vs. moisture content
253
Figure 4. The apple vapor pressure gradient over temperature vs. temperature.......................253
Figure 5. Flow diagram for the simulation.............................................................................. 271
Figure 6. Moisture content distribution obtained at three time steps........................................272
Figure 7. Temperature profiles obtained at three time steps.....................................................273
Figure 8. Moisture profiles at four mesh sizes and two drying times......................................273
Figure 9. Temperature profiles at four mesh sizes and two drying times.................................274
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LIST OF TABLES
Chapter 1. Drying of Biological Materials using Microwave Energy
Table L Microwave drying model classification........................................................................ 13
Table 2. Heat and mass transfer modeling for microwave drying.............................................. 22
Chapter 2. Evaluation of quality attributes for dehydrated biological materials
Table 1. Typical quality changes during drying (adapted from Karel. 1991: Bimbenet and
Lebert. 1992)...................................................................................................................... 32
Table 2. Vitamin losses in selected foods during drying, adapted from a) Yang and Atallah.
1985: b) Fellows. 1988: c) Jayaraman et al.. 1990: d) Jayaraman and Gupta. 1995: and e)
Sokhansanj and Jayas. 1995............................................................................................... 33
Table 3. Parameters defined in Eq. (5) for selected enzymatic reactions (adapted from Luyben
eta!.. 1979)........................................................................................................................ 38
Table 4 Activation energy for non-enzymatic browning in selected foods...............................39
Table 5. Densities used for grains/legumes and fruits/vegetables.............................................. 43
Table 6. Terminology used for density definition of selected biomaterials in literature............45
Table 7. Moisture content dependency of the densities of selected agriculture products.......... 48
Table 8. The moisture content dependency of porosity for different materials..........................50
Table 9. The shrinkage correlations for different bio-materials.................................................51
Table 10. Evaluation methods for rehydration ability................................................................55
Table 11. Color functions used in literature to model human color perception.........................58
Table 12. Classification of texture characteristics......................................................................58
Chapter 3. Heat and Mass Transport Modeling for Microwave Drying of Hygroscopic
Porous Media at Low and Medium Moisture Ranges
Table I. Correlations for thermal, thermodynamic, and mass transport parameters..................92
Table 2. Input parameters used in numerical investigation.........................................................99
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Chapter 4. Determination of Moisture Diffusivity of Red Delicious Apple Tissues by
Thermogravimetric Analysis
Table I. Diffusivity values for the 1st and 2nd failing rate period............................................ 126
Table 2. Apple diffusivity data................................................................................................129
Chapter 5. Determination of Dielectric properties of Apple Tissues as a Function of
Moisture Content at Two Temperatures
Table I. Comparison between measurements with metal base and foam base......................... 142
Table 2. Dielectric properties of Red Delicious at 60°C and eight moisture contents.............. 155
Table 3. Dielectric properties of Red Delicious at 22°C and fourteen moisture contents
155
Table 4. Coefficients in Eqs (4) and (5).................................................................................... 156
Chapter 6. Microeave Finish Drying of Diced Apples in a Spouted Bed
Table I. Standard deviations of the final moisture contents from different drying processes.. 174
Table 2. Lightness for apple dices dried with different methods as compared with fresh apple
fleshes...............................................................................................................................176
Chapter 7. Combined Microwave and Spouted Bed Ddrying of Diced Apples: Effect of
Drying Conditions on Drying Kinetics and Product Temperature
Table I. Color measurement results (L*a*b*). darkness factor b*/a*. and total color difference
AE for diced apples............................................................................................................190
Table 2. Calculated equilibrium moisture. Xe. based on Roman et al. (1982) tabulated values of
C and Xm for apples held at the indicated relative humidity..............................................195
Table 3. Effective moisture diffusivities in apples obtained using different drying methods.. 198
Chapter 8. Microwave and Spouted Bed Drying of Frozen Blueberries: The Effect of
Drying and Pretreatment Methods on Physical Properties and Retention of Flavor
Table L. Blueberry drying time comparison............................................................................210
Table 2. Blueberry color measurement results.........................................................................214
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Table 3. Compound list of blueberry samples detected by purge-and-trap injection with gas
chromatography/fid under differing preteatments............................................................219
Appendix A
Table L Bound water diffusivity data from literature..............................................................242
Table 2. Comparison of the magnitude of the coefficients in moisture equation.....................252
Table 3. The magnitude of the pressure derivatives.................................................................254
Table 4. A comparison of the magnitude of the coefficients in temperature equation.............256
Table 5. A comparison of the magnitude of the coefficients in pressure equation...................258
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DISSERTATION OUTLINE
This dissertation is organized into eight self-contained chapters accompanied by two
appendixes. The first and second chapters are review articles regarding microwave drying of
biological materials and quality evaluation of dehydrated biological materials. Chapter 3
presents the theoretical analysis for the heat and mass transfer mechanisms involved in
microwave drying. A three-equation microwave drying model was developed to characterize
the transport of heat, free water, bound water, and vapor in hygroscopic porous media when
heat is generated volumetrically. The Crank-Nicolson scheme was used to solve the partial
differential equations. Experiments were conducted with diced apples to validate the model. In
this study, an effort was made to study and experimentally determine the transport and
dielectric properties needed in the modeling. The intrinsic permeability and relative
permeability were determined and are reported in Chapter 3. Chapter 4 presents the
determination of effective moisture diffusivity of apple tissue using the thermogravimetric
technique. Chapter 5 presents the determination of moisture dependent dielectric properties of
apple tissue at different temperatures.
Chapter 6 describes development of a laboratory-scale system to demonstrate the
unique advantages of combined microwave and spouted bed drying (MWSB). Experiments
with diced apple demonstrated uniform heating could be achieved. Chapter 7 presents the
drying kinetics and temperature changes of diced apple during MWSB drying. Chapter 8
presents the results of MWSB drying of blueberries to further evaluate this technique in
physical properties and flavor improvements. Appendix A includes detailed procedures of both
the theoretical analysis and the numerical technique used in the heat and mass transfer model
development. Appendix B is a collection of computer programs used in the numerical analyses.
Since the dissertation is composed of published and completed manuscripts. The format
of each article follows the style of the target journal. A list of the published chapters and
chapters accepted for publication as of December I. 1999 includes:
I
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Chapter 4
Feng. H.. Tang. J. and Dixon-Warren. St J.. 2000. Determination of moisture diffusivity of Red
Delicious apple tissues by thermogravimetric analysis. Drying Technol.. 18(5).
Chapter 6
Feng. H. and Tang, J.. 1998. Microwave finish drying of diced apples in a spouted bed. J. Food
ScL. 63. pp. 679-683.
Chapter 7
Feng. H.. Tang, J. Cavalieri. R. P.. 1999. Combined microwave and spouted bed drying of
diced apples: Effect of drying conditions on drying kinetics and product temperature, an invited
paper for the Special Hall Issue, Drying Technol., 17. pp. 1981-1998. 1999.
Chapter 8
Feng. H.. Tang. J.. Mattinson. D. S. and Fellman. J. K.. 1999. Microwave and spouted bed
drying of blueberries: The effect of drying and pretreatment methods on physical properties and
retention of flavor volatiles. J. Food Processing and Preservation. 23. pp 463-479.
2
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CHAPTER 1
DRYING OF BIOLOGICAL MATERIALS USING MICROWAVE ENERGY
INTRODUCTION
The term '‘microwave” usually refers to electromagnetic radiation in the frequency
range of 300 MHz to 300 GHz. It is the propagation of energy through space by means of timevarying electric and magnetic fields (Stuchly and Stuchly. 1983). It is unique to microwaves
that as they travel through a lossy medium, an increase in temperature throughout the medium
can be observed. This has lead to many applications in the food industry and our daily life. An
example is the widespread application of home microwave ovens. It is estimated that the annual
sale of home microwave ovens in the United States is on the order of S1.5 —2.0 billion
(.Schiffmann. 1995). The microwave heating effect is due to an interaction between the
microwave and the medium, which results in part of the microwave energy to dissipate
volumetrically in the form of heat. The mechanisms under which the energy dissipates depend
on the characteristics of the medium and the frequency of the wave. In the frequency range of
our interest, the mechanisms may include free water polarization (y dispersion), bound water
polarization (8 dispersion), Maxwell-Wagner polarization ((3 dispersion), and ionic
conductivity. The quantification of such energy conversion can be realized utilizing knowledge
of electromagnetic theory together with an understanding of the dielectric properties of the
medium. The volumetric heat generation in microwave heating distinguishes this technique
from other surface heating methods and brings about such advantages as rapid heating, high
energy efficiency, and easiness in process control.
Drying is one of the most energy consuming unit operations in the process industries. In
a drying process, a large amount of energy is needed to provide both the sensible heat and the
energy for phase change of moisture. The high energy consumption is not only from the
evaporation of water but from the low energy efficiency during the failing rate period of a
drying process, hi the falling rate period, drying becomes inefficient because ( I) case hardening
yields a layer with high heat and mass transfer resistance: (2) temperature gradient could be in
the opposite direction of the moisture gradient; and (3) product temperature is limited to the
wet bulb temperature. A higher evaporation enthalpy for water in medium and low moisture
ranges also contributes to increased energy consumption. When drying foods and agricultural
3
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products, this low energy efficiency and accompanying prolonged drying time result in severe
quality degradation in the products. It is evident that for conventional drying, where the heat is
supplied externally, low energy efficiency and hence, poor product quality is inevitable. It is
the disadvantages of the conventional drying methods that provide microwave heating vast
opportunity as a new drying method for improving both energy efficiency and product quality.
The advantages of microwave drying arise from the volumetric heating and internal
vapor generation. As a result, an internal total gas pressure gradient builds up and most of the
moisture leaves the product as a vapor. This, in turn, results in a significant reduction in drying
time. In microwave drying of foods, a reduction in drying time up to 25 - 90% (Prabhanjan et
al.. 1995) and an increase in drying rate of 4 to 8 times (Brygidyr et al.. 1977). when compared
to convective drying, have been reported. Other advantages are summarized in the following
paragraphs:
1) High energy efficiency in the falling rate period can be achieved. It is partially due to
the fact that the energy is directly coupled into the moisture, which eliminates the need to
transfer heat from the low moisture surface into the interior. It is also the result of an increased
driving force for moisture transfer because of the generation of elevated internal vapor
pressure.
2) Casehardening may be avoided or lessened because of the surface moisture
accumulation and even the liquid pumping phenomena. The unique surface moisture
concentration in microwave drying has been widely reported (Turner et al.. 1998: Ni et al..
1999). The favorable moisture profiles produced in microwave drying provide a high
possibility to lessen the surface moisture depletion and the casehardening encountered in
conventional drying.
3) An improvement in product quality can also be achieved. Better aroma retention
(Nury and Salunkhe, 1968: Feng et al.. 1999). faster and better rehydration (Probhanjan et al..
1995: Drouzas and Schubert. 1996: Feng and Tang, 1998), better color (Tulasidas et al.. 1995:
Feng and Tang, 1998), and higher porosity (Torringa et al., 1996) have been reported for
microwave dried food products.
A significantly shortened drying time, improved product quality, and many other
advantages in microwave drying seem to pave the road for widespread application of this
relatively new technology. Industrial acceptance of this technique, however, has been slow. It
4
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may be partially due to certain drawbacks in microwave drying (Nijhuis et al., 1996). A major
drawback is the nonuniformity in heating. This is the result of an uneven microwave field in the
cavity caused by the superposition of the sinusoid microwaves. This is an inherent
characteristic of microwaves. The second is the control of the mass transfer rate. In some cases,
the mass transfer rate is too high, causing puffing and even disintegration of the product. The
third is the historically high investment cost and low life-span of the magnetron. Today,
however, both capital equipment costs and operating costs for microwave drying have been
reduced to a level comparable to conventional drying methods (Schiffmann. 1995). Methods
have been developed to improve heating uniformity. The remaining obstacles tor the
application of microwave drying could be a lack of understanding of the microwave interaction
with product, a lack in dielectric property data, and a lack of an effective means to predict the
moisture and temperature history and distribution during microwave drying. The reluctance for
industry to adopt new technology will also hinder the application of microwave drying. In order
to promote the application of microwave heating techniques, studies of the interaction between
microwaves and product are highly desirable. The development of means to predict the heating
pattern using coupled heat and mass transfer analysis is essential to both the understanding of
the physics and the control of such a drying operation. We can foresee a promising future for
the application of microwave energy in drying as we gain better understanding of both the
technical and theoretical aspects of this technology.
INTERACTION BETWEEN MICROWAVE AND LOSSY MATERIALS
To understand the interaction between microwaves and a product, it is necessary to
examine the nature of microwaves and the response of a product to microwave radiation. The
ultimate goal is to predict the heating pattern in microwave drying and to provide direction to
operation and quality control. Since heating nonuniformity is a major factor that could cause
potential problems in microwave drying, an effort must be made to examine uneven heating by
studying both the dielectric properties and the microwave propagation.
Dielectric property as influenced by moisture, temperature, and other factors
Dielectric properties of a material determine how much heat can be produced when it is
exposed to microwave radiation and the way the heat is generated. The electrical parameter of a
5
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dielectric material that defines its interaction with electromagnetic fields is the complex
permittivity e = e' - j£". It is composed of a real part. e'. called the dielectric constant, and an
imaginary part, the loss factor, e". The dielectric constant represents the ability of a material to
store the electric field energy in the material, while the loss factor determines how much energy
is dissipated in the form of heat. Microwave heat generation at any point in a material is given
by:
P = 5.56 x 10~* x fe E1
( I)
where P is the conversion of microwave energy into thermal energy per unit volume (W/cm ’). f
is frequency (GHz), e" is loss factor (unitless), and E is the local electric field intensity (V/cm).
The constant 5.56 x IO'4 has unit of F/cm. When microwave travels through a material, its
intensity decreases because part of its energy dissipates in the form of heat. The decay can be
measured by the penetration depth Dp. The penetration depth is defined as the depth from the
product surface where the available power drops to 37% ( l/e) of its surface value. Dp can be
estimated by:
f
D = ----- ----'
y
f £r
1+
v
\
1 - O .S
0. 5
'
( 2)
-I
M 2 e'f5
where Xq is the wavelength in free-space (m). From Eqs (I) and (2), it can be seen that
microwave heat generation depends on both the loss factor e" and the local electrical field
intensity E. The penetration depth, on the other hand, is a function of both dielectric constant
and loss factor. What makes microwave heating complicated is the fact that dielectric
properties are dependent upon temperature and moisture.
Moisture dependency
Moisture content is a very important factor that affects dielectric properties. For
example, the dielectric constant for free water is as high as 78, while for solid materials its
value is in the order of 2 (Schiffmann, 1995). In general dielectric properties decrease with
6
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moisture decreases as illustrated in Figure L The critical moisture content Mc is used to
delineate the free water and the bound water. Water at moisture content below the critical
moisture is called bound water, while the one above Me is called free water. A sharp decrease
in dielectric properties as moisture is reduced is attributed to the reduction in the mobility of
water dipoles. The bound water has a hindered ability to follow the rotation of the
electromagnetic field and. hence, a reduced ability to extract energy from the field.
C
o
o
I
s
o
o
a
tc
Me
Mean moisture con ten t, M
I I
1 1
w
O
uO
Mc
Mean moisture content . M
Figure I. Moisture content dependency of dielectric properties (Metaxas and Meredith. 1983).
7
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Temperature effect
The temperature dependency of dielectric properties is complex because more than one
dispersion mechanisms can be involved- This has been well documented in the literature. Sun et
al. (1995) reported, that for food products, the dielectric constant decreased with temperature
increase, while the loss factor increased with temperature when salt content was high but
decreased if salt content was low. In a study for the determination of dielectric properties of pea
puree. Tong et al. (1994) noticed that at 915 MHz the loss factor increased with temperature,
while at 2.450 MHz it decreased with increased temperature until reaching a minimum at
temperatures between 25 to 75 °C. Goedeken et al (1997) showed that the dielectric constant
increased when temperature increased from 20 to 65°C then became nearly constant from 60 to
95°C. while the loss factor increased linearly from 25 to 95°C and decreased when no salt was
present. To fully understand the temperature effect, one needs to understand the dielectric
dispersion due to free water, bound water, and ionic conduction. Figure 2 illustrates both the
frequency dependency and temperature effect of different dispersion mechanisms in microwave
heating. From Figure 2 we can see that, in the microwave frequencies (300MHz to 300GHz).
the bound water, free water, and ionic dispersions may be involved. The percentage of bound
water and free water determines the positive or negative response of dielectric properties to
frequency and temperature changes. The influence of ionic conduction is always positive when
temperature increases.
Porosity effect
The effect of porosity on the dielectric properties is due to the low dielectric properties
of air. Air has a dielectric constant of I and loss factor of zero. Therefore, air is considered as
transparent to microwaves. High porosity materials have more air trapped, and thus lower
dielectric properties.
8
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Ionic
conductivity
Effect of increasing
temperature
Free water (Y)
0.1 MHz
100 MHz
Effect of
increasing
temperature
20,000 MHz
L og(f)
Figure 2. Frequency and temperature effects of different dispersion mechanisms on loss factor
(Tang et ai.. 1999).
Heating Uniformity
Nonuniformity due to geometry
Microwaves behave like a beam of light. Reflection and transmission may occur when
they reach an object. The transmitted microwaves may focus in a region of the object because
of the geometric effect. Figure 3 shows some of the possibilities where local focusing occurs.
In case (a), the microwave decay takes place at the surface and the surface region receives more
microwave radiation than the rest of the material. In case (b), the exponential decay of
microwaves from both sides of a material may. by superposition, form a central overheated
area. In case (c), waves from two sides of a rectangular shaped object may cause comer
overheating. No maner how uniform a microwave field is in an unloaded cavity, localized
overheating due to geometry is likely to occur.
9
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I l l 11
s
focusing
region
(a)
(b)
r
.
(c)
Figure 3. Microwave power density distribution inside a material. Arrows indicate incident
microwaves
Nonuniformity due to electromagnetic field
Microwaves are sinusoidal propagating electromagnetic waves. At any point in space,
the magnitude of the local electromagnetic field intensity changes with both time and direction.
Microwaves can be totally reflected at a metallic surface and partially absorbed by lossy
materials. In a drying cavity with metal walls, the incident microwave from a magnetron will
form a complex wave pattern inside the cavity because of the superposition of the reflected
waves from the walls, forming hot spots and cold spots. Figure 4 shows the microwave power
distribution in a microwave cavity. Comparison is made between cavities with and without a
mode stirrer (Zhang and Datta. 1999). It is obvious that, even with the assistance of a mode
stirrer, the nonuniform microwave distribution can be only improved but not eliminated.
Means to overcome nonuniform heating
Nonuniform heating in a microwave cavity will cause problems regarding both quality
degradation and microbial safety. In order to use the microwave heating technique, one has to
address and overcome this problem. Efforts have been made in recent years to address this
issue. One means of improving microwave heating is to alter the distribution of the microwave
radiation using novel forms of packaging. This method reduces the microwave exposure at
regions where the focus effect occurs or the local material has a different dielectric property
(George 1993). An alternative is to constandy change the spatial location of the products during
10
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heating. The turntable design in a domestic microwave oven is an example. This method is
especially useful for industrial application of microwave to such areas as drying, blanching,
pasteurization and sterilization. There are three ways to provide a time averaged, spatial
homogeneous heating for products. One is to agitate the products. Welt et al (1992) achieved a
uniform temperature distribution in an artificial liquid food using agitation. The apparatus is
suitable for solutions with viscosity less than or equal to 0.2 Pa-s. The limitation of this method
is that it is only suitable for liquid foods. Another method is to mechanically change the spatial
location of the product. Torringa et al (1996) used a shaft driven by a motor in a microwave
drying test to rotate the drying chamber. Numerous designs can be worked out following this
idea.
Fluidization provides pneumatic agitation of particles inside a fluidized bed. The
incorporation of fluidization technology with microwave makes it possible to obtain uniform
microwave heating. Research recently conducted at Washington State University (Feng and
Tang. 1998) resulted in uniform microwave heating of evaporated apple dices, utilizing a
special fluidized bed. the spouted bed technique. Other methods are aimed at the change of the
microwave field itself using newly developed and more expensive techniques, such as the
variable frequency technique (Qiu and Hawley. 1998) and the phase control heating technique
(Zhang and Datta. 1999).
II
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[••!
t£d
25 a m
3
SO mm
B
ISO mm
E
S
ifc j
275 mm
ka H lS
75 mm
B
175 mm
E
l
iC J
300
mm
'• 0
lOQmm
i
200 mm
125 mm
S
®
“
2S°m m
KJ ^
f f l
ff eeZ^Vj
325 mm
LA _J
JSOmm
(a)
25m m
SOmm
75 mm
100 mm
125 mm
ISO m m
175
200m m
325 mm
250m m
275 mm
300m m
325 mm
Itf
350
(b)
Figure 4. Microwave power distribution at different heights in a cavity with (a) and without (b)
a mode stirrer (Zhang and Datta, 1999).
HEAT AND MASS TRANSFER MODELING IN MICROWAVE DRYING
Microwave drying involves simultaneous transport of heat, mass, and momentum
accompanied by volumetric heat generation. Internal heat generation facilitates an internal total
gas pressure gradient that distinguishes microwave drying from other drying methods. It also
12
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produces a positive temperature gradient in contrast to that when heat is supplied to the product
surface. Accurate estimation of internal heat generation is a challenge because of the
complicated responses of dielectric properties to temperature, moisture, porosity, and
composition changes. Traveling microwaves can also decay, focus, and superimpose to further
complicate the calculation of the source term in the energy equation. Special care must to be
taken when analyzing the heat and mass transfer characteristics in microwave drying.
Microwave drying models can be classified into three categories which are tabulated in Table
I.
Table I. Microwave drying model classification.
Models
Exam ple
P aram eters) needed
Empirical model
DPage's model
drying constant k
^exponential model
drying constant k and exponent
Fick's second law
effective diffusivity Del,
Diffusion model
(mass transfer model)
Heat-Mass transfer model ( I)
thermal physical properties for water, vapor and
— multiphase media model
Whitaker model
air. porous properties
Luikov model
phenomenological coefficients
— continuum physics model
Philip & DeVries
thermal physical and transport properties for the
i unsaturated porous media)
model
medium
(porous media model)
Heat-Mass transfer model (2)
— continuum physics model
Heat-Mass transfer model (3)
The empirical models
Empirical models are simple to apply. The most commonly used empirical models are
Page's equation (Page. 1949) and the exponential models. Page's equation can be written:
F
- F
= e x p ^~
'
(3)
13
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where X, Xo. and X* are moisture content at time t. time t = 0. and at equilibrium condition with
surrounding air, respectively, k; and n are constant. This equation has been used by Prabhanjan
et al. (1993) and Tulasidas et al. (1993) to analyze microwave drying of wheat and grapes.
Various exponential equations were also used in microwave drying studies by Adu et al.
(1994). Skansi et al. (1995). and Drouzas et al. (1999) for microwave drying of a variety of
biological materials. Beke (1992). Beke et al. (1995). and Khraisheh et al. (1995) used different
regression methods to correlate drying rates to such parameters as the moisture content,
microwave power density, microwave frequency, temperature, air flowrate. and sample
geometry. An effort was also made to correlate drying time (Kumar. 1982: Prabhanjan et al..
1995) and moisture loss (Wright and Porterfield. 1971) to various controllable parameters.
Diffusive theory
Moisture migration in a porous medium can be driven by a concentration gradients for
liquid or by a partial vapor pressure gradient for vapor. The governing equation for such
moisture transport is Fick's second law:
dr
(4)
= d iv { p 0 g ra d X )
where Deff is effective moisture diffusivity. Eq. (4) can be solved in closed form for constant
moisture diffusivity, no shrinkage, and sufficient surface mass transfer rate so that equilibrium
moisture content with air can be reached at any time during the drying. Solutions for Eq. (4)
with various geometrical and boundary condition have been given by Crank (1975). The
solution for a sphere is given by:
4/rID„r
(5)
where d is the diameter of the sphere and t is time. It has been found that under certain
conditions, only the Erst term in the infinite series is important. For instance, in the falling rate
14
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period and when the moisture ratio ( X - Xe)/(Xo - Xe) is less than 0.3 (Feng et al.. 2000). only
the first term in Eq. (5) is predominant and a simplified equation results:
*T.
XQ- X ,
— exp[
izz
-2 _ 1
(6)
dz
The effective moisture diffusivity in Eq. (6) can be related to temperature by an
Arrhenius-type equation. Efforts were also made to correlate it with moisture changes. The
diffusion model has been used to study microwave drying of agricultural and food products.
Ptasznik et al. (1990) used the first term in the solution of Ftck's second law to simulate the
drying of broad bean. Shivhare et al. (1993) used the first 15 terms to model microwave drying
of soybean and an agreement with experiment results was attained. A similar study for the
microwave drying of potato was conducted by Bouraoui et al. (1994). Adu and Otten (1996a)
tried to take into consideration the variable diffusion coefficient in a simulation of microwave
drying of white bean.
Heat and mass transfer models
Simultaneous heat and mass transfer takes place in a microwave drying. An analysis of
coupled moisture and energy transport is therefore often used to elucidate the underlying
physics. The representative methods for such an analysis were (I) the irreversible
thermodynamics approach proposed by Luikov (1966): (2) the unsaturated porous media theory
proposed by Philip and de Vries (1957): and the volume averaging technique suggested by
Whitaker) 1977). Methods originated from various simplified approaches have also been used.
Simplified approaches
A simplified heat and mass transfer model considering both the liquid and vapor
transport was developed by Lu et al. (1998. 1999) to analyze microwave drying of sliced and
spherical food products. A careful analysis was conducted to estimate the microwave power
generation inside the product. The model was validated by experiments and good agreement
was achieved. A comparison of their model predictions for moisture content with experiments
for spherical potato samples is given in Figure 5.
15
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4
m
at
01
•*1 a
e
e
c
«0
e
s
1
z
1
Drying tia« (tccoadt)
ISO
300
4SQ
0
0
0.S
0.8
1
Dimensionless radius, r/r.
Figure 5. Comparison between model predicted and experimentally determined moisture
distribution (Lu et al.. 1998).
Grolmes and Bergman (1990) proposed a microwave drying model to characterize the
drying of nonhygroscopic material. They used a macro-balance method to generate the
governing differential equations. They observed three drying regimes. An initial regime
occurred in which the material was heated convectively and dielectrically, followed by a
transition regime and ultimately, a final regime during which the material was dielectrically
heated and convectively cooled. Melendez et al. (1989) developed a heat and mass transfer
model utilizing the characteristic drying curve method. The model simultaneously solved the
energy and mass balance equations for air and the wet and dry regions of the solid.
Philip and de Vries method
A two-dimensional formulation based on the Philip and de Vries theory (1957) was
developed by Lian et al. (1997) to simulate the drying of a slab in a microwave cavity. In Philip
16
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and de Vries theory, the total potential for moisture transport consists of two components, the
temperature potential and the capillary potential. Lian et al. introduced moisture content and
temperature to take the place of the potentials. Coupled heat and mass transfer equations were
obtained. They assumed a uniform microwave distribution at the slab surface and used
Lambert’s law to calculate the decay of microwave into the slab. Experimentally obtained
average moisture content compared well with their predictions.
Luikov method
The Luikov method is basically a phenomenological model. It is concise and
symmetric. Bajza (1997) employed this method to analyze heat and mass transfer during
microwave drying of tanned leather. The coupled heat and mass transfer equation Bajza
developed is:
ax
ar
32X
a 2r
pCp — = X T— +/Cif—^ + p M — + Q
dt
dr
a.ta.t-
(7)
a x _ a2x _ a2r
dr
a .t
a .t
( 8)
where p is density. Cp is specific heat. KT is thermal conductivity. KM is moisture gradient
induced heat transfer coefficient. Ah is latent heat. Dm is moisture diffusivity. and Dj is the
temperature gradient induced moisture transfer coefficient. The heat source Q can be calculated
based on Eq. (I). The model was validated with experiments under different conditions and
agreement was achieved. Jun et al. (1999) proposed a similar model for one-dimensional
transport in spherical coordinates. Their model prediction compared well with experimental
results for apple drying. It is well known that for the Luikov model, some coefficients are not
directly related to physical phenomena and therefore are difficult to evaluate. The moisture
gradient induced heat transfer coefficient Km and the temperature gradient induced moisture
transfer coefficient D r in Bajza’s model were not well defined and values were not presented.
The corresponding coefficients in Jun et al. study were also not well documented.
17
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Whitaker method
The partial differential drying equations are usually “point “ equations. They are meant
to describe the transport behavior in microscale. However, there is a need to define the scale in
an analysis. A homogeneous material at macroscale may be heterogeneous at microscale. For
cellular porous food products, materials are heterogeneous if we examine them at cell level. A
precise description of the transport in such materials at the cell level requires the transport
equations for the gas. liquid, and solid phases within and outside the cell separately. The
complexity and heterogeneity of the food matrix prevent a general solution for the detailed
moisture and temperature field at this level. To overcome this problem, physical phenomena in
porous media are generally described by “macroscopic’* equations, valid at a length scale
termed the Representative Elementary Volume (REV) (Bories. 1991). A method based on this
idea was first proposed by Whitaker (1977) and has been widely used in the heat and mass
transfer analysis of drying. Whitaker gave a rigorous derivation of the drying governing
equations by means of a volume averaging technique. The equations are representative on the
REV to averaged values of microscopic variables. The advantage of this method is that the
physics of the model are well presented, the assumptions are clear, and most importantly, the
transport parameters are well defined and measurable. However, rigorous derivation following
Whitaker’s method is seldom used in recent drying studies. Many drying models are developed
by implicitly referring to his method (Moyne and Perre. 1991).
Early studies in microwave drying implicitly using the Whitaker method were
conducted by Wei et al. (1985) and Jolly and Turner (1989). The models they developed were
for nonhygroscopic porous media. Wei et al. noticed an increase in both the liquid volume
fraction and air density toward the sample surface. A pressure maximum built up inside the
sample before it fell to nearly atmospheric pressure. Jolly and Turner reported the significant
influence of sample size on predicted temperature and moisture profiles.
The importance of the gas pressure gradient in microwave drying was not fully
recognized until Turner and Jolly (1991) noticed that without considering the pressure effect, it
was difficult to account for the phenomena of “water pumping”. They also realized the
importance of the contribution of the gas pressure to product quality. They introduced a third
transport equation, a total gas pressure equation, into the drying model. Since then, the
importance of the additional driving force due to the gaseous pressure gradient in microwave
18
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healing has been well documented in microwave drying studies. Turner and Rudolph (1992)
utilized this approach to simulate the drying of glass beads. Torringe et al. (1996) used a vapor
equation in place of the total gas pressure equation to analyze the drying of food products.
Constant and Moyne (1996) studied the microwave drying behavior of light concrete
considering the moisture, temperature, and total pressure effect. They predicted and
experimentally demonstrated the liquid pumping phenomenon. A recent study conducted by
Turner et al. (1998) extended their previous model to hygroscopic media. The formulation they
proposed is the following:
dx
ar
■+aTI
ar
dr
dx
dr
ar
dX
a
dx
ar
Kx l — +KTl
dz
d£L _ d
dr
3^
aT+ar 3 ! r +tt" ar
a
a=
(9)
dx
ar
3/*.
Kx l - ^ ^ K TZ— + KPZ^ K
dX
dT
trl +<t>
3 P..
( 10)
(in
where ay and Ky are capacity and kinetic coefficients, respectively. Subscript i could represent
moisture, temperature, pressure, and gravity while j = I. 2. and 3. Pg is total gas pressure.
Turner et al. also carefully examined the microwave power distribution by solving the electric
field equations under the plane wave assumption. Model predictions agreed with their
experiments conducted with wood. It is worth mentioning that most of the heat and mass
transfer studies in microwave drying were for nonhygroscopic materials. Comprehensive
microwave drying analysis for hygroscopic porous media relating to foods and agricultural
products is not available.
Two-region model
A mathematical model was developed by Chen and Pei (1989) to analyze simultaneous
heat and moisture transfer during drying. They assumed the existence of a receding evaporation
zone separating the material into a wet zone and a dry zone. A heat source term accounting for
dielectric heating was introduced in the energy equation. Effort was made to consider the
19
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bound water movement using the capillary flow mechanism. This method was applied to the
microwave drying analysis of hygroscopic and nonhygroscopic materials in a later study (Chen
and Schmidt* 1990). Moisture and temperature predictions were found in agreement with
experiments for polymer pellets, glass beads, and alumina spheres. Jansen and Wekken (19911
published a similar analysis.
Important considerations in the simulation of microwave drying
Transport mechanisms
An appropriate appreciation of the transport mechanisms involved in microwave drying
is the most important aspect in heat and mass transfer analysis. A close look at the drying
literature reveals that, in a sense, the history of drying modeling is a chronological record of the
understanding of the transport mechanism(s). Classic studies conducted by Sherwood (1929).
Ceaglske and Hougen (1937). and King (1971) utilized single mechanism, such as liquid
diffusion, vapor diffusion, and capillary flow to describe the drying of solids. These models
were aimed at studying the drying of certain materials under certain conditions. To address the
complexity of drying problems and to be applicable to a wide spectrum of materials, more
complicated models were developed using multi-mechanism approaches. The most cited
studies under this category were the works of Krischer. Luikov. and Whitaker. The theory of
Philip and de Vries and the receding front theory were also used in coupled heat and mass
transfer studies. In recent years, a consensus has been reached that a drying process is the one
with the simultaneous transport of heat, free water, bound water, vapor water, and air and that a
complete description of a drying problem requires the use of three coupled nonlinear partial
differential equations to account for the effect of moisture, temperature, and pressure fields
(Bories, 1991: Moyne and Perre. 1991). Different mechanisms have been assigned to the
transport of different liquid and gaseous fluxes. The inclusion or exclusion of bound water
transfer determines whether the model can be used to analyze hygroscopic materials or not. A
summary of the mechanisms used in microwave drying analyses is given in Table 2.
20
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Determination o f the heat source term due to microwave heat generation
In microwave heating and drying, heat generation analysis is crucial for an accurate
estimation of the heat source term in the energy equation. There are three factors that must be
considered. The first is the material itself. The heat source term in microwave drying is a
complex function of location, local temperature, local moisture content, local porosity, and
local composition. The complexity also comes from the interactions among the above
mentioned parameters. For example, the decay of microwave energy determines the local
electromagnetic field intensity and hence the heat generation. This decay is a function of the
dielectric constant e'and the loss factor e" while e' and e" themselves are a complex function of
temperature and moisture content. On the other hand, the temperature and moisture are function
of location. In order to master the complex changes caused by the material itself, we need to
understand the changes of e' and e" as function(s) of temperature and moisture content. If
porosity change is considerable, we also need to know the moisture dependency of porosity.
The second factor is the microwave distribution at the surface and inside the materiel.
From the previous section we know that microwave heating is not uniform. Hot and cold spots
exist. These are caused by the nonuniform distribution of the electromagnetic field inside the
cavity. It can be seen that the microwave distribution is not uniform, both at the surface and
inside the product. An accurate calculation of the distribution of electromagnetic field results
from solution of the Maxwell equation together with knowledge of dielectric properties and
heat and mass transfer equations. Such a complete solution remains a major challenge. Various
approaches used to solve this problem adopted simplified assumptions. The most important
assumption is the uniform distribution of microwave energy at product surface. Under this
assumption, the distribution inside the product was assumed to be (I) uniform (Chen and
Schmidt. 1990: Adu and Otten, 1996b): (2) exponentially decayed (Wei et al.. 1985: Lian et at..
1997): (3) decayed following empirical relations (Constant et al.. 1996: Ni et al.. 1999): and (4)
decayed calculated by solving electric field equations (Constant et al., 1992: Turner et al..
1998).
21
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T uble I, Heal and m uss trnn.sl'ei m odeling lor m icrow ave drying.
R e fe re n c e
T h e o ry
F re e w ater
Capillary flow
P re se n t stu d y
W hitaker
(im plicitly)
Ju n et al.,
1999
N i et « l„
1999
Luikov
T u rn e r el al„
1998
W hitaker
(im plicitly)
Cupilliiry flow
L in n et ul,,
1997
Philip & tie
Vires theory
D arcy’s law
B njztt, 1997
Luikov
C o n stu n t et
n l„ 1996
T ra n sp o rt m e c h a n ism
B o u n d w ater
V ap o r
Capillary
Chemical
(low +
potential
diffusion
NA*
NA
NA
Capillary How
NA
Capillary
llow +
diffusion
Capillary
(low
M olecular
diffusion
A ir
Capillary
(low +
diffusion
NA
Cnpillary
(low +
diffusion
Cnpillary
flow +
diffusion
Picks law
P o w er
e stim a tio n
F.mpirical
NA
Empirical
Electric field
analysis
Lambert law
NA
NA
NA
NA
W hitaker
(im plicitly)
Capillary llow
NA
Capillary
(low +
diffusion
T o rrin g n et
n l„ 1996
Lumped
diffusion
F ick's law
NA
NA
NA
A d u an d
O lte n , I9 9 6 h
Lumped
diffusion
P ick's law
NA
NA
NA
C o n stu n t el
ill., 1992
W hitaker
(im plicitly)
C apillary (low
NA
Capillary
llow
Capillary
llow +
diffusion
T u rn e r nnd
Jo lly , 1991
W hitaker
(implicitly)
Capillary llow
NA
Capillary
llow
Capillary
llow +
diffusion
NA
Capillary
flow +
diffusion
NA
Empirical
Uniform
throughout the
sample
Uniform
throughout the
sample
Electric field
analysis
Elecliic field
analysis
N u m erical
m eth o d
FDM
CrankNicnlson
M o d el
v alid atio n
Average moisture,
tem perature und
pressure were
measured
Pow er
m e a su re m e n t
Incident &
relleclcd
FEM
Average moisture
& tem perature
Not conducted
Incident
M oisture
Incident
Average moisture
Incident
M oisture
Rated pow er
o f the oven
Incident &
reflected
FDM
CrunkNicolson
FDM
Control
volume
technique
FEM ; Using
commercial
CFD software
NA
NA
FDM
Control
volume
technique
FDM
Average moisture,
tem perature, and
pressure
M oisture nnd
lemperniure
Incident &
relleclcd
FDM
M oisture and
lemperniure
Incident &
rellecled
FDM
Control
volume
technique
FDM
Control
volume
technique
Not conducted
NA
Not conducted
NA
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
uhle 2. H um m nt m uss trn n slc r m o d e lin g Ibr m ic ro w a v e A13C
‘
;
R e fe ren ce
T h e o ry
T ra n sp o rt m echim ism
P rec w ider
V ap o r
B o u n d w ilier
T w o region
Ciipilhiry flow
Capillary
C h o n nnd
NA
model
(low +
S ch m id t,
diffusion
1990
W hituker
NA
NA
Jo lly nnd
NA
T u rn e r, 1989
T w o region
Cnpillary llow
D arcy's law
Capillary
C h e n nnd
model
llow +
P ci, 1989
diffusion
W hiinker
Capillary flow
W ei el u l„
NA
Capillary
(im
plieiily)
llow
1985
it; not tivniliihlc o r not a p p lic a b le
A ir
Capillary
llow +
diffusion
NA
Capillary
llow +
diffusion
NA
P ow er
esiim u iio n
Uniform
throughout die
sample
N u m erical
m eth o d
Integral
method
NA
NA
Lambert law
NA
M oving FKM
PDM
M odel
v alid atio n
M oisture and
temperature were
measured
P o w er
m cu su rem en l
Incident &
reflected
NA
NA
Only hot-air
drying tests were
conducted
Not conducted
NA
NA
The third factor is the experimental determination of the microwave power absorbed by
the product. This power absorption determines the assumed uniform surface value of the
microwave power density which is the starting point for all the power distribution calculations.
An incorrect measurement of the absorbed power would lead to an incorrect estimation of the
heat source term and hence incorrect temperature and moisture distributions. The accurate
estimation of absorbed power is dependent upon instrumentation and the experimental system
used in the study. An absorbed power measuring system must have direction coupler for
measuring both the incident and the reflected power. The completion of such a system also
needs a stub turner to adjust the matching, a circulator to protect the magnetron, and a stand­
alone magnetron to generate the power. The absorbed power is the difference between the
incident and the reflected power if the loss in the waveguide and in the cavity is negligible. In
some microwave drying studies, however, the information about the absorbed power
determination was not reported. Some research groups only reported the incident power or
rated power of microwave ovens, probably due to limitations of their experimental systems.
Model validation
Product temperature, moisture, and pressure need to be measured to validate the
models. In a microwave field, the measurements can only be performed with fiber optical
probes. Probes for temperature and pressure measurement are available in the marketplace but
at relatively high prices. The typical sampling rate is one second which may not be fast enough
to record rapid temperature and pressure changes for high power and high moisture microwave
drying. The resolution for presently available fiber optic pressure probes is 1 kPa. which is only
good for high intensity and high moisture drying applications. As mentioned in the previous
section, the ability to accurately measure the microwave power absorbed by the sample is very
important.
Numerical analysis
The resulting microwave drying equations are coupled and highly nonlinear. Numerical
techniques have to be used to solve these equations. Chen and Schmidt (1997) provided a good
summary of the numerical techniques used in the simulation of microwave drying. These
methods include (1) the Orthogonal-CoIIocation method proposed by Wei et al. (1985); (2) the
24
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Control-Volume Finite Difference Method (Turner and Jolly, 1991); (3) the Moving Finite
Element Method (Chen and Pei. 1989); and (4) the Integral Method (Chen and Schmidt. 1990).
The Control-Volume Finite Difference Method was proposed by Patankar ( 1980) and has been
widely used in numerical heat transfer studies. The application of the-Moving Finite Element
Method is to facilitate calculation for receding evaporation front models. The integral Method
was introduced to address the efficiency in numerical calculation. In this method, the
temperature and moisture profiles need to be given, by assumed parabolic and polynomial
functions. The Crank-Nicolson finite difference scheme was also used because of its high
accuracy (Ni et al.. 1999).
FINAL REMARKS
Microwave drying technique is gaining a renewed interest in both academia and
industry. The unique volumetric heat generation and accompanied advantages pave the road for
its application in enhancing drying rate and improving product quality. Progress has been made
in prolonging the life-span of magnetrons and lowering the capital investment. Techniques to
overcome the heating nonuniformity problem have also been developed or are under
investigation. The techniques and instrumentation for the measurement of dielectric properties
have been fully developed and more and more dielectric properties have been measured and
reported. The introduction of fiber optic techniques into microwave drying research has
provided means to measure both the temperature and pressure changes during drying, a
revolutionary technique that has not been available until the last decade. The heat and mass
transfer mechanisms in microwave drying have been and are still being investigated to provide
insight into the underlying physics in this unique drying process. With all of the progress, an
increase in the application of microwave energy in industrial drying can certainly be foreseen.
REFERENCES
Adu. B.. Otten. L. and Brown. R. B.. 1994, Modeling thin layer microwave drying of soybeans.
Can. Agr. Eng., 36, pp. 135-141.
Adu. B. and Otten, L.. 1996a. Diffusion characteristics of white beans during microwave
drying, /. Agric. Engng. Res.. 64, pp. 61-70.
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Adu. B. and Otten, L.. 1996b. Modeling microwave heating characteristics of granular
hygroscopic solids. J. Microwave Power and Electromagnetic Energy. 31. pp. 35-42.
Bajza. 22. 1997. The influence of fatliquor concentration on microwave drying kinetics. J. Soc.
Leather Technologists and Chemists. 81, pp. 227-230.
Beke. J.. 1992. Microwave drying of com. In Drying '92. Mujumdar. A. S.. ted.). Elsevier
Science Publishers, pp. 607-616.
Beke. J.. Mujumdar. A. S. and Bosisio. R. G.. 1995. Drying of fresh and rewetted shelled com
in microwave Reids. Drying Technol.. 13, pp. 463-475.
Bories. S. A.. 1991. Fundamentals of drying of capillary-porous bodies, in Convective Heat and
Mass Transfer in Porous Media. S. Kakac et al. (eds.). Kluwer Academic Publishers.
Dordrecht.
Bouraoui. M.. Richaed. P. and Durance. T.. 1994. Microwave and convective drying of potato
slices. J. Food Process Eng.. 17. pp. 353-363.
Brygidyr. A. M.. Rzepecka. M. A. and McConnell. M. B.. 1977. Characterization and drying of
tomato paste foam by hot air and microwave energy. J. Inst. Can. Sci. Technol. Aliment.
10. pp. 313-319.
Ceagiske. N. H. and Hougen. O. A.. 1937. Drying granular solids. Ind. Eng. Chem.. 29. pp.
805-813.
Chen. P. and Pei. D. C. T.. 1989, A mathematical model of drying processes. Int. J. Heat Mass
Transfer. 32. pp. 297-310.
Chen. P. and Schmidt. P. S.. 1990. An integral model for drying of hygroscopic and
nonhygroscopic materials with dielectric heating, Drying Technol.. 8. pp. 907-930.
Chen. P. and Schmidt. P. S.. 1997. Mathematical modeling of dielectrically-enhanced drying.
In Mathematical Modeling and Numerical Techniques in Drying Technology. Turner. I.
And Mujumdar, A. S. (eds.). Marcel Dekker. Inc.. New York. pp. 439-478.
Constant. T., Perre, P. and Moyne. C.. 1992. Microwave drying of light concrete: from
transport mechanisms to explanation of energy savings. In Drying '92. Mujumdar. A. S.
(ed.), Elsevier Science Publishers.
Constant, T.. Moyne, C. and Perre. P.. 1996. Drying with internal heat generation: theoretical
aspects and application to microwave drying, AIChE
42, pp. 359-368.
Crank. J.. 1975. The Mathematics of Diffusion (2nd ed.). Clarendon Press, Oxford.
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Drouzas. A. E. and Schubert, H., 1996, Microwave application in vacuum drying of fruits. J.
Food Eng., 29, pp. 203-209.
Drouzas. A. E.. Tsami. E. and Saravacos, G. D.. 1999, Microwave/vacuum drying of model
fruits gels. J. Food Eng., 39, pp. 117-122.
Feng . H. and Tang. J.. 1998. Microwave finish drying of diced apples in a spouted bed. J.
Food Sci.. 63. pp. 679-683.
Feng. H.. Tang, J.. Mattinson. D. S. and Fellman. J. K.. 1999. Microwave and spouted bed
drying of blueberries: the effect of drying and pretreatment methods on physical properties
and retention of flavor volatiles. J. Food Processing and Preservation. 23. pp. 463-479.
Feng, H.. Tang, J. and Dixon-Warren. St J.. 2000. Determination of moisture diffusivity of red
delicious apple tissues by thermogravimetric analysis. Drying Technol.. 18(5).
George. R.M.. 1993. Recent progress in product, package and process design for microwavable
foods. Trends in Food Sci. Technol.. 4, pp. 390-394.
Goedeken. D. L.. Tong, C. H. and Virtanen. A. J.. 1997. Dielectric properties of a
pregelatinized bread system at 2450 MHz as a function of temperature, moisture, salt and
specific volume. J. Food Sci., 62. pp. 145-149.
Grolmes. J. L. and Bergman. T. L.. 1990. Dielectrically-assisted drying of a nonhygroscopic
porous material. Drying Technol., 8. pp. 953-975.
Jansen. W. and van der Wekken. B.. 1991. Modeling of dielectrically assisted drying. J.
Microwave Power and Electromagnetic Energy. 26. pp. 227-236.
Jun. W.. Zhang, J.. Wang, J. and Xu. N., 1999. Modeling simultaneous heat and mass transfer
for microwave drying on apple. Drying Technol.. 17, pp. 1927-1934.
JoIIv. P. and Turner. I.. 1989, Microwave drying of porous media. In Proceedings o f the Fourth
Australisian Heat and Mass Transfer Conference. University of Canterbury. Christchurch.
Hew Zealand, pp. 331-342.
Khraisheh. M. a. M., Cooper, T. J. R. and Magee. T. R. A.. 1995. Investigation and modeling of
combined microwave and air drying, Trans. IChemE. 73. Part C. pp. 121-126.
King. C. J.. 1971. Freeze Drying o f Foods. Butterworth. London.
Kumar, A., 1982, Microwave drying of wet polyester fibers. Int. J. Electronics. 52. pp. 491495.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Lian. G., C. S. Harris, R. Evans and M. Warboys. 1997. Coupled Heat and Moisture Transfer
During Microwave Vacuum CryingJ . Microwave Power and Electromagnetic Energy.
32, pp. 34-44.
Lu. L.. Tang, J. and Liang, L., L998, Moisture distribution in spherical foods in microwave
drying. Drying Technol., 16, pp. 503-524.
Lu. L.. Tang. J. and Run. X.. 1999. Temperature and moisture changes during microwave
drying of sliced food. Drying Technol.. 17. pp. 413-432.
Luikov. A. V.. 1966. Heat and Mass Transfer in Capillary-Porous Bodies. Pergamon Press.
London.
Melendez. W.. Flake. B. A. and Schmidt. P. S.. 1989. A process simulation model for
convective and dielectrically-enhanced single-zone tunnel dryers. In Simulation o f Thermal
Energy Systems. Boehm. R. F. and El-Sayed. Y. M.. (eds.), ASME. New York. pp. 9-16.
Metaxas. A. C. and Meredith. R. J.. 1983. Industrial Microwave Heating. Peter Peregrinus Ltd..
London. 1983
Moyne. C. and Perre. P., 1991. Processes relation to drying: Part I, theoretical model. Drying
Technol.. 9 . 1135-1152.
Ni. H.. Datta. A. K. and Torrance. K. W. (1999) Moisture transport in intensive microwave
heating of biomaterials: a multiphase porous media model. Int. J. Heat and Mass Transfer.
42, 1501-1512.
Nijhuis. H. H.. Torringa. E.. Luyten. H.. Rene. F.. Jones. P.. Funebo. T. and Ohlsson. T..
Research needs and opportunities in the dry conservation of fruits and vegetables. Drying
Technol.. 14. pp. 1429-1457.
Nury. F. S. and Salunkhe, D. K., 1968. Effects of microwave dehydration on components of
apples. ARS 74-45, USDA.
Page, G. E., 1949. Factors influencing the maximum rates of air drying shelled com in thinlayer. M.S. thesis, Purdue University. Indiana.
Patankar. S. V.. 1980, Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing, New
York.
Philip. J. R. and D. A. de Vries, 1957, Moisture Movement in Porous Materials under
Temperature Gradient, Trans. Am. Geopgys. Union. 38, pp. 222-232.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Prabhanjan. D.G.. Raghavan. G.S.V. and Bosisio. R. G., 1993. Microwave drying of wheat
using surface wave applicator. Powder Handling and Processing. 5. pp.73-77.
Prabhanjan- D.G.. Ramaswamy. H.S. and Raghavan. G.S.V.. 1995. Microwave-assisted
convective air drying of thin layer carrots. J. Food Eng. 25, pp. 283-293.
Ptasznik. W.. Zygmunt, S. and Kudra, T.. 1990. Simulation of RF-assisted convective drying
for seed quality broad bean. Drying Technol.. 8, pp. 977-992.
Qiu. Y and Hawley M. C. 1998. Computer controlled variable frequency microwave processing
of graphite/epoxy in a single mode cavity. Proceedings of 33rd Microwave Power
Symposium. Int. Microwave Power Inst.
Schiffmann. R. F.. 1995. Microwave and dielectric drying, In Handbook o f Industrial Drying.
Mujumdar. A. S.. (ed.), Marcel Dekker. Inc.. New York. pp. 345-372.
Sherwood. T. K.. 1929. The drying of solids, Ind. Eng. Chem.. 21. pp. 12-16.
Shivhare. U.. Raghavan. V.. Bosisio. R. and Giroux. M.. 1993. Microwave drying of soybean at
2.45 GHz. J. Microwave Power and Electromagnetic Energy. 28. pp. 11-17.
Skansi. D.. Bajza. Z. and Arapovic. A.. 1995. Experimental evaluation of the microwave drying
of leather. J. Soc. Leather Technologists and Chemists. 79. pp. 171-177.
Stuchly. S. S. and Stuchly. M. A.. 1983. Microwave drying: potential and limitations. In
Advances in Drying, Hemisphere Publishing Corporation. New York. 2. pp. 53-71.
Sun. E.. Datta. A. and Loba. S.. 1995, Composition-based prediction of dielectric properties of
foods. J. Microwave Power and Electromagnetic Energy. 30. pp. 205-212.
Tang. J.. Feng, H. and Lau. M.. 1999. Microwave heating in food processing, manuscript.
Tong, C. H.. Lentz, R. R. and Rossen. J. L.. 1994. Dielectric properties of pea puree at 915
MHz and 2450 MHz as a function of temperature. J. Food Sci.. 59. pp. 121-134.
Torringa. EM., van Dijk. E J. and Bartels. P.S., 1996. Microwave puffing of vegetables:
modeling and measurements. In Proceedings o f 31st Microwave Power Symposium, Int.
Microwave Power Inst., Manassas. VA.
Tulasidas. T. N.. Raghavan, G. S. V. and Norris. E. R.. 1993, Microwave and convective drying
of grape, Trans. ASAE, 36, pp. 1816-1865.
Tulasidas, T. N., Raghavan, G. S. V. and Mujumdar, A. S., 1995. Microwave drying of grapes
in a single mode cavity at 2450 MHz -H: quality and energy aspects. Drying Technol., 13,
pp. 1973-1992.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Tamer. I. W. and Jolly. P. G.. 1991. Combined microwave and convective drying of a porous
material. Drying Technol.. 9. pp. 1209-1269.
Turner. I. W. and Rudolph. V.. 1992. Convective and microwave enhanced drying of glass
beads. In Drying '92. Mujudar. A. S. (ed.), Elsevier Science Publishers, pp. 553-572.
Turner. I. W.. Puiggali. J. R. and Jomaa. W.. 1998. A numerical investigation of combined
microwave and convective drying of a hygroscopic porous material: A study based on pine
wood. Trans. IChemE.. 76, Part A. pp. 193-209.
Wei. C. K... Davis. H. T.. Davis. E. A. and Gordon. J.. 1985. Heat and mass transfer in water­
laden sandstone: microwave heating. AIChE J.. 31. pp. 842-848.
Welt. B. A.: Tong. C. H. and Rossen. J. L. 1992. An apparatus for providing constant and
homogeneous temperatures in low viscosity liquids during microwave heating. Microwave
world. 13.9-13.
Whitaker. S.. 1977. Simultaneous Heat. Mass. Momentum Transfer in Porous Media: A Theory
of Drying. Adv. In Heat Transfer.. 13. pp. 119-203.
Wright. M. E. and Porterfield. J. G.. 1971. Heating and drying peanuts with radio-frequency
energy. Trans. ASAE. pp. 629-637.
Zhang. H. and Datta. A. K.. 1999. Electromagnetics of microwave heating: magnitude and
uniformity of energy absorption in an oven, manuscript
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CHAPTER 2
EVALUATION OF QUALITY ATTRIBUTES FOR DEHYDRATED BIOLOGICAL
MATERIALS
INTRODUCTION
Drying is our oldest preservation method. It reduces moisture content and lowers water
activity of a perishable food product to a safe level (a«. < 0.6. see Ftg. I) to prolong shelf life
and add value. Compared to foods produced with other preservation methods, dehydrated
products have almost unlimited shelf-life and substantially lower transportation, handling and
storage costs. Dried foods provide opportunities for maximum convenience, flexibility, and
economics as industrial or food service ingredients.
Various physical, chemical, biochemical and biological changes accompany the drying
of biomaterials. The removal of water from biomaterials by applying heat, however, degrades
the functionality of the original bio-matrix and may result in unfavorable quality changes.
Major changes that may occur during drying are summarized in Table I.
Dried foods
©
<5
QC
c
o
o
<0
©
GC
©
_>
3
©
tr
isotherm
O.t
0.2
0.3
0.4 0.5 0.6
WaterActivity
0.7
0.8
0.9
1.0
FIGURE I. Global food stability map (Labuza, 1970).
31
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Table I. Typical quality changes during drying (adapted from Karel. 1991: Bimbenet and
Lebert. 1992)
Physical
shrinkage
loss of rehydration capacity
textural changes
case hardening
cracking or disintegration
loss of volatile aroma components
loss of elasticity
migration of solutes
crystallization or change of crystalline structure
Chemical and biochemical
discoloration
enzymatic reactions
non-enzymatic browning
oxidation of lipids, pigments and vitamins
protein quality degradation due to browning, oxidation, and denaturation
Biological
decomposition of microorganisms
loss of biological activity or germination ability
Potential physio-chemically related quality changes that take place in a food products
during drying are illustrated in Figure I. During drying, moisture is removed from the foods and
water activity decreases and passes peaks of enzymatic reactions, nonenzymatic browning, and
lipid oxidation. It is, therefore, inevitable that foods suffer a loss in quality. Typical losses in
vitamins during drying in several food systems are listed in Table 2.
32
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Table 2. Vitamin losses in selected foods during drying, adapted from a) Yang and Atallah.
1985: b) Fellows. 1988; c) Jayaraman et al.. 1990: d) Jayaraman and Gupta.1995: and e)
Sokhansanj and Jayas. 1995.
Loss (9c)
Food
Vitamin A
Thiamin
55b
Vitamin B-
Niacin
0b
tob
Vitamin C
Folic Acid
Bioun
ls 6
I0b
I0b
30b
to6
I0b
56b
Fruits*
6b
Apncots
14“
96“
13“
74“
0“
76“
(unsulfued and sun dried)
Apncots
t sulfited and sun dried)
Apricots
(sulfited and air dried)
00
Apricots
22“
(sulfited and drum dried)
Blueberry (freeze dried)
I9J
46-
11-
Blueberry (air dried)
51*
50-
56-
Blueberry (vacuum dried)
50-
47-
89-
Blueberry
42-
40-
83-
(microwave +- air dried)
Carrots (freeze dried)
60“
Carrots (air dried)
29c
81“
Cauliflower
83c*
(salt & sugar long +- air
drying)
Cauliflower
o i­
(salt & sugar long +■ air
drying)
Chicken (freeze dned)
5-6‘
4-8"
Fig (sun-dried)
48b
42b
37b
Milk ispray dried)
Milk (drum dried)
Pork (freeze dried)
5-30b
Pork (air dried)
50-706
Potato (air dried)
Selected veg.* (air dried)
IS '
5b
5-9e
<I0b
<I0e
* mean loss from fresh apple, apricot, peach and prune
- include peas, com, cabbage, and beans
★ compared with untreated dried
33
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The quality of dehydrated bio-products depends, to some extent, on the quality of the
raw materials. Quality evaluation involves measurements of some physio-chemical changes,
which are usually product and process specific. In practice, quality attributes of dried
biomaterials are determined by their end use. which, to a large extent, is dictated by consumer
preferences. Quality inspections of final dehydrated products are usually conducted in terms of
texture, flavor and aroma, color or appearance, nutritive value, and sensory evaluation.
To fully understand the quality change of biomaterials and. hence, attain control over
product quality during drying and storage, we need to have insight into the factors that affect
the quality degradation kinetics and assure effective means to evaluate the quality changes. The
objectives of this paper are to examine the factors that are crucial to the control of dehydrated
product quality and review the progress in the determination of physical quality attributes.
FACTORS AFFECTING PRODUCT QUALITY DURING DRYING
Several factors affect the rate of quality degradation of a bio-product during drying.
Generally recognized important factors include temperature, moisture content or water activity,
and drying time (Strumillo et al.. 1996a). Other parameters, such as pressure, oxygen. pH.
composition (fats, sugar, protein, etc.). coreactant level, presence of trace metals and other
catalysts, and light intensity, may also play an important role in certain circumstances (Lee et
al.. 1977: Franzen et al.. 1990). Factors that affect drying rate will also contribute to the quality
changes of final products. Dipping, blanching, and osmotic treatments usually yield better
quality, mainly because these treatments reduce the times of exposure to high temperatures
(Salas and Labuza. 1968: Suarez et al.. 1984: Kim and Toledo. 1987: Lenart. 1996). A
processing atmosphere with reduced temperature and/or pressure {e.g. freeze drying and/or
vacuum drying) can achieve some of the highest quality retention among drying techniques
(Yang and Atallah. 1985). Reducing drying time by applying volumetric microwave heating
(Garcia et al.. 1988: Bouraoui et al.. 1994: Prabhanjan et al.. 1995: Feng and Tang, 1998) or by
high-temperature-short-time (HTST) drying (Teixeira et al.. 1969: Kim and Toledo, 1987:
Strumillo et al., 1994) also reduces quality deterioration. The above-mentioned techniques to
improve product quality retention during drying provide either a reduction in drying
34
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temperature (freeze drying) and oxygen content (vacuum drying, freeze drying, and inert gas
drying), or a reduced drying time (pretreatment, volumetric drying. HTST drying).
Recently, Strumillo et al. (1994. 1995) demonstrated that modifications of the physical
properties of products, using a selected pretreatment before drying." leads to better quality
retention. They mixed the biomaterials to be dried with porous and hygroscopic carriers to
reduce quality losses. A similar method was used to achieve an atmospheric freeze drying
(Wolff and Gibert. 1990), in which a porous adsorbent was added to obtain high quality
dehydrated products at atmospheric pressure. Since no vacuum system is needed in this method,
production costs can be relatively low compared to conventional freeze drying methods.
Examples of how operating parameters affect the quality attributes of a dehydrated
product are presented in Figures 2 and 3. Figure 2 shows the influence of drying temperature on
lentil germination at 16 to 20% initial moisture content. A sharp decrease in germination was
observed when drying temperature reached 70°C. The influence of moisture content is not
significant in Figure 2. Figure 3 illustrates the optimum operation range for drying lentils. The
upper temperature limits are set to prevent development of a brown color that would downgrade
lentils, and to prevent germination loss of more than 5%. The limits for moisture are for
effective mechanical harvesting without causing significant shattering losses or threshing
difficulty.
QUALITY CHANGE KINETICS
Quality changes take place in the post-harvest storage or in the post-mortem period,
during drying, and in the post-drying storage. If we use Q0 as a quantitative measure of the
original quality attributes of raw materials. QD for the quality of dried products. Qc for the
quality when it is to be consumed or put into end use. and Qf for the final quality of the product
when designated shelf life is reached, the quality changes experienced by a product from raw
material to the point where quality of the product becomes unacceptable can be qualitatively
represented in Figure 4. The quality changes are characterized by three-stage quality
degradation with a significant rate of change occurring at the drying stage. Reaction pathways
leading to quality changes in foods are complicated. The kinetics of the quality changes,
however, can be simplified by the following relationship:
35
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no
100Canadtan N o . I
Canadian N o.2
. M. = 16*
* M. = S3*
40-
' M. = 20*
10
20
30
40
60
40
70
10
•o
Drying temperature, °C
Figure 2. Drying time and germination of lentils. The dashed lines represent minimum
germination for Canadian No. I and No. 2 lentils. (Tang and Sokhansanj. 1993)
brawn color
70
SO
0
uf
cc
1
50
2
40
LU
0.
b rittle
'/ .
Safe
LU
I—
30
20
MOISTURE CONTENT. %w.b..
Figure 3. Optimum operation range for drying lentils (Tang and Sokhansanj, 1993)
36
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( i = I. n. or h d
at
(U
where [A] is the quality attribute for a selected quality index, k is the rate constant which is
process and product specific, n is the order of the reaction, the subscripts i = I. H and HI
represent the postharvest (for plants, fruits and vegetables, and grains) or postmortem (for
animals) storage, the drying process, and the product storage, respectively. Stage IE is often
referred to as the shelf life of a finished product, in the case of food products. In Eq. 1. [A] can
be the concentration of aroma components, vitamins, pigments, and soluble solids: the enzyme
activity: the microbial count: the germination rate: the biological activity: or physical attributes
such as porosity and rehydration capacity.
Postharvest or
postmortem
storage
Product storage
Drying
End use
r~
Without drying
Shelf life
Time
Figure 4. Quality change vs. history of food product
Quality changes in many food products exhibit either zero (n = 0) or first (n = 1) order
kinetic behavior. A zero-order or pseudo-zero-order reaction was widely observed for overall
quality of frozen foods, nonenzymatic browning, and chlorophyll loss (Karel and Nickerson.
1964; Saguy et al., 1978; Resnick and Chirife, 1979; Samaniego-Esguerra et al.. 1991, Taoukis
37
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et al., 1997). A first-order reaction behavior was reported for ascorbic acid degradation (Luyben
et al.. 1979: McMinn and Magee. 1997a). thiosulphinate loss (Samaniego-Esguerra. 1991).
color loss (Chou and Breene. 1972), microbial destruction (Bruin and Luyben. 1980). texture
loss (Taoukis et al., 1997). and enzyme inactivation (Luyben et al.. 1979).
The factors affecting product quality can be included in the degradation kinetics
equation by a rate constant which can either lump various effects into a single expression or
isolate different factors using separate correlations. In the former case, the expression may take
a form of
k = / ( temperature. moisture. time. 0 2. pH. composition, etc.)
(2)
For the latter, a variety of correlations are available in literature. The temperature
dependence of quality decay kinetics is usually described by an Arrhenius type equation (Saguy
and Karel. 1980):
£ /
I RT)
fc, = kQTexp (
(3)
where kor = Arrhenius factor for temperature dependence. EA= activation energy. R = universal
gas constant, and T = absolute temperature. The moisture dependence can be written as
(Strumillo and Adamiec. 1996):
~ k ox X m
(4)
where kox = coefficient, X = moisture content, and m = constant. The moisture and temperature
dependency can also be taken into account in Eq. (3) by relating the Arrhenius factor and/or the
activation energy to moisture content and/or temperature using regression methods. Luyben et
al. (1979) considered the moisture dependency of both the Arrhenius factor and the activation
energy by:
38
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Ea= A -b B-exp(-CX)
\nkt = D -r £-exp(-CX)
(5)
where A. B. C. D and E are constant, ko is the Arrhenius factor. Values for parameters in Eq.
(5) of selected enzymatic reactions were given by Luyben et al. (1979) and are listed in Table 3.
Another correlation, as proposed by Strumillo and Adamiec (1996). integrated both moisture
and temperature dependency, for a drying process, into Eq. (3). It takes the form of
ku= (+.56x tO-5-6.84 x 10~*X+2.14x [O^T-lASx I0‘s Xr)exp
2.15x10-'
RT
(
6)
Table 3. Parameters defined in Eq. (5) for selected enzymatic reactions (adapted from Luyben et
al.. 1979)
_______Parameter_______________ Catalase________________ Lipase___________ Alkaline phosphatase
A
2.585 x 10*
3.898
4.832x10*
B
-2.057x10*
1.237x10*
-4.832x10*
C
3.699
4.880
11.366
D
86.27
-9.743
164.62
E
-85.95
38.509
-190.53
Non-enzymatic browning is a common reaction during drying of many foods that causes
discoloration and nutrient loss. The activation energy values for non-enzymatic browning of
selected foods are listed in Table 4. Note that the activation energy increases when water
activity decreases (Hendel et al.. 1955: Mizrahi et al.. 1970: Samaniego-Esguerra. 1991). As a
result, the activation energy during storage of a dried product is higher compared with the
activation energy during drying. This is because water tends to decrease the temperature
sensitivity of the reaction as moisture concentration increases (Labuza and Saltmarch. 1981).
Taking advantage of this dependence of nonenzymatic browning on water activity may include:
I) reducing drying temperature during the last stage of drying to minimize nonenzymatic
browning; 2) avoiding temperature variation during dried product storage to reduce
nonenzymatic browning.
39
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Table 4 Activation energy for non-enzymatic browning in selected foods
Food
apricot
a*
NA
X’
Temperature
E,
(g HiO/g solid)
(“O
(kcal/mole)
0.24
22-49
26
potato
raisin
Stadtman et al..
1946
(in storage)
(during drying)
Reference
NA
0.6-0.8
0.05
37
0.09
32
Hendel et al..
28
1955
0.15
40-80
0.33
25
1.1
25
NA
21
24
Copley and Van
Arsdel. 1964
0.01
40
cabbage
0.20
38
Mizrahi et al..
(in storage)
0.32
34
1970
carrot
NA
37
0.43
32
0.51
29
0.62
28
-0.15-0.75
NA
60-90
-125-80
(during drying)
skim milk
1985
NA
0.5-3.5
35-130
35-24
(dried)
carrot
Franzen et al..
1990
NA
0.03-0.33
60-90
92-47
(during drying)
Muller and
Bauer. 1990
onion
0.32
(in storage)
0.43
NA
20-40
0.56
onion
Eicheretai..
0.29-0.95
190
Samamego-
142
Esguerra. 1991
128
NA
40-80
139-121
(during drying)
Rapusas and
Driscoll. 1995
cheddar cheese
0.51
powder
0-62
(in storage)
0.75
hazelnut
NA
22
NA
20-40
19
K ilicetal.. 1997
18
0.05-0.25
30-80
37“
(during drying)
Lopez et al..
1997
dough
(microwave heating
with susceptor to get
Zuckerman and
NA
NA
150-200
46-50
Miltz. 1997
surface browning)
a: average of shelled and unshelled hazelnut (Negret).
40
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MOISTURE DETERMINATION
Moisture content measurement is crucial for studying drying operations and quality
control. An ever-increasing number of techniques are available for this purpose. A summary of
some of the most widely used follows:
1) Air oven and vacuum oven method: Oven drying at different conditions is the most widely
used method. It is recommended by AACC (1983), AOCS (1984). USDA (1986). AOAC
(1990), and ASAE (1990) as the official method for moisture determination in a range of
dehydrated products. The air oven method is mainly used for grains and cereals while the
vacuum oven method is used for fruits, vegetables, plants, and many other biomaterials.
Vacuum oven drying is also used to measure the moisture content of moist products in various
drying experiments. Two major factors that affect the accuracy of measurement are the drying
time and the temperature. Van Arsdel (1963) listed as many as seven distinguishable different
vacuum-oven procedures specified by AOAC for the moisture content determination of some
products. The specified temperature among the seven methods ranges from 60 to 100UC and the
time from 5 to 40 hours. For products not specified in the standards, the time and temperature
chosen are very much dependent on the experience of the people who conduct the tests. It is not
unusual to find in the literature that, for the same product, different research groups use
different drying conditions, which makes a comparison of their results difficult. In some cases,
the weight loss in oven drying may be caused by factors other than water evaporation.
Precautions must be taken for heat sensitive, high sugar, and high volatile content products.
2) Karl Fisher titration method: The Karl Fisher titration method is a rapid and sensitive
method suitable for use in a well equipped laboratory with skilled operators (Stitt. 1958). It is
more appropriate for low moisture and high sugar content products (Pomeranz and Meloan.
1994). This test is based on the non-stoichiometric reaction of water with iodine and sulfur
dioxide in pyridine-methanol solution. It usually yields reliable moisture content (Young, 1991)
and can be used as a reference to justify the results from oven methods (Hart et al., 1959:
Christensen, 1974).
41
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3) Distillation methods: In distillation methods, heat is applied by immersing the sample in oil
or some non-aqueous liquids. The mass or volume loss of the distilled water is collected and
measured directly. Distillation methods cause less decomposition of the products than some
oven drying methods (Giese, 1995).
4) Electrical methods: Electrical methods use the moisture dependency of such electrical
properties as resistance, capacity, and dielectric constant. They are fast and simple methods
compared with many others (Pomeranz and Meloan. 1994).
5) Infrared and near-infra red methods'.: Infrared methods are based on the absorption of energy
at the wavelengths corresponding to water molecule vibration. They have been used for on-line
moisture measurement and work best when a large number of similar samples is tested (Giese.
1995).
In a drying experiment, the initial and final moisture content is usually measured with
the foregoing methods. The intermediate weight loss readings are taken by ordinary gravimetric
methods (such as weighing on an electric balance). The weight losses are then converted to
moisture content with reference to the initial and final moisture contents.
Moisture profile measurement is necessary to validate a particular drying model. This
can be achieved by the Nuclear Magnetic Resonance (NMR) (Ruan et al.. 1991: Pel and
Brocken. 1996), the Magnetic Resonance Imaging (MRI) (Schmidt et al.. 1996). the Scanning
Neutron Transmission (SNT) (Ketelaars et al.. 1997). and the y-ray attenuation method (Chiang
and Petersen, 1987: Gong and Plumb. 1994). In-site measurement of moisture content is
important to both the drying model evaluation and the production control. Methods developed
for in-site measurement include infrared and electric sensors.
PHYSICAL QUALITY ATTRIBUTES AND THEIR DETERMINATION
Quality determination of dried products is accomplished by measuring certain physical
attributes, such as rehydration capacity, bulk density, texture, and color, or degradation of
specified chemical compounds, such as ascorbic acid, thiolsulphinates, etc. The criterion for
quality evaluation is product specific and only selected key quality attributes need to be
42
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evaluated- This section focuses mainly on the quality indices related to the physical properties
of foods and agriculture products.
Density
The density of a biomaterial is needed for the design of drying and handling equipment,
for quality evaluation, for the modeling of heat and mass transport, and for calculation of other
important physical properties, such as porosity and shrinkage. Generally, density is mass per
unit volume of a substance. Different density definitions arise from the way the volume and the
mass are specified for a particular product and particular application. For most bioproducts,
various volumes that can be distinguished are presented in Figure 5. The densities defined in
terms of the volume(s) involved are given in Table 5 for two types of biomaterials. Detailed
definitions for these materials are given in the following sections.
Open pore
Internal pore (VJ
Dry solid + water
(Vs + V)
Figure 5. Volumes (pore structure) can be distinguished in a biomaterial
43
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Table 5. Densities used for grains/legumes and fruits/vegetables.
Grains/legumes
Fruits/vegetables
bulk density
bulk density
for packing design
particle density
bulk density
solid densitv
particle density
—
dry solid density
For fruits and vegetables, substantial structural changes are experienced during drying,
which results in considerable shrinkage and poor rehydration capacity. The relationship
between pore structure and the drying condition predict drying behavior and quality changes.
The density definitions for fruits and vegetables were given by Zogzas et al. (1994) as
M,+Mw
M,+Mw
M,
P^ T 7
171
where Va, Vs. and Vw are the volume of air trapped in internal pores of a food, the volume of
dry solid, and the volume of the water. Pb. pp. and ps are bulk, density, panicle density, and solid
density. Ms and Mw are the mass of the dry solid and water, respectively. In the density
definition, the mass of air (Ma) trapped in the internal pores of foods is negligible compared to
that of solid and water.
The densities used in literature for either quality analysis or heat and mass transfer
calculation need to be scrutinized since different densities were often interchangeably used
without considering the significant difference. Table 6 presents densities available in the
literature for fruits, vegetables, and other products whose internal structural changes during
drying are also important. Densities named with same term often refer to different mass and
volume components among researchers. A clear and consistent definition for the densities is
needed. If we are concerned with handling and package equipment design, a bulk density other
than the one defined in Eq. (7) can be used
p‘*
Ms+Mw
V.+V.+V.+V.
(8)
44
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where pbP is the bulk density of a food product when determined with a hectometer. Similarly.
V' is the air volume inside the hectometer but excluding the air inside the particles. The assay
methods for the volumes and the masses involved.in Eqs. (7) and (8) include:
( 1) total volume Vs + Vw + Va: The total volume of a food product can be evaluated using
different volumetric displacement methods. One widely used method is the liquid displacement
method. The liquid used may be water, toluene, n-heptane. or mercury (Lozano et al.. 1980:
Zogzas et al.. 1994). However, water is often used because the error due to water uptake is
usually negligible. This is illustrated in Figure 6. which shows the changes in density of dried
apple dices with submerging time obtained by the water displacement method (Feng and Tang.
1997). Sometimes, an impermeable film or a coating is used to prevent liquid absorption, when
considerable error due to absorption is expected. The coating method is not suitable for
materials of irregular geometry because extra error will be introduced from air trapped in the
package. Fine glass beads (Marousis and Saravacos. 1990). rapeseeds (AACC. 1983). and
Maku lotus seeds (Diamente et al.. 1993) can also be used to measure the total volume.
(2) particle volume Vs + Vw: Particle volume is usually determined with a gas pycnometer. The
sample must be ground into a fine powder to eliminate air trapped in the pores.
(3) total mass M, + Mw: Gravimetric balances can produce satisfactory results.
(4) solid mass Ms and solid volume V,: Solid mass and volume can be determined by drying the
sample in an oven to a constant weight, grinding it into fine powder, and using a density bottle.
For heat sensitive biomaterials, an optimum drying time must determined by preliminary tests.
45
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T able I. T erm inology used lor density definition o f selected hiom alerials in literature
Reference
M , + M*
M , + M*
v 4+ v w+ v, + v;
V4 + Vw + v a
M , + M*
VTft + V
Tw
true density
M,
Product
v,
Mal6 et al., 1998
bulk density
potato
Feng und Tang, 1998
bulk density
McMinn and Magee,
1997b
upparent density
true density
potato
Quintero-Fuenles e tal,,
bulk density
solid density
chip
apple
1997
Schmalko et al., 1997
Patil and Sokhansanj,
1995
wood
apparent density
bulk density
particle density*
alfalfu
Dons} et al„ 1996
bulk density
substance density
apple and potato
Rapusas and Driscoll,
appurcnt density
true density
onion
Wang and Brennan, 1995
density
density of dry
sample
potato
Karathonos and
Kostaropoulos, 1995
bulk density
solid density
apple
Zogzas et al„ 1994
bulk density
particle density
Saca and Lozano, 1992
bulk density
particle density
bananas
Marousis and Saravacos,
1990
bulk density
particle density
corn starch
1995
dry solid density
N/A
Kim and Toledo, 1987
bulk density
blueberry
Yang and Atnllah, 1985
bulk density
blueberry
Lozano el al„ 1980
Sullivan et al., 1980
bulk density
* measured with a pycnometer for individual stem and leaf
bulk density
substance density
apple
apple
[000
10
—
ea
9 -4
.5
8
"3
r 900
~
<
7 -
i J o « o
o o
o
o
o
5
10
[5
20
25
so
- 700
■=
- 600
— — ,— |— ,— |— ,— |— ,— |— i— |— i— j— i— |— i— i— i—
0
800
30
35
40
|—
45
i— i— •— r
50
500
55
D ipping tim e (second)
Figure 6. Density reading vs. dipping time for water displacement method (Feng and Tang.
1997)
Because the pore structure of many biomaterials, such as fruits and vegetables, is
complex, some discrepancies can be distinguished in literature for the definition and
determination of particle density. The pores in fruits and vegetable can be categorized into open
pores and internal pores (see Fig. 5). If a pycnometer is used for a whole piece of product, the
volume measured is the one that eliminates open pores but includes internal pores, unless the
open pores are interconnected to the surface. Density determined using this method was
referred to as particle density by Lozano et al. (1980) and Patil & Sokhansanj (1995). This
density does not match the particle density defined in Eq. (7) since the internal pore volume is
not excluded. To eliminate the internal pores, the product has to be ground into fine powder.
However, grinding will introduce additional error due to moisture loss as long as the moisture
content of the product is higher than the equilibrium moisture content at the grinding
temperature. Grinding is also not suitable for wet materials because they tend to agglomerate
and form a sticky paste (Madamba et al.. 1994). One way to avoid this problem is to calculate
47
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particle densities defined in Eq. (7) using the dry solid density ps, which can be accurately
determined without difficulty- The particle density can be calculated by
M +Af.
PsPw
v,+ K
p » + ( p ,- p J x
(9)
where p* is the density of water and X = MW
/(MW+ Ms) is the moisture content (wet basis) of
the product.
The density of a biomaterial depends on moisture content. Various models are proposed
to correlate the moisture dependency of densities. Table 7 summarizes selected correlations
from literature.
Table 7. Moisture content dependency of the densities of selected agriculture products
D e n s ity
Bulk, d
e n s ity
M
Pbp
C o rre la tio n
a te r ia l
a lf a lf a
PbP = P „
pb =
apple
Bulk d
+- e x
p (C X )
g a r lic
Pb = A + BX + CX2
o n io n
p b = A + B X + C X 2 +• DX;
fr u its
&
.
0
x
_
fn X )
w o o d
o n io n
x ..
{
*
o
J
Pb = A +■BX'
Schmalko et al.. 1997
p „ = A + BX
Rapusas and Driscoll.
1995
Lozano et al.. 1983
Pp
fr u its
&
Rapusas and Dnscolt.
1995
Lozano etal.. 1983
D
H -C -e x p
d e n s ity
Wang and Brennan.
t995
Madamba et al.. 1994
pb = A + B e x p (c X : )
v e g e ta b le s
P a n ic le
Patil and Sokhansanj.
1995
Lozano et al.. 1980
-e x p (A X )
p o ta to
e n s ity
Pb
A
R e fe re n c e
Pp= A + B| - . c - e* p | D | - ]
v e g e ta b le s
s ta rc h
pp = A + B X + CX2 + DX5 + EX*
Marousis and
Saravacos. 1990
Porosity
Porosity is an important structural property. It is related to functional properties such as
rate of rehydration, water uptake during rehydration, adsorption and absorption, diffusion
coefficient, and catalytic properties (Karathanos et al., 1996). A summary of the methods used
48
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to determine porosity and related properties, such as pore size distribution and specific surface
area was given by Karathanos et al. (1996). Some recently developed techniques include:
Ni adsorption (Hager, et al.. 1997).
HPLC determination of pore distribution (Grunwald et al.. 1990).
NMR for void volume measurement (Perkins et al.. 1997), and
inverse size-exclusion chromatography (ISEC) method (Berthold and Salmen. 1997).
Porosity £ used in drying quality evaluation can be evaluated by
£•=
Ya
= £ i ~ PJL
V,+VwW t
ph
= i
-E
(10)
jl
ph
Porosity £. as defined in Eq. (10). is often used for fruits and vegetables, or for other
materials for which internal structure changes during processing are important. Porosity such
defined is also called internal or particle porosity because it refers to the porosity of individual
panicles (Madamba et al.. 1994). Eq. (10) can be used to obtain product porosity change in
drying tests using bulk and particle density data.
On the other hand, porosity used by research scientists in the field of soil, chemical
engineering, and petroleum engineering where moisture transport in unsaturated porous media
is the main concern is defined as
e' =
V +V
V.+V.+V
— ---- —
( I I)
The porosity used in researches of grains and legumes is defined differently. According
to Thompson and Issacs (1967). the porosity for grains and legumes is the space in the bulk
grain which is not occupied by the grain itself. This definition is widely used as a physical
property of grains and legumes. The correlations for moisture dependent porosity for selected
biomaterials are listed in Table 8.
49
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Table 8. The moisture content dependency of porosity for different materials
M
e =
w h e a t, c a n o la
p u m p k in
c u m in
A
+
B X + C X 2
+ B X
0 .0 7 -0 .2 2
A + B e x p ( C X )
D
o n io n
L a n g
E — A
£ =
e t a l..
L 9 9 4
J o s h i e t a l..
1 9 9 3
S in g h
a n d
G o s w a m i.
L o z a n o
1 .5 -7 .4 5
e t a l..
1 9 9 6
1 9 8 0
■e x p ( E X ) - r F • e x p ( G X )
+
B X
r
D X '
X
A
+
(
B —
+ C
X 0
(w o o d )
R e fe re n c e
0 .0 4 - 0 .4
£ = A
a p p le
p o ta to
' r a n s e
0 .1 7 - 0 .2 7
s e e d
s e e d
v e rb a m a te
X
C o rre la tio n
a te r ia l
E =
A
+
U .0 6 - 4 .U
X
U
0 .0 5 -
T
—
1
o
R a p u s a s
a n d
D r ts c o ll.
M
a n d
M
c M
in n
a g e e .
1 9 9 5
1 9 9 7 b
fre s h *
J
B X
0 .0 - 1 .5
S c h m a lk o
e t a l..
1 9 9 7
* moisture content for fresh potato
Shrinkage
During the course of drying, the volume of a bioproduct is reduced as a resuit of
moisture removal. The corresponding internal structural changes may include the contraction or
collapse of the porous matrix and the development of stresses and strains. Serious shrinkage
can cause formation of cracks in the product. Shrinkage also reduces heat and mass transfer
rates during drying (Ratti. 1994). and may significantly affect the quality of dried product
(Achanta and Okos. 1995). One explanation for shrinkage given by Achanta and Okos (1995)
stated that the biopolymers cannot support their weight and collapse under gravitational force
when moisture is removed. Another explanation by Lefeuvre et al. (1990) postulated that
internal forces formed due to constraints and nonuniform moisture, the temperature distribution
inside the sample, together with the internal friction during deformation, were the determinant
factors for the shrinkage behavior of a material. Shrinkage and the glass transition temperature
Tg are related. Shrinkage mainly develops in the rubbery state while in the glassy state, when
temperature is lower than Tg. shrinkage is hindered (Achanta and Okos. 1995).
Shrinkage can be characterized in terms of unidimensional, surface, and volumetric
reductions. Unidimensional shrinkage can be measured with calipers (Mate et al., 1998: Ratti.
1994) or magnetic displacement sensors (Lefeuvre et al.. 1990). Surface reduction can be
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
monitored by photographic methods (Suzuki et al., 1976). Volume reduction can be determined
by different displacement methods (Ratti. 1994: Sjoholm and Gekas. 1995).
In the literature, shrinkage of a biomaterial is related to moisture content. A common
assumption is that the volume reduction relates linearly to the moisture content. However,
numerous tests resulted in a non-linear shrinkage versus water content relationship, especially
in the low moisture content range (Lozano et al.. 1983: Jomaa and Puiggali. 1991: Tang and
Sokhansanj, 1993: Ratti. 1994: Madamba et al.. 1994: Wang and Brennan. 1995: Feng and
Tang. 1998). Patil and Sokhansanj (1995) noticed that the linear correlation was only suitable
for small volume changes. Besides moisture content, drying rate (Lefeuvre et al.. 1990). air
velocity (Ratti, 1994), and air temperature and air humidity (Lang et al.. 1994) also influence
shrinkage.
A summary
is wgiven in Table 9.
w
* of the correlations of shrinkage
w
Table 9. The shrinkage correlations for different bio-materials
Material(s)
Correlation
X'range
Reference
soybean
V/V„ =■I + AX
0.09-0.25
Deshpande et al.. 1993
lentil
V/V„ = expl-A(X„-X)j
0.05-0.24
Tang and Sokhansanj. 1993
green alfalfa
V/V„ = exp(-AX)
NA
Patil and Sokhansanj. 1995
carrot, potato, sweet
V X+A
VH X* + A
NA
Suzuki et al.. 1976
<7.45
Lozano etal.. 1980
NA
Simaletal.. 1994
apple
0.02- 1.7
Sjoholm and Gekas. 1995
potato
0.2 - 1.0
Khraisheh et al.. 1997
NA
Lozano etal.. 1983
03-5.0
Jomaa and Puiggali. 1991
potato, radish
apple
potato
pear, carrot, potato,
V/V„ = A+BX
sweet potato, garlic
V =A+B----, D X 1- C
r •exp(------)
D
—
V„
X,
X+E
NA
V
A(l+X)
Va B+CX +D •exp(£+FX 2j
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 9. The shrinkage correlations for different bio-materials (com.)
X'range
Correlation
Material(s)
potato, carrot, apple
V„
x„ x a
JL = C+D-XVu
xn
x„
X.
Reference
NA
Ratti. 1994
0.5-
McMinn and Magee. 1997b
X„
potato
fresh**
NA
V/V„ = / + AfX - X j
NA
Liu etal.. 1997
potato
AL= A+ BX
0.2-4.0
Wang and Brennan. 1995
0.15-6.5
Feng et al.. 2000
apple
wheat, canola
AL= A + (B+C-RH +D- T)AX
NA
Lang etal.. 1994
mushroom
AL=A + BX+CXZ
NA
Rivaetal.. 1991
carrot
L/Lo = exp(Bt)
NA
Ruiz-Cabrera et al.. 1997
gelatin
AL —Ldrymuter ( I + £ X)
NA
Bonazzi et al.. 1997
*AL: linear shrinkage: NA: not available or not applicable; A. B, C. D and E are constants: e is
the linear shrinkage coefficient. ** see Table 8.
Shrinkage of fruits and vegetables can also be obtained from experimental data for
density and moisture content (Saca and Lozano. 1992; Wang and Brennan. 1995). They state
V __ p ^ j l + X ) _ W
Vu pb(l+X„) pbV„
where W and pb are sample weight and bulk density at time t. pbo, X„v and V0 are the bulk
density, the moisture content, and the volume of the fresh fruits and vegetables (at t = 0).
Rehydration capacity
Rehydration capacity of a dehydrated product is an important quality attribute. It
provides a good indication as to whether the various processing conditions were correctly
applied (Somogyi and Luh. 1975). During the drying process, the bio-matrix of the material
52
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may be irreversibly damaged to various degrees. This may include a loss of the elasticity of cell
walls, a reduced swelling ability of starch gel. loss of the osmotic properties of cell walls,
coagulation of the protoplasmic proteins (Gane and Wager. 1958). and destruction of
membranes and structural proteins, which are capable of forming gels by enclosing water in a
three-dimensional network of protein chains (Brooks. 1958). Rehydration ability is then a
measure for the severity of the destruction caused by drying.
Rehydration tests are conducted by submerging dehydrated products in water or other
liquids at designated temperature(s) for a selected time. The conditions used in rehydration tests
could be a combination of the following:
•rehydration temperature T:
T = boiling point (BP) (Sullivan et al.. 1980: Yang and Atallah. 1985)
T = room temperature (Riva et al.. 1991: Szentmarjay et al.. 1996)
room temperature < T < BP (Moreno-Perez et al.. 1996: Gothendapani et al.. 1997)
•rehydration pressure P:
atmospheric pressure (used by most researchers)
vacuum (Yang and Atallah. 1985)
•draining method: (Loch-Bonazzi et al.. 1992; Prabhanjan et al.. 1995)
drained on metal sieve or filter paper, by gravity or applying gentle suction
These methods have been developed based on the end-use of the dehydrated products.
For example, if used for soup mix. water at boiling temperature is used, whereas, for breakfast
cereal products, water at room or refrigeration temperature may be used. Different methods for
the rehydration evaluation have been proposed in literature. There seems to be no generally
recognized method and confusion may arise from some of the methods used. A collection of the
major approaches for rehydration evaluation is given in Table 10 and a concise analysis is given
thereafter.
hi a reconstitution test, the mass exchange between the rehydrated dry sample and the
pool of water can be analyzed by defining
53
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M0 = insoluble solid + soluble solid(l) + water0
Mdh = insoluble solid +- soluble soIid( I ) + waterdh
(13)
Mth = insoluble solid + soluble solid(2) + waterdh + waterw ^ ^
where M is mass of the sample; the subscripts "o". ”dh”. and ’Th” represent the initial state
before drying, the dehydrated state, and the rehydrated state of the sample, respectively. During
rehydration, part of the soluble solid in the sample, such as sugar, is dissolved in the water pool
while the sample takes up water. The soluble solid (2) is then smaller than the soluble solid ( I).
The water removed during drying is evaluated by
water removed
= Mo - Mdh = water0 - waterdh
(14)
= Xo-Mo - Xdh’Mdh
where Xo and Xdh are the wet basis initial moisture content and the moisture content after
drying, respectively.
The water regained during rehydration is given by
water regained
= Md, - Mdh + soluble solid ( I) - soluble solid (2)
54
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(15)
Table 10. Evaluation methods for rehydration ability
Notation
coefficient o f rehydration
(COR) ’
Formula
Mn M j l- X „ )
M„ M j l - X j
R eference(s)
Van Arsdel. 1963
Jayaramen et al.. 1990
Prahanjan et at.. 1995
McMinn & Masee. 1997a
rehydration ratio( I)
(RR)
water regained
dry matter
Sullivan et al.. 1980
Yang & Atallah. 1985
Saca &. Lozanc. 1992
rehydration ratio(2)
(RR)
Prabhanjan et al.. 1995
Cai and Chang. 1997
McMinn and Magee. 1997a
rehydration ratio( 3)
(RR)
rehydration capacity
(R O
rehydration
water regained(t)
water regained(«>)
water regained
water removed
Ertekin and Cakatoz. 1996
Loch-Bonazzi et al.. 1992
Feng & Tang. 1998
x*
Szentmaijay et al.. 1996
water regained
rehydration coefficient
Moreno-Perez et al.. 1996
Different rehydration evaluation methods are usually based on the water regained or the
rehvdrated sample mass compared with a reference. The reference could be the dry matter, the
water removed, or the dehydrated sample mass. Because the dehydrated sample mass includes
residual water, it is inconvenient in practice to compare samples from different batches and
from different manufacturers because of the difference in residual water content. The dry matter
reference is independent of residual water, but its physical meaning is not well defined and
therefore its value is not very indicative. In contrast, rehydration capacity, defined as the water
regained during rehydration versus water removed during drying, is a clearly defined parameter.
It indicates the capacity of a dehydrated product to regain its lost water, and therefore indicates
the extent to which product's original structure has been damaged during drying. A rehydration
capacity of about unity means a nearly total recovery of the product's water holding capacity
and. hence, a superior quality retention. However the water regained is difficult to evaluate
55
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using Eq. (15) because solid leaching is difficult to estimate. In practice, the solid loss during
rehydration is usually negligible. Thus, the rehydration capacity (RC) can be evaluated by
water regained _ M rk- M
water removed M „—M ^
(16)
In many cases, the weight of a sample before drying (M0) is unknown, but the initial
moisture content of the product can be estimated from literature data. The rehydration capacity
is then calculated by using moisture content as
where X' is the moisture content on a dry basis (g water/g dry matter). Rehydration capacity of
a dried product can be related to structural parameters. Yang and Atallah (1985) proposed a
linear relationship between the rehydration ratio and bulk density pbP which is given as:
(18)
R R = A + Bpbp
Rehydration kinetics were investigated by Garcfa-Reverter et al. (1994) and McMinn
and Magee ( 1997c). The model proposed by Garcfa-Reverter et al. is:
(19)
where X’ is moisture content (dry basis), subscripts i and e represent initial moisture content for
dehydrated sample and equilibrium moisture content, respectively. Eq. (19) takes a similar form
as the drying model, implying comparable kinetics for both adsorption and desorption. The
model suggested by McMinn and Magee correlates the rehydration ratio to rehydration time
with the following:
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
RR
=
A + Bt + C t '
(
20)
A. B and C in Eqs 18. 19. and 20 are constants.
Color
Without pretreatment, most fruits and vegetables suffer significant discoloration during
drying due to non-enzymatic browning. Some grain products, such as lentils, are also evaluated
during drying by examination of color. Therefore, color measurement is an important means of
assessing the quality of food products. Color change during drying not only characterizes the
degree of the quality degradation but affects consumer acceptance of the product as well.
Color is the human perception of the reflected light from an object. The external color
of dried products is a manifestation of the internal changes that occurred during drying, which
may include physical and chemical changes that alter either the surface reflection or the surface
light absorption characteristics of the products.
Color is a three-dimensional entity. Different color systems are utilized to describe the
color changes. The Hunter Lab and CIE L*a*b* are among the most widely used (Shewfelt and
Prussia. 1993). These scales quantify the degrees of lightness (L*). redness or greenness (+/a*), and yellowness or blueness (+/- b*). The L*a*b* values of a product can be measured with
colorimeters. Because humans perceive color in terms of lightness, hue. and chroma by the
integration of some very complex signals, different methods are used to convert from the
machine language, the L*. a*, and b* readings, to functions which model human color
perception. The functions often used are summarized in Table 11.
Texture
Texture is an important aspect of food quality, sometimes even more important than
flavor and color (deMan. 1990). Textural data are also useful in the design of processing,
handling, packaging, and storage systems. The texture of a dried product is determined by its
chemical composition and physical structure. Texture evaluations are usually conducted by
57
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mechanical tests or by sensory analysis. A widely used classification of textural characteristics
was given by Szczesniak (1963) as shown in Table 12.
Table 11. Color functions used in literature to model human color perception
Function
Description
Reference(s)
Hue angle: tan'l(b/a)
color name such as red. blue, or green
used in much
literature
Chromat C): (a* +■b*)l/_
brightness or saturation
same as above
Total color difference (AE)
total amount of color change
same as above
amount of change in hue
HunterLab
correlates well with visual
Kostaropoulos and
observations
Saravacos. 1995
ratio: a/b
indication of darkness
Tulasidas et al.. 1995
white index(WI):
color change with reference to white
Lopez-Malo et al..
100 - [(L - Lo)2+ a2 +• b2]I/2
(Lo = 92.89 for white)
1997
(L-Lo)/ Lo or (a-ao)/ao or
color change
Robbers et al.. 1997
(b*bo)/bo
Lo. ao. and bo as reference color
[(L - Lo)' + (a - ao)~ + (b - fao)—
]1/2
Hue difference(AH):
[AE2+ (L-L0r + (C-Co)I],c
ratio: L/(a/b)
58
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Table 12. Classification of texture characteristics
Mechanical characteristics
Primary parameters
hardness
cohesiveness
viscosity
elasticity
adhesiveness
Geometrical characteristics
Class
particle size & shape
particle shape & orientation
Other characteristics
Primary parameters
moisture content
fat content
Secondary parameters
brittleness
chewiness
gummiess
Popular terms
soft—»firm—>hard
crumbly—»crunchy—»brittle
tender-*chewy—»tough
short—mealy—»pastv—»gummy
thin—^viscous
plastic—^elastic
stickv—Hackv—>20 oev
Examples
gritty, grainy, coarse, etc.
fibrous, cellular, crystalline, etc.
Secondary parameters
oiliness
greasiness
Popular terms
drv—»moist—>wet—»waterv
oily
greasy
FINAL REMARKS
Quality degradation during drying is inevitable. High quality or less degradation can be
achieved by a thorough understanding of the interaction between the kinetics of quality loss and
the rate of the moisture loss during the course of the dehydration. Quality evaluation can be
conducted based on the physical attributes summarized in this article. It can also be evaluated
by chemical and microbial analyses such as an estimation of vitamin loss. The physically
orientated quality attributes are more popular since they are. in many applications, not only
required product characteristics, but also serve as an overall indication of the quality change in
products as moisture is removed. The methods used in quality evaluation, however, must be
clearly understood and standardized so that a common language can be used to quantify the
quality changes in a specific drying technique. Standardization will also benefit the research,
development, and evaluation of new drying techniques.
59
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REFERENCES
1. AACC. 1983. AACC Approved Method. 44-15A. 8th ed. Minneapolis. MN: American
Association of Cereal Chemists. Inc.
2. Achanta, S. and Okos, M.R. 1995. Impact of drying on biological product quality, in Food
Preservation by Moisture Control, Fundamentals and Applications, (ed.) G.V. BarbosaCanovas and J. Welti-Chanes. (ed.). Technomic Publishing Co.. Inc.. Lancaster. PA.
3. AOCS. 1984. Official and tentative methods.
4. ASAE Standards. 1990. 37Ul ed. 1990. S358.2. S353. S4I0.1. S487. and S352.2. MI.
ASAE.
5. AO AC. 1990. Official Methods o f Analysis. Washington. DC. Official Analytical Chemists.
6. Berthold, J. and Salmen, L. 1997. Effects of mechanical and chemical treatments on the
pore-size distribution in wood pulps examined by inverse size-exclusion chromatography. J.
o f Pulp and Paper Sci.. 23. p245.
7. Bimbenet, J.J. and Lebert, A. 1992. Food drying and quality interactions. In Drying '92.
(ed.) A.S. Mujumdar. Elsevier Science Publishers. London - New York. pp42-57.
8. Bonazzi, C., Ripoche, A. and Michon, C. 1997. Moisture diffusion in gelatin slabs by
modeling drying kinetics. Drying Technol.. 15(6-8). pp2045-2059.
9. Bouraoui, M., Richard, P. and Durance, T. 1994. Microwave and convective drying of
potato slices. J. Food Processing Eng.. 17. pp353-363.
10. Brooks, J. 1958. Structure of animal tissues and dehydration. In Fimdamental Aspects of
the Dehydration o f Foodstuffs. Soc. Chem. Ind.. pp8-I3.
11. Bruin, S. and Luyben, K. Ch. A. M. 1980. Drying of food materials: a review of recent
developments, hi Advances in Drying, 1980. (ed.) A.S. Mujumdar.
12. Cai, T.D. and Chang, K.C. 1997. Processing to improve quality of dehydrated precooked
pinto beans. J. Food Sci.. 62. pp 141-144.
13. Chiang, W.C. and J.N. Petersen. 1987. Experimental Measurement of Temperature and
Moisture Profiles During Apple Drying. Drying Technol. 5. pp2549.
14. Chou, H. and Breene, W.M. 1972. Oxidation decoloration of p-carotene in low-moisture
model systems, /, Food Sci., 37, pp66-
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15. Christensen, CJVL 1974. Storage o f Cereal Grains and Their Products. Minneapolis. MN:
American Association of Cereal Chemists. Inc.
16. Copley, M.J. and Van Arsdel, WJB. 1964. Food Dehydration, v.2. Products and
Technology. Avi Pub. Co.. Westport. Connecticut.
17. deMan, JJVI. 1990. Principles o f food chemistry, Van Nostrand Reinhold. New York.
18. Deshpande, S.D., Bal, S. and Ojhaz. T.P. 1993. Physical properties of soybean. J. Agric.
Eng. Res.. 56. pp89-98.
19. Diamente, L.M., Munro, P.A. and Weeks, M.G. 1993. Volume, porosity and moisture
distribution changes during the drying of rennet. lactic and mineral acid casein particles.
Trans IChemE. 71. Part C. pp33-39.
20. Donsi, G., Ferrari, G. and Nigro, R. 1996. The effect of process conditions on the
physical structure of dehydrated foods: An experimental analysis. Trans IChemE. 74. Part
C. pp73-80.
21. Eicher, K., Laible, R. and Wolf, W. 1985. The influence of water content and temperature
on the formation of Maillard reaction intermediates during drying of plant products. In
Properties o f Water in Foods. Simato. D. and Multon. J.L. (Ed.). Martinus Nijhoff
Publishers, Dordrecht. The Netherlands.
22. Ertekln, F.K, and Cakaloz, T. 1996. Osmotic dehydration of peas H. Influence of osmosis
on drying behavior and product quality. /. Food Processing and Preservation. 20. ppl05119.
23. Fellows, P. 1988. Food Processing Technology. Ellis Horwood Ltd.. Chichester. England.
24. Feng H. and Tang, J. 1997. Unpublished data.
25. Feng H. and Tang, J. 1998. Microwave finish drying of diced apples in a spouted bed. J.
Food Sci.. 63(4), pp679-683.
26. Feng, H., Tang, J. and Dixon-Warren, St J. 2000. Determination of moisture diffusivity
of Red Delicious apple tissues by thermogravimetric analysis”. Drying Technology. 18(5).
27. Franzen, K., Singh, R.K. and Okos, M.R. 1990. Kinetics of nonenzymatic browning in
dried skim milk, J. Food Eng.. 11, pp225-239.
28. Garcfa-Reverter, J., Bourne, M.C. and Mulet, A. 1994. Low temperature blanching
affects firmness and rehydration of dried cauliflower florets, J. Food Sci.. 59. pp 118 l-l 183
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29. Gane, R. and Wager, H.G. 1958. Plant structure and dehydration. In Fundamental Aspects
o f the Dehydration o f Foodstuffs. Soc. Chem. Ind., pp3-7.
30. Garcia, R., Leal, F. and Rolz, C. 1988. Drying of bananas using microwave and air ovens.
Int. J. Food Sci. & Technol., 23, pp81-90.
31. Giese, J. 1995. Measuring physical properties of foods. Food Technol. Feb.. pp54-63.
32. Gong, L. and Plumb, O. A. 1994. The Effect of Heterogeneity on Wood Drying. Part H:
Experimental Results. Drying Technology. 12(8). pp2003-2026.
33. Gothandapani, L., Parvathl, K. and Kennedy, Z.J. 1997. Evaluation of different
methods of drying on the quality of oyster mushroom (Pleurotus sp). Drying Technol.. 15(68). pp 1995-2004.
34. Grunwald, M., Burtscher, E. and Bobleter, O. 1990. HPLC determination of the pore
distribution and chromatographic properties of cellulosic textile materials. J. Applied
Polymer Sci.. 39(2), pp301 -317.
35. Harger, J., Hermansson, M. and Wimmerstedt, R. 1997. Modeling steam drying of a
porous ceramic sphere: experiments and simulations. Chem. Eng. Sci.. 52(8). pp 1253-1264.
36. Hart, J.R., Feinstein, L. and Goiumbic, C. 1959. Oven methods for precise measurement
of moisture in seeds. In USDA Marketing Research Report No.304. Washington. DC: U.S.
GPO.
37. Hendel, C.E., Silveira, V.G. and Harrington, W.O. 1955. Rates of nonenzymatic
browning of white potato during dehydration. Food Technol.. Sep.. pp433-438.
38. Jayaraman, K.S., Gupta, D.K.D. and Rao, N.B. 1990. Effect of pretreatment with salt
and sucrose on the quality and stability of dehydrated cauliflower. Int. J. Food Sci.
Technol.. 25, pp47-60.
39. Jayaraman, K.S. and Gupta, D.K.D. 1995. Drying of fruits and vegetables. In Handbook
o f Industrial Drying, (ed.) A.S. Mujumdar. Marcel Dekker. Inc., New York.
40. Jomaa, W. and Puiggall, J.R. 1991. Drying of shrinking materials: modeling with
shrinkage velocity,Drying Technol.. 9(5). ppl27l-I293.
41. Joshi, D.C., Das, S.K. and Mukherjee, R.K. 1993. Physical properties of pumpkin seeds.
/. Agric. Eng. Res.. 54, pp219-229.
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42. Karathanos, V.T. and Kostaropoulos, A.E.. 1995. Air-drying kinetics of osmoticaliy
dehydrated fruits. Drying Technol., 13(5-7), ppI503-152I.
43. Karathanos, V.T., Maroulis, Z.B., Marinos-Kouds, D. and Saravacos, D.G. 1996.
Hygrothermal and quality properties applicable to drying. Data sources and measurement
techniques. Drying Technol.. 14(6), ppL403-l4I8.
44. Karel, M. and Nickerson, J.TJR. 1964. Effects of relative humidity, air. and vacuum on
browning of dehydrated orange juice. Food Technol.. 18. pp 10445. Karel, M. 1991. Physical structure and quality of dehydrated foods. In Drying '91. ted.)
A.S. Mujumdar and I. Filkova. Elsevier Science Publishers. Amsterdam.. pp27-35.
46. Ketelaars, A.A J., Pel, L„ Coumans, W J . and Kerkhof, PJ.A.M. 1997. Drying kinetics:
a comparison of diffusion coefficients from moisture concentration profiles and drying
curves. Chem. Eng. Sci.. 50, pp 1187-1191.
47. Khraisheh, M.A.M., Cooper, T J.R . and Magee, T.R.A, 1997. Shrinkage characteristics
of potatoes dehydrated under combined microwave and convective air conditions. Drying
Technol.. 15(3&4). ppI003-I022.
48. Kilic. M., Muthukumarappan, K. and Gunasekaran, S. 1997. Kinetics of nonenzymatic
browning in cheddar cheese powder during storage. /. Food Processing and Preservation.
21.pp379-393.
49. Kim, M.H. and Toledo, R.T. 1987. Effect of osmotic dehydration and high temperature
fluidized bed drying on properties of dehydrated rabbiteye blueberries. J. Food Sci.. 52.
pp980-989.
50. Kostaropoulos, AJL and Saravacos, G.D. 1995. Microwave pre-treatment for sun-dried
raisins. J. Food Sci.. 60. pp344-347.
51.Labuza, T.P. 1970. Properties of water as related to the keeping quality of foods. In
Proceedings o f the Third International Congress on Food Science and Technology, Institute
of Food Technologists. Chicago. IL.. pp6I8.
52. Labuza, T.P. and Saltmarch, M. 1981. The nonenzymatic browning reaction as affected
by water in foods, hi Water Activities: Influence on Food Quality. Rockland. L.B. and
Stewart, G P . (Ed.). Academic Press, New York.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53. Lang, W., Sokhansanj, S. and Rohani, S. 1994. Dynamic shrinkage and variable
parameters in bakker-arkema’s mathematical simulation of wheat and canola drying. Drying
Technol.. 12(7), ppI687-I708.
54. Lee, Y.C., Kirk, J.R., Bedford, CX. and Heldman, D.R. 1977. Kinetics and computer
simulation of ascorbic acid stability of tomato juice as function of temperature. pH and
metal catalyst. J. Food Sci.. 42, pp64055. Lefeuvre, S., Sadeghi, Me, Majdabadino, M. and Audhuy, M. 1990. Shrinkage of
porous materials during microwave drying, Drying Technol.. 8(5). pp 1049-1060.
56. Lenart, A. 1996. Osmo-convective drying of fruits and vegetables: technology and
application. Drying Technol.. 14(2), pp391-413.
57. Liu, H., Zhou, L. and Hayakawa. K. 1997. Sensitivity analysis for hvgrostress crack
formation in cylindrical food during drying, J. Food Sci.. 62(3). pp447-450.
58. Loch-Bonazzi, C X ., Wolff, E. and Gilbert, H. 1992. Quality of dehydrated cultivated
mushrooms (Agaricus bisporus): a comparison between different drying and freeze-drying
processes. Lebensm.~Wiss. U.-Technol.. 25. pp334-339.
59. Lopez, A., Pique, M.T., Boatella, X, Romero, A., Ferran, A. and Garcia, J. 1997.
Influence of drying condition on the hazelnut quality: HI. Browning, Drying Technol..
15(3&4). pp989-I002.
60. Lopez-Malo, A., Palou, E., Welti, J., Corte, P. and Argalz, A. 1997. Moisture sorption
characteristics of blanched and osmotically treated apples and paravas. Drying Technol..
I5(3&4), ppl 173-1185.
61. Lozano, J.E., Rotstein, E. and Urbicain, MX. 1980. Total porosity and open-pore
porosity in the drying of fruits. J. Food Sci.. 45. pp 1403-1407.
62. Lozano, J.E., Rotstein, E. and Urbicain, MX. 1983. Shrinkage, porosity and bulk density
of foodstuffs at changing moisture content. J. Food Sci.. 48, ppI497-I502.
63. Luyben, K.Ch.A.M., Liou, J.K. and Bruin, S. 1979. Enzyme degradation during drying
processes. In Food Process Engineering, Vol. 2, (ed.) P. Linko and J. Larinkari, Applied
Science Publishers Ltd., London, pp 192-209.
64. Madamba, P.S., Driscoll, R.H. and Buckle, K.A. 1994. Shrinkage, density and porosity of
garlic during drying, J. Food Eng.. 23, pp309-319.
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65. Marousis, S.N. and Saravacos. G.D. 1990. Density and porosity in drying starch materials.
J. Food Sci.. 55, pp 1367-1372.
66. Mate, JJ., Quartaert, C., Meerdink, G. and van’t Riet, K. 1998. Effect of blanching on
structure quality of dried potato slices. J. Agric. Food Chem.. 46. pp676-681.
67. McMinn, W.A.M. and Magee, T.R.A. 1997 (a). Quality and physical structure of a
dehydrated starch-based system. Drying Technol. 16(6-8), pp 1961- 1971.
68. McMinn, W.A.M. and Magee, T.R.A. 1997 (b). Physical characteristics of dehydrated
potatoes - part L J. Food Eng.. 33. pp37-48.
69. McMinn, W.A.M. and Magee, T.R.A. 1997 (c). Physical characteristics of dehydrated
potatoes - part II. J. Food Eng.. 33, pp49-55.
70. Mizrahi, S., Labuza, T.P. and Karel, M. 1970. Computer-aided predictions of extent of
browning in dehydrated cabbage, J. Food Sci.. 35. pp799-803.
71. Mohsenin, N.N. 1970. Physical Properties o f Plant and Animal Materials. Gordon and
Breach Science Publishers. New York.
72. Moreno-Perez, L.F., Gasson-Lara, J.H. and Ortega-Rivas. E. 1996. Effect of low
temperature-long time blanching on quality of dried sweet potato. Drying Technol.. 14
(7&8), pp 1839-1857.
73. Muller, K. and Bauer. W. 1990. Detection and Kinetics of Chemical Reaction During
Drying of Foods. MacCarthy. D. (Ed.). Elsevier Applied Sci. Publ.. London-New York.
74. Patil, R.T. and Sokhansanj, S. 1995. Physical and nutritional changes in green alfalfa
during high temperature drying. ASAE paper No. 95-5639.
75. Pel, L. and Brocken, H. 1996. Determination of moisture diffusivity in porous media using
moisture concentration profiles. Int. J. Heat Mass Transfer. 39. pp 1273-1280.
76. Perkins, T.W ., Roots, T.W. and Lightfoot, E.N. 1997. Measuring column void volumes
with NMR, Analytical Chemistry. 69( 16), pp3293-3298.
77. Pomeranz, Y. and Meloan, CJL 1994. Food Analysis, Theory and Practice. Chapman &
Hall. New York.
78. Prabhanjan, D.G., Ramaswamy, H.S. and Raghavan, G.S.V. 1995. Microwave-assisted
convective air drying of thin layer carrots. J. Food Eng.. 25, pp283-293.
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79. Quintero-Fuentes, X., Ahneida-Dominguez, H.D. and Rooney, L.W. 1997. Evaluation
of the structure and texture quality of baked chips, EFT97 paper 59A-20, Institute of Food
Technologists, Annual Meeting, June 14-18, 1997. Orlando. Florida.
80. Rapusas, R.S. and Driscoll, R.H. 1995. Thermophysical properties of fresh and dried
white onion slices. /. Food Eng., 24, ppI49-I64.
8 1. Rattl, C. 1994. Shrinkage during drying of foodstuffs. J. Food Eng.. 23. pp91-105.
82. Resnick, S. and Chirife, G. 1979. Effect of moisture content and temperature on some
aspects of nonenzymatic browning in dehydrated apple. J. Food Sci.. 44. pp60l-605.
83. Riva, M., Schiraldi, A. and Di Cesare. L.F. 1991. Drying of agaricus bisporus mushrooms
by microwave-hot air combination. Lebensm.-Wiss. U.--Technol.. 24(6). pp479-483.
84. Robbers, M., Singh, R. and Cunha, L.M. 1997. Osmotic-convective dehvdrofreezing
process for drying kiwifruit. J. Food Sci.. 62. pp 1039-1047.
85. Ruan, R., Schmidt, S J ., Schmidt, A.R. and Litchfield, J.B. 1991. Nondestructive
measurement of transient moisture profiles and the moisture diffusion coefficient in a potato
during drying and absorption by NMR imaging. J. Food Processing Eng.. 14. pp297-313.
86. Ruiz-Cabrera, M.A., Salgado-Cervantes, M.A., Waliszewski-Kubiak, K.N. and
Garcia-Alvarado, M.A. 1997. The effect of path diffusion on the effective moisture
diffusivity in carrot slabs. Drying Technol.. 15(1), ppI69-l8I.
87. Saca, S.A. and Lozana, J.E. 1992. Explosion puffing of bananas. Int. J. Food Sci. &
Technol.. 27, pp419-426.
88. Saguy, I., Mizrahi, S., Villota, R. and Karel, M. 1978. Accelerated method for
determining the kinetic model of quality deterioration during dehydration. J. Food Sci.. 43.
ppI86I89. Saguy, I. and Karel, M. 1980. Modeling of quality deterioration during food processing
and storage. Food Technol.. Feb. pp78-85.
90. Salas, F. and Labuza, T.P. 1968. Surface active agents effects on drying characteristics of
model foods systems. Food Technol.. 22. pp80-84.
9l.Samaniego-Esguerra, C.M., Boag, I.F. and Robertson, GX . 1991. Kinetics of quality
deterioration in dried onion and green beans as a function of temperature and water activity,
Lebensm.-Wiss. U.-Technol., 24, pp53-58.
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92. Schmalko, M.E., Morawicki, R.O. and Ramallo, L A . 1997. Simultaneous determination
of specific heat capacity and thermal conductivity using the finite-difference method. /.
Food Eng.. 31. pp531-540.
93. Schmidt, S.J., Sun, X. and Litchfield, JJJ. 1996. Applications of magnetic resonance
imaging in food science. Critical Reviews in Food Sci. and Nutrition. 36. pp357-385.
94. Shewfelt, R X . and Prussia, SJE. 1993. Postharvest Handling: A Systems Approach.
Academic Press. INC.. New York.
95. Simal, S., Rossello, C., Bema, A. and Mulet, A. 1994. Heat and mass transfer model for
potato drying, Chem. Eng. Sci., 49(22), pp3739-3744.
96. Singh, K.K. and Goswami, T.K. 1996. Physical properties of cumin seed. J. Agric. Res..
64. pp93-98.
97. Sjoholm, I. And Gekas, V. 1995. Apple shrinkage upon drying. J. Food Eng.. 25. ppl23130.
98. Sokhansanj, S. and Jayas, D.S. 1995. Drying of foodstuffs. In Handbook o f Industrial
Drying, (ed.) A.S. Mujumdar. Marcel Dekker. Inc.. New York. Miller. P.S. pp589-.
99. Somogyi, L.P. and Luh, B.S. 1975. Dehydration of fruits. In Commercial Fruit
Processing, J. G. Woodroof and B. S. Luh. (ed.), AVI Pub. Co.. Westport, Conn.
100.
Stadtman, E.R., Barker, H A ., Haas, V.A. and Mackinney, G. 1946. Studies on the
storage of dried fruit. HI. The influence of temperature on the deterioration. Ind. Eng.
Chem.. 38. pp324~329.
101.
Stitt, F. 1958. Moisture equilibrium and the determination of water content of
dehydrated foods. In Fundamental Aspects o f the Dehydration o f Foodstuffs. Society of
Chemical Industry. London.
102.
Strumillo, C., Zbicinski, I. and Lui, X.D. 1994. Drying of thermosensitive materials in
a vibrofluidized bed dryer. In Proc. S'* Polish Drying Svmp., June 19-22, Warsaw. Poland.
2, pp306-314.
103.
Strumillo, C., Zbicinski, I. and Lui, X.D. 1995. Thermal drying of biomaterials with
porous carriers. Drying Technol., 13(6-7), pp 1447-1462.
104.
Strumillo, C. and Adamiec, J. 1996 (a). Energy and quality aspects of food drying.
Drying Technol., 14(2), pp423-448.
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105.
Suarez, C., Londn, M. and Chirefe, J. 1984. A preliminary study on the effect of
ethyl oleate dipping treatment on drying rate of grain com. J. Food Sci.. 49, pp236-238.
106.
Sullivan, J.F., Craig, J.C., Konstance, R.P., Egoville, M J. and Aceto, N.C. 1980.
Continuous explosion-puffing of apples./. Food Sci., 45. pp 1550-1558.
107.
Suzuki, K., Kubota, K., Hasegawa, T. and Hosaka, H. 1976. Shrinkage in
dehydration of root vegetables. /. Food Sci.. 41. pp 1189-1193.
108.
Szczesniak, A.S. 1963. Classification of textural characteristics. /. Food Sci.. 28.
pp385-389.
109.
Szentmarjay, T., Pallai, E. and Regenyi, Zs. 1996. Short-time drying of heat-sensitive
biologically active pulps and pastes. Drying Technol.. 14 (9). pp209I-2l 15.
110.
Tang, J. and Sokhansanj, S. 1993. Geometric changes in lentil seeds caused by drying.
/. Agric. Eng. Res.. 56. pp313-326.
111.
Taoukis, P.S., Labuza, TJP. and Saguy, I.S. 1997. Kinetics of food deterioration and
shelf-life prediction. In Hand Book o f Food Engineering Practice, (ed.) Valentas. KJ..
Rotstein. E. and Singh. R.P.. CRC Press. New York.
112.
Teixelra, A.A., Dixon, J.R., Zahradnik, J.W. and Zinsmeister, E. 1969. Computer
optimization of nutrient retention in the thermal processing of conduction-heated foods.
Food Technol.. 23. pp845-850.
113.
Thompson, R.A. and Issacs, G.W. 1967. Porosity determination of grains and seeds
with air comparison pycnometer. Transactions ASAE. 10. pp693-696.
114.
USDA. 1986. Moisture Handbook. United States Department of Agriculture. Federal
Grain Inspection Service.
115.
Tulasidas, T.N., Raghavan, G.S.V. and Mujumdar, A.S. 1995. Microwave drying of
grapes in a single mode cavity at 2450 MHz-H: quality and energy aspects. Drying Technol..
13(8&9). ppI973-1992.
116.
Van Arsdel, W.B. 1963. Vol. I: Principles, in Food Dehydration, (ed.) W.B. Van
Arsdel and M J. Copley, AVI Publishing Company, Inc., Westport. Connecticut.
117.
Wang, N. and Brennan, J.G. 1995, Changes in structure, density and porosity of
potato during dehydration, /. Food Eng., 24( I), pp6I-76.
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118.
Wolff, E. and Gibert, H. 1990. Atmospheric freeze-drying part I: design, experimental
inverstigation and energy-saving advantages. Drying Technol.. 8(2), pp385-404.
119.
Yang, C.S.T. and Atallah, W A . 1985. Effect of four drying methods on the quality of
intermediate moisture Iowbush blueberries. /. Food Sci.. 50, pp 1233-1237.
120.
Young, J.H. 1991. Moisture. In Instrumentation and Measurement fo r Environmental
Sciences, (ed.) Z. A. Henry, G. C.. Zoerb and G. S.Birth, ML ASAE.
121.
Zogzas, N.P., Maroulis, Z.B. and Marinos-Kouris, D. 1994. Densities, shrinkage and
porosity of some vegetables during air drying. Drying Technol.. 12(7). pp 1653-1666.
122.
Zuckerman, H. and Miltz, J. 1997. Prediction of dough browning in the microwave
oven from temperatures at the susceptor/product interface. Lebensm.-Wiss. U.-Teclmol.. 30.
pp519-524.
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Chapter 3
HEAT AND MASS TRANSPORT MODELING FOR MICROWAVE DRYING OF
HYGROSCOPIC POROUS MEDIA AT LOW AND MEDIUM MOISTURE RANGES
ABSTRACT
In this study, a heat and mass transfer model was developed to simulate microwave and spouted
bed combined drying (MWSB) of a hygroscopic porous material, diced apples. Moisture
transport mechanisms were analyzed by examining the microstructure and possible transport
passages in the material. A total gas pressure equation was introduced to address internal vapor
generation in microwave drying. The resulting governing equations were simplified using a
scaling technique and numerically solved with the finite difference method. An experiment was
designed to measure both the intrinsic and the relative permeability of apples. All the physical,
thermodynamic, thermal, transport, and dielectric properties used in the simulation were for
apples and were either from our measurements or from the literature. Model predictions agreed
well with experimental results. The simulation demonstrated that for medium and low moisture
porous media, a surface moisture accumulation similar to that observed for high moisture, high
microwave power drying can be observed early tn the drying process. The moisture profile in
the apple dices suggested the importance of capillary flow in microwave drying. A temperature
leveling effect was realized both numerically and experimentally. This unique feature in
MWSB drying paves the way for the application of this technique.
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INTRODUCTION
In industrial drying, heat is usually supplied to a product externally by a stream of hot fluid
(air or steam). The temperature gradient is. therefore, established in the opposite direction from
the moisture gradient. The product temperature is limited to that of the heating fluid. Foods,
fruits and vegetables consist of matrixes of biopolymers. The drying of these materials is
further complicated by shrinkage of the materials at the surface after removal of surface
moisture. This phenomenon is commonly referred to as "case hardening''. Case hardening is
characterized by a higher resistance to both heat and mass transfer compared to rest of the
material In order for foods to reach a final moisture low enough to prevent unfavorable
biochemical reactions and microbial growth, either prolonged drying time or high temperatures
must be used. This causes severe quality degradation in dried products. Freeze drying can yield
superior product quality but the high cost limits its application to high value products. Drying
techniques that can produce product with relatively low cost and high quality, therefore, need to
be developed to address this problem.
Electromagnetic waves at frequencies from 300 MHz to 300 GHz. known as microwaves,
have an ability to directly interact with moisture and generate heat volumetrically. This
eliminates the need to transport heat from the case-hardened surface into the wet core where the
heat is needed. Microwave energy has been combined with hot-air drying to shorten drying
time, especially in the falling rate period (Garcia et aL. 1988: Prabhanjan et al.. 1995: Torringa
et al.. 1996). Besides increasing the drying rate and energy efficiency, products dried with this
technique have better quality, mainly due to a substantial reduction in drying time. The
application of microwave drying, however, has been hindered by a major barrier - the uneven
heating that results in a microwave cavity (MuDin. 1995). Efforts have been made to overcome
this problem. For particulate materials, the microwave and spouted bed combined drying
technique (MWSB) has been successfully used to overcome this problem (Feng & Tang. 1998).
Experiments with a heat sensitive product, diced apples, at moisture content of 22.4% (wb),
yielded a uniform and light color in the dried product, showing that uniform heating was
achieved. Temperatures of the products during drying were fairly uniform. Details of the results
were presented elsewhere (Feng and Tang, 1998: Feng et aL. 1999a). The objectives of this
study were to produce a theoretical basis to understand the heat and mass transfer mechanism
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involved in microwave and spouted bed combined drying and to develop a predictive drying
modeL
Many attempts have been made to model microwave drying of different materials. An
extensive review is beyond the scope of this paper. However, a close look at the major
contributions made in the past two decades can provide an insight into the main aspects
involved in the modeling of microwave drying. Microwave drying is accompanied by an
internal vapor generation due to the volumetric heating. As a result, a pressure gradient is
developed during drying (Turner and Jolly, 1991). The moisture transport driven by this gas
pressure gradient makes microwave drying distinctly different from conventional hot-air
drying. Early works conducted by Le Pourhiet et al. (1982). Jolly and Turner (1989). and
Jansen and van der Wekken (1991) used two transport equations to describe the temperature
and moisture fields, without considering the pressure effect. Later. Turner and Jolly (1991)
found that without considering the pressure effect, it is difficult to account for the phenomenon
of “water pumping”. They also realized the importance of the contribution of the gas pressure
to product quality. They introduced a third transport equation, a total gas pressure equation,
into the drying model The importance of the additional driving force due to gaseous pressure
gradient in microwave heating has been well recognized in more recent studies of heat and
mass transfer conducted by Constant et al. (1996), Torringa et al (1996), and Ni et al (1999).
There are a number of physical mechanisms that may be important in a particular drying
application. For a porous medium composed of free water, bound water, vapor, air. and solid
matrix, moisture transport through the solid matrix can be in the form of either diffusion or/and
capillary flow driven by individual or combined effects of moisture, temperature, and total
pressure gradient. Bulk migration of both liquid and vapor due to convection is also possible.
The predominant mechanisms that control the moisture transfer depend on the materials used
(hygroscopic/non-hygroscopic. porous/non-porous), the drying condition, and the way heat is
supplied (external/volumetric). In microwave drying, free water transport has been attributed to
either diffusion (Torringa et aL; 1996: Adu and Otten, 1996) or capillary flow (Constant et al.,
1996: Lian et aL. 1997: Turner et aL. 1998: Ni et aL, 1999). For vapor migration, diffusion
(Lian et aL, 1997), capillary flow (Turner et aL, 1998: Ni et aL. 1999), and capillary and
diffusion (Chen and Schmidt, 1990: Constant et al, 1996) were used by different research
groups as the mechanisms that govern the vapor transport. Few studies considered the
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migration of bound water, even though it is well known that water in medium and low moisture
ranges behaves differently from free water. This is partially due to the fact that most of the
previous studies for microwave drying were for non-hygroscopic materials. A few publications
that discuss bound water migration in microwave heating, however, assumed different
mechanisms. Turner et al. (1998) assumed that bound water transfer was caused by diffusion
while Chen and Pei (1989) employed a capillary mechanism to characterize bound water flow.
The effect of internal convection was studied by Ni et al. (1999).
Previous efforts in developing comprehensive governing equations for drying have often
been hindered by a lack of thermal and transport properties. Capillary pressure, intrinsic
permeability, relative permeabilities, effective moisture diffusivity. bound water diffusivity.
and thermal conductivity are among the important thermal and transport properties needed for a
comprehensive simulation of drying. The temperature or/and moisture dependency of these
parameters is essential to a simulation of practical importance. Unfortunately, for hygroscopicporous materials, data for these properties are often not available, especially for foods and
agricultural products. For example, data for capillary pressure and bound water diffusivity are
not existent for foods and agriculture materials. Permeability data are also absent, except the
single-phase permeability data for bread reported by Goedeken and Tong (1993). In order to
overcome the difficulties, either selected constant values or data for other materials were used
in many previous drying simulations. This weakened the reliability of the conclusions drawn
from those works and made simulations less useful for practical applications. In the case of
microwave drying, the dielectric constant e' and loss factor s" need to be known to evaluate the
microwave penetration depth and the heat generation. They are both functions of moisture and
temperature. Dielectric properties measured as function of temperature and moisture are also
not available for most biomaterials.
A specific problem associated with microwave heating is the nonuniform electromagnetic
field distribution. This creates difficulty in the heat generation analysis since the field is not
uniform at both the product surface and the interior. A precise analysis for the heat generation
should include an electromagnetic analysis by coupling the heat and mass transfer with the
Maxwell equations. However, the electromagnetic problem in the microwave cavity itself is
still a challenge (Constant et aL. 1996). The approaches used in drying literature to address this
problem include (1) assuming a uniform field distribution throughout the sample (Chen and
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Schmidt, 1990: Adu and Otten. 1996): (2) assuming a uniform field at the sample surface and
the decay of the wave in the sample was estimated using the Lambert's law (Wei et al.. 1985:
Tinn et al.. 1997): (3) assuming a uniform field at the surface and the decay of the wave in the
sample was estimated by an empirical equation (Constant et al.. 1996: Ni et aL. 1999): (4)
assuming a
u n if o r m
field at the surface and the power distribution in the sample was obtained
using the Poynting theorem (Constant et aL. 1992: Turner et aL. 1998). The last approach
requires knowledge of local electric field intensity. This was done by solving the electric field
equation under the assumption of a uniform plane wave casting on the sample surface. In many
cases, the sinusoidal traveling electromagnetic waves and their superposition in the drying
cavity discredit the assumptions of both uniform surface field and plane wave.
The objectives of this study were (I) to analyze the moisture transport mechanism in a
cellular material, diced apples, during microwave drying: (2) to develop and experimentally
validate a predictive model for MWSB drying of the hygroscopic porous media (the apples):
(3) to simplify the model using scaling analysis: (4) to determine the permeabilities required in
the simulation. The dielectric property determination is not covered in this paper but in a
separate publication (Feng et aL. 1999b). In this research, efforts were focused not only on
developing a comprehensive MWSB drying model to understand the underlying physics in this
drying process, but also on developing a simulation model considering temperature and/or
moisture dependent thermal and transport properties of the same product. All the thermal,
thermodynamic, physical, transport, and dielectric properties and relations were either from our
measurements or from the existing literature.
MOISTURE TRANSPORT MECHANISM IN CELLULAR MATERIALS
Many foods and agricultural products are cellular materials. In order to understand the
moisture transport mechanism in these materials during microwave drying, it is necessary to
investigate the microstructure of a typical cellular tissue, the status of the water in the tissue,
and possible passages for moisture migration. In the following section, we consider fruits and
vegetables. Three kinds of tissues can be identified in fruits and vegetables: epidermal tissue
which is the outermost layer of cells: parenchymatous tissue, which composes the cells that
produce and store nutritional substance; and vascular tissue, which provides ducting r h a r carries
a solution of mineral and nutrients (Lewicki and Lenart. 1995). All tissues are a collection of
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cells. A typical plant cell and its major components are illustrated in Figure I. Water exists
either in the vacuole, which contains a solution of mineral, sugars, and other organic
compounds or in the protoplasm, a viscous fluid of protein and lipoproteins. The cell wall and
plasmalemma are semipermeable to water. Water can also migrate through plasmodesmata to
neighboring cells.
Plant tissue can be considered as a hygroscopic capillary-porous medium that is divided
internally into numerous repeating units as shown in Figure 2 (Lewicki and Lenart. 1995). The
water in a plant tissue can be classified in accordance with its physicochemical state as ( I )
liquid water existing in the cell (in protoplasm and vacuoles), vascular tissues, and intercellular
spaces. (2) vapor existing in intercellular space and vascular tissues, and (3) constitutive water
bound chemically in cell walls. Obviously, the liquid water that exists within a cell and that in
either vascular tissues or intercellular spaces are different in terms of resistance to migration.
The water inside the cell has to penetrate the cell wall to reach either vascular or intercellular
space. The cellular water in foods is referred to as bound water in the drying literature
(Rotstein. 1986: Chen and Pei. 1989) and water in vascular tissues and intercellular spaces
corresponds to the free water. However, truly free water does not in plant tissue. This is the
reason why no obvious constant rate period can be observed in the drying of fruits and
vegetables (Bruin etaL, 1980).
B 0
Tonoplast
Protoplasm
P lasm odesm ata
x Vacuole
N u c te u s i
\ Intercellular s p a c e
Figure L Cell structure (simplified) (Lewicki and Lenart. 1995).
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Cells
C apillaries
(V a s c u la r tissu e !
P ores
(in te rc e llu la r s p a c e s l
Figure 2. Plant material is a capillary-porous medium (Lewicki and Lenart. 1995).
The intercellular spaces usually form an inter-connected system (Lewicki and Lenart. 1995)
that provides passages for water migration to both the product surface and the vascular tissues.
The possible paths for moisture migration (either liquid or vapor) in plant tissue during drying
may include:
a) from vascular to surface (epidermis or artificial surface)
b) from intercellular space to surface
c) across cell walls to either vascular tissue or intercellular space
d) across cell walls to other cells or from cell to surface
The resistance to water transport increases in the following sequence
d) > c) > b) > or = a)
Transport through plasmodesmata may only be important in the very moist stage. After
that, deformation, shrinkage, and collapse of the cellular structure may block this passage.
Water transport mechanisms through paths a) and b) could be capillary flow due to pressure
differences, molecular diffusion, surface diffusion, and vaporization-condensation sequencing.
Water migration through paths c) and d) could be diffusion. However, when severe shrinkage
or deformation occurs and other passages are partially blocked, transport through path d) m ay
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be the major pathway. It can be seen that bound water transport is important in the drying of
cellular materials because cellular water constitutes a major source of water. Internal vapor
generation during microwave drying can enhance moisture transport in all mechanisms by
creating a pressure gradient to facilitate capillary flow or by increasing diffusivity to enhance
the diffusive flow (Feng et aL. 1999b).
MODEL DEVELOPMENT
Assumptions
Heat. mass, and momentum transport during drying was assumed to take place in a
hygroscopic porous material. The material was considered to be homogeneous, isotropic, and
non-shrinkable on the macroscale. Free water transport is assumed to be governed by the
generalized Darcy's law. which includes the total pressure gradient to account for the
microwave volumetric heating effect. Bound water transport is assumed to be driven by
chemical potential difference (Stanish et aL. 1986: Gong. 1992). Transports in gas phase is
assumed to occur as the result of both convection and diffusion. Other major assumptions are:
1) local thermodynamic equilibrium exists: that is the solid. liquid, and gas phases are at the
same average temperature at any moment in the control volume. This assumption is
supported by the study conducted by Turner and Jolly (1991) in dielectric assisted drying of
brick.
2) solid, liquid, and gas phases are continuous.
3) binary gas mixture of air and vapor obeys the ideal gas law.
4) vapor pressure as a function of moisture content and temperature can be estimated using
sorption isotherms.
5) the model material used in this study, diced apples, can be treated as an equivalent sphere.
6) microwave radiation is uniform over the sphere's surface. This is justified by the uniform
color observed in dried diced apples and the small temperature variations measured during
MWSB drying (Feng and Tang, 1998).
7) electromagnetic field intensity is uniform throughout the apple dice. This can be justified by
comparing the penetration depth of 2450 MHz microwave in diced apples to the size of the
apple dices (5mm in diameter). Penetration depth, is a measure of the decay of microwave
energy when it is traveling into a material. It is defined as the depth from surface to where
77
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the magnitude of the incident microwave decays to 37% ( I/e) of its surface value. For 2450
MHz microwave energy, the penetration depth in the diced apples is 26mm at 25%
moisture content (w.b.) while at 4% moisture content, the penetration depth is 360mm.
Both are significantly larger than the dimension of the apple dice.
The drying governing equations are derived at a macroscopic level. Variables involved in
this study are averaged values over a control volume. This approach was first proposed by
Whitaker (1977) and has been widely used in heat and mass transfer studies relating to drying
of porous media (Bories. 1991).
Transport Relations
Fluid velocity in a multi-phase porous media is given by the generalized Darcy's law:
u
— (w , - P , g h - — {VP, - w . - P , g )
M,
Mr
U
(I)
( 2)
where the capillary pressure. Pc, is defined Pc = Pg - Pf. The application of Darcy's law
requires the fluid to be Newtonian, incompressible, immiscible and with negligible inertial and
viscous effects (Bories. 1991). The introduction of relative permeability krt- and krf takes into
account the competition between the liquid and gas flow inside the capillaries and extends
Darcy's law to unsaturated porous media. For liquid transport, it is assumed that only the free
liquid is governed by Darcy's law (Stanish etaL. 1986).
Diffusive flux of vapor and air is governed by the Pick’s law:
\
(3)
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Fick's law is only valid when the medium's pore size is small compared to the mean
molecular free path so that the medium can be treated as continuous and when the diffusions
due to Soret's effect and pressure diffusion are not important- In drying- the separation of the
air-vapor mixture caused by the Soret's effect and pressure diffusion is very small and can be
ignored (Bories- 1991). The size of intercellular spaces in apples is in the range of 2.6 x 10" to
6.7 x to-1 m while the size of the parenchyma cells is in the range of 6. 7 x 10‘5 to 4.9 x IO'4 m
(Mohsenin. 1986). Hence, the condition for applying Fick’s law is satisfied for apples. It is
suggested that when the pore size is greater than IO'7 m. the interaction between the gas and the
solid matrix is negligible and therefore the Knudsen effect is also not important <Moyne and
Perre. 1991) in this study. In capillary-cellular biomaterials, bound water migration is very'
complex. The bound water flow may take place along very fine capillaries or through the cell
wall. Chen and Pei (1989) pointed out that the bound water transfer cannot be simply defined
as a diffusion process. In this study, a universal driving force, the chemical potential gradient
was considered as the driving force for the bound water flow (Gong. 1992). The bound water
transport is written:
(4)
From the local thermodynamic equilibrium assumption, the chemical potential of bound
water equals to the chemical potential of vapor. Thermodynamic relations for vapor, hence, can
be used to express the bound water flux. Detailed derivation can be found in Stanish et al.
(1986).
Thermal diffusion is controlled by Fourier's law
(5)
In drying problems, the effective thermal conductivity. Xeff. takes into consideration the
conductive heat transfer through the material as well as the increase in heat transfer due to the
local evaporation-condensation mechanism (Moyne and Perre. 1991).
79
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Mass Fluxes
The liquid, vapor, and air fluxes can be written in accordance with their transport
mechanisms as:
Kkn
n = p . u r = - p . VP, = - p
Kkn
V (P .-P )
-
Free water
Mr
(6)
Mr
eVP
Bound water nh = phuh =-Dh(l-e')(----P,
S
—VT)
Mv
t7)
Vapor
^nr
P
nv = p,Mv + j v = - p , ------- VP -p D ^ .V f— )
Me
Me
(8)
Air
Kk„
o
nu = paSa + j a = -p a----- -VP + p ( D „ V n
(9)
Me
Me
Kkrv
n„ =nu +nv = - p . ----------VP
Gas
*
(10)
M e
The transport caused by gravity is ignored in Eq. (6).
Mass Balance
The mass balance equations for free water, bound water, vapor, and air can be written:
Freewaten
BX. „
(l-e )p , ——-+ V -n = -m
dr
(II)
BX
Bound water ( l- e ) p t — —+ V-nh = - m h
dr
Vapor
(12)
3X
(I- £ ) P ' — ±-+Vn^=m + mh
(13)
Of
Air.
dX
( i - e)Pi_ ^ L + 7
=0
(14)
Of
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Note Xw = Xf +- Xb + Xv = Xi, where Xi = X,- + Xb. The sohd density. ps. instead of the
apparent solid density of the material is used in Eqs. (II) to (14) because it is a measurable
parameter and is a constant during drying for a specific materiaL
Heat Balance
The total energy equation for a representative elementary volume states (Bird et ai. I960):
(15)
(a)
(b)
(c)
(d)
(e) (/)
In Eq (15)
(a)
heat storage term
(b)
convection term due to temperature gradient
(c)
conduction term
(d)
viscous dissipation term
(e)
work done by pressure
(f)
internal heat source term
The viscous dissipation and pressure work are usually negligible. Hence Eq (15) reduces to
an enthalpy balance equation:
(16)
where
ph = p rhr + p J K + p j i x +(pf +pb)ht
(17)
puh = p j i j i , + P*kA +[pf£f + PPh K
(18)
81
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Governing equations
For the spherical geometry considered in this study, transport is assumed to occur only in
the radial direction. Hence a one dimensional problem in spherical coordinates was formulated.
The total moisture transport equation can be obtained by adding Eqs.( 11). (12) and (13) and
written as:
dX,
I 3
'd X ,
n
^d T
„
(19)
In Eq. (19).
Dx = D ( + Dx + DX
Dt = D / -f-D t +D f
( 20)
DP = Dp +Dp + Dp
In Eq. (20). moisture transport due to moisture, temperature, and pressure gradients is the
sum of the contributions of free water, bound water, and vapor. The temperature equation was
obtained by substituting Eqs. (5). (17). and (18) into the enthalpy balance equation (16):
^
z ax,
„
D j x T ~ ^ T + ^TTr
,ar
„
.a ? /
Tpr
( 21)
The total pressure equation was obtained from the air balance equation (14) and can be
written as:
C
™ L+C
px dt
dP„
n dt
pp
dt
i a
z dX,
Dir
+ D£rz^ + D t r zdP*
rz dr
dr
dr
dr
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( 22)
In Eqs. (19). (21). and (22). Dr* and Crr are kinetic coefficients and capacity coefficients.
respectively. The subscripts i and j could be for temperature, moisture, and pressure while the
superscript k could denote air. free water, bound water, and vapor. The expressions for these
coefficients are given in Appendix A.
Initial and boundary conditions
Initial conditions can be written as:
X /U = /U y,c)
(23)
=^>
PS1I1®1*= pdJm
Moisture transported to the air-particle interface from the interior of the material can leave
the interface as either liquid or vapor, depending upon the intensity of the drying. The moisture
flux arriving at the surface from the interior of the material can be expressed as:
+fiv)-n = -{ l-£ )P'{Dx VXt +Dt VT + DpVP{)•«
=("/
(24)
In the spouted bed. because of the pneumatic agitation, the diced apples experience
constant circulation. It is reasonable to assume that the moisture arriving at the interface from
the interior of the material evaporates immediately and is carried away by the hot air stream.
The moisture flux leaving the interface by convection can be expressed as Fm.„ I _ = £(pvs pv_ )hm. The mass transfer boundary condition in spherical coordinates is then given by:
’
dX[
37-
dPs ^
Di 1 T +Dt 37+£>'17
=e(p„
(25)
-R,
An energy balance over the interface requires that, at the direction normal to the interface,
the heat flux arriving at the interface from the interior of the material equals the heat flux
leaving the interface by convection, that is Fheat I+ = FheaI i _ where
83
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n + hvnv n + htirif + n j- n
(
26 )
^«or|- =Mr„ - T r)+hana -n+h,nv -n + h,{nf +nb)-n
Thus, the temperature boundary condition writes:
(27)
Pressure boundary condition can be written as:
Pj r=R„ —Pjm
(28)
The symmetry condition at the center of the sphere must be satisfied:
_ar
r=t)
dr
MODEL REDUCTION
The resulting set of equations that govern microwave drying is given in Eqs. (19). (21).
(22), (23). (26), (28). and (29) with liquid moisture content Xl? temperature T. and gas pressure
Pg as independent variables. These nonlinear partial differential equations are highly coupled
and their solution in closed form is not available. To simplify the equations and further
elucidate the physics that govern the transport, we used scaling method to analyze the
magnitude of each term in the drying equations. Another purpose in model reduction is to avoid
the use of the unknown transport properties, such as the bound water diffusivity and the
capillary pressure of apples, provided the contributions of the associated terms can be proven to
be negligible through the scaling analysis. The following scaling groups are used (Plumb et al.,
1986):
84
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where Pma* and Tma* are maximum pressure and temperature that might occur in the model
food, evaporated diced apples, during microwave drying, tc is the time needed for fluid to
achieve maximum velocity due to pressure gradient in the spherical sample.
Substituting (30) into (19). (21). and (22) we obtained nondimensioniized drying
equations:
dX?
dt'
'~TX
d
R ;r ': dr'
P.Y
n'
dr'
("Dr d r‘
T dr'
P dr'
(3H
te
dt'
(32)
inU -v c m. +
n - * H +D'
.
+ u tt
u tp
dr
dr
xmax *0 ^d T ‘
— “ - r C p r -------------------
tc dt
— r
dr
) + 0,, O*
dP'fZ
r aax
t - p
/tftw
x*p• m
** am
t w
-77,
x 0 dx;
--u
~ t ,
I
d
f^r*1 dr*
^
k D o ------
-T0 d r
X0 dXl
r t-7T
r
tc dt
I
C
r •if
R^X^r'1 dr'
r,
dr*
dr*
(33)
.V
-------------r i / j .
---------
3r*
D ,a
dr*
ar*
The coefficients with prime O are listed in Appendix A. The corresponding boundary
conditions are:
' o i H L + o f ^ I l +D . ^
*0
dr
dr
dr*
r =t
0~g)Px
(P's
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(
34 )
A -tff ^ n e a
d T
Rn
dr
= h ( T „ - T ri) - ! i T ; ( T n a x - T 0 )
r =L
■\«*
A h ,(l-£ )p s
( D
'
+
D *
) X 0 _ L
L
3 p*
37**
+
( D
/
or
^ D b )(.TB a x - T 0 ) —
or
+ D ^ P ma
ar
(35)
(36)
P*l r - I = 0
dx;\
dr
dp :
d r ' Ir . =0
dr'
~ d7
(37)
A comparison of the coefficients of each nondimensionlized term can provide guidance in
determining which terms are less important. In the analysis, a derivative with coefficient at
least one magnitude smaller than the others was considered negligible. The quantification was
achieved by using typical values of the physical, thermal, and transport parameters in the
capacity and kinetic coefficients. For moisture dependent parameters, two extreme moistures
Xo = 7.0 (db) and Xt =0.1 (db) were used to give the range of the coefficients. For temperature
dependent parameters, an average drying temperature of 343 K was used. Detailed analyses can
be found elsewhere (Feng, 1999b) and the resulting simplified equations are the following:
d X
dt'
.\
v d x ; -.r ( p ^ - p ^ P r
dp;
r,
Ls+ff A n
;
/? o X 0 r ’2
d r
d r
r ^ -r dr
d r
*
d ?
R b '1
p
I- £ T
., a r
d r'
+
,
P f
(38)
dr'
+d>„4>'
(39)
d r'
(I C) p xp < x c d x ; | £ c M a p ^ - p ttm d p ;
P f
i
a
R fr - dr
tc
d r
dr
r 't
(40)
r1 - {V*p rm x - p* asm )P
JHa — • * dF*
P .
d r
*
In Eq. (40), C is given in Appendix A. The simplified boundary conditions are:
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ax;
p^
l-£
dr*
A-trr
- p^
•\
p f x k n- dpt
pt llf
dr'
e p y - K (.»
k - 0
r =1
(l-e )p r
I^irn T, ) 37"
= f t ( r _ - 7 ; 1) - / lr ; ( r nax- r 0 )
Rn
d r’ r =1
ax;,
M v( I - s ) p r
dr'
*0
(42)
- p m ) Pf x k n. dp;
l-e
p , p 7- dr'
i tft.
=0
dx;
(4L)
ar'
dr' r . , " d r '
J K
(37)
r =0
In Eqs. (36) to (42). all the thermo-transport properties for apples are either available in the
literature or measured in this study. The effective moisture diffusivitv Deff lumps the
contribution of both bound water and free water and can be determined with a hot-air only
drying test in which the internal vapor generation is negligible. Another experiment was
designed to measure the intrinsic and relative permeabilities and is discussed in the following
section.
PHYSICAL. THERMAL. THERMAL-PHYSICAL, AND TRANSPORT PARAMETERS
Porosity
Porosity, when dealing with fluid flow in unsaturated porous media, is defined as
V. +V.
—
£ = ----*v,+ vt +vt
(43)
while the porosity used in the drying of fruits and vegetables is often given as
* '= ------------------=
(44)
V,*V,+V,
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For apples. Kxokida and Maroulis (1999) gave the following correlation:
g '=
I ", 8'>
1.889 + X,
(45)
By converting from porosity e' to e using the correlation for apples we have:
1.282 + 1.65(1.899 + X, )X,
£— ,
x/
■ .
(l + l.65X,Xl.899 + X,)
(46)
Vapor pressure
The vapor pressure inside and at the surface of the diced apples is given by its sorption
isotherm relation:
Pv =PMXi-T)
(47)
The sorption isotherm (p (Xi, T) for apples is given by Feng el al. (1999a) by fitting data
reported by Roman et al. (1982):
„
C X maw
X,=------------------------
(l-«J[l-H C -l)awI
P
(water activttv a = —-)
py
(48)
K
where the parameters Xra and C are given by:
ln(Xm) = - 7.036 + —
& ln(C) = -9385 + ^ = ^ -
Surface heat transfer and mass transfer coefficient h and hra
The Nusselt number in spouted bed drying is defined as:
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(49)
In spouted bed drying, Markowski (1992) used a correlation for Nusselt number:
yO.S51
N u =
0 .0 0 4 5
A r ^
R e 0664
(51)
ta n ^ -
V
~
J
The dimensionless surface mass transfer coefficient. hm, is estimated by the Sherwood
number by:
The surface mass transfer coefficient for spouted bed drying is not available in the
literature. The Lewis analogy was used to estimate the Sherwood number. Sh. and hence the
mass transfer coefficient. hm. The particle Archimedes number. Ar, and particle Reynolds
number are given in Notation.
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Other parameters
Other parameters used in the model are presented in Table I.
Table I. Correlations for thermal, thermodynamic, and mass transport parameters
Parameter
Correlation
Reference
Viscosity of gas
fi f (T) = /i r-„ exp(c -bT-~cT' ~ dT' -eT*)
Turner. 199 lb
p.m= I x 10"4: a = 29.619: b = 0.152: c = 0.648 x
10"4: d = 0.815 x 10"*: e = 0.120 x I0‘s
Viscosity of tree water
/ z , ( n = ^ f0{ r l / ; / ( a + h / r - c / r : + d / r 5)}
Turner. 199 lb
a = 0.672: b = 85.229: c = 2111.475: d =
106417.0: Pgo = I x 10"*
Latent heat Ahv
Mu = 3167.2-2.432 7
Steam table
Effective thermal
4,^ = 0.12631 + 0.0595 Xi
DonsietaJ.. 1996
conductivity of apple a*#
Thermal conductivity of
A,
= 0.0035 +7.67 x 10'" *T
air a,
Specific heat of apple
Cpeif
Air-vapor binary
diffusivity D1V
Effective diffusivity of
apple Drff
27.21 X,
C^
=1W +
D —'’ "’O v i n
*
”
,
Niesteruk. 1996
,♦ * /
101325 ( T Y '75
Pt U73.I5 J
{ al + a2* X, )
Dtff =uO*exd ------------------ —
V
T
J
Stanish et aL. 1986
This study
aO = 6.273 x LO"4: al = 5.843 x LO3
a2 = -2.038x
102
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Table L Correlations for thermal, thermodynamic, and mass transport parameters (com.)
This study
Loss factor of apples
e '= a l -ha2T + a}T'-baAX-has X T
e"
+a6 X T 1 -t-a7 X 1 -bas X 1r -h a ^ X '
at = -23.5999: a2 = 0.158233: a3 = 0.000256978:3 4 = -1.87998: a5 =
0.00768435; 36 = -5.6363 x 10*6: a7 =
0.0289568; ag = -7.66337 x 10'5; aq = 4.09947 x tO*5
PERMEABILITY DETERMINATION
Theory
For gas flow in an unsaturated gas-liquid porous medium, the gas phase velocity is
calculated using the generalized Darcy's law given in Eq. (2). The gravity term in Eq. (2) can
be ignored compared to the gas pressure term. For a cylindrical sample of thickness H. the
average gas velocity in the axial direction can be estimated by:
-
u
K( e) kn APv
------------ VP = -------------- —
M,
H
03)
The average gas flowrate Qg is related to pressure drop APg across the sample by:
„
fl,
_
K(£)
APa
,54,
The intrinsic permeability K(e) is a function of the pore structure. Eq. (54) was used to
design an experiment to determine the permeabilities. By measuring the flowrate and pressure
drop, the slope on a flowrate vs. pressure drop curve can be used to calculate the permeability.
The intrinsic permeability. K(e). and relative permeability, kfg. are averaged values over the
sample thickness.
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Experimental
An experiment setup was developed to measure both the gas flowrate and the pressure drop
across the sample (Figure 3). Three experiments were designed to determine the effect of
porosity on the intrinsic permeability and the effect of moisture content on the relative
permeabilities. In experiment one, apple was sliced and freeze-dried to yield bone dry samples.
Freeze drying was used to keep the original pore structure of the apples. The freeze-dried
samples had a saturation below the irreducible level. Samples with thickness 3.5 mm and
diameter of 14 mm were then cut out of the slices for the permeability determination. Each
cylindrical sample was put in an airtight sample holder to measure the flowrate and the pressure
drop. In this experiment, the intrinsic permeability,
K q,
corresponding to intact pore structure
and single phase flow, can be determined from the pressure drop and flowrate readings.
Air
Tap water
Pressure
difference
iL
Flowrate
Sample
To sink
Water bath I
Water bath 2
Figure 3. Setup for permeability determination.
In experiment two. the effect of porosity was determined. The freeze-dried apple slices
were pressed into different thickness and hence possessed different porosity. The intrinsic
permeability K(e) determined this way was a function of porosity e.
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la experiment three, the relative permeability of gas krg was determined. The freeze-dried
samples were conditioned in desiccators with salt solutions at water activity of 0.753 and 0.843.
respectively. When equilibrium was reached, the moisture contents of the samples in two
desiccators were 36.0% and 60.0% (db) respectively. In order to prevent moisture change
during the measurement, the air flowing through the conditioned sample was controlled at an
relative humidity in equilibrium with sample's moisture content. The relative humidity
adjustment was achieved by using an air humidifier, a low temperature water bath to ensure the
dew point, and a high temperature water bath to raise saturated air to room temperature. The
dew point was determined from the psychometric chart so that when raised to room
temperature, a required relative humidity was reached. The conditioned sample was put in the
sample holder to measure the pressure drop and flowrate. The gas permeability. BC*. was
measured in this experiment. The relative permeability of gas phase
was then calculated by:
K,
(55)
In order to estimate the relative permeability for samples at the above two moisture
contents, we had to determine the porosity of conditioned samples and hence determine the
corresponding K(e). The porosity of the conditioned sample can be calculated using Eq. (43).
The intrinsic permeability
K (e )
and porosity relation were determined in experiments 2 and
given in Eq. (57). The relative permeability of the gas phase. krg. can thus be calculated from
Eq. (55). A simple relation was used to determine the relative permeability of the liquid phase:
(56)
Results
Figure 4 shows the intrinsic permeability as a function of porosity E . The data were fitted
to the Kozeny model:
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E(g) = 3.691xI0'12 ■ e
,
R 1 =0.95
The relative permeabilities obtained in this study are shown in Figure 5. By definition, the
relative permeability of the gas phase equals zero at saturation of unity and unity at saturation
of zero. These two points were used in the relative permeability correlation. A simple
exponential relation was developed using both the experimentally determined relative
permeability values and the values from the definition. The correlation of relative permeability
dada to the saturation level S is given by:
kri = l.0 le'UA*s
R1 = 0.96
®
4 e - l
(581
Experimental
Kozeny model (R~ = 0.95)
W
&
0 .4 0
0 .4 5
0 .5 0
0 .5 5
0 .6 0
0 .6 5
0 .7 0
0 .7 5
0 .8 0
Porosity E
Figure 4. Intrinsic permeability vs. porosity.
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1.0
w
0.8
=
ati
0.6
Relative permeability (k^j
Relative permeability (k.t;
•
0 .4
Experimental
>
~
0.2
0.0
0.0
0.2
0 .4
0.6
0.8
1.0
Saturation S
Figure 5. Gas and liquid relative permeabilities as a function of saturation.
NUMERICAL TECHNIQUE
The moisture, temperature, and pressure equations, together with the boundary conditions
were solved using the finite difference method. The sphere with a diameter of 5mm. was
divided into N layers with a thickness 8 = l/N. 15 elements and hence N+l=I6 nodes were
used. A time step of 0.5 s was selected in the simulation. The Crank-Nicolson scheme was used
to discretize the partial differential equations for the internal nodes. It has been proven that the
Crank-Nicolson method is second-order accurate in both time and space (Ozosik. 1994).
Another advantage of the Crank-Nicolson method is that it has no restriction on the size of the
time step At for computation. The boundary conditions at node 0 and N were discretized with a
three-point formula to achieve the same accuracy with internal nodes. The moisture,
temperature, and gas pressure equations were solved simultaneously. Hence, the assembled
matrix has adimension of 3(N+I) x 3(N+l). A program was written using MatLab to solve this
matrix. The parameters needed in the calculation are given in Table 2. Details of the numerical
study can be found in Feng (1999c).
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EXPERIMENTAL
A microwave and spouted bed combined dryer was developed for the drying tests to
validate the model simulation. This system consisted of a microwave supply system and a hot
air system (Figure 6). In the microwave supply system a magnetron generated the microwaves,
a wave-guide transmitted the wave to the drying cavity, a directional coupler with power
meters measured power compoments. A circulator with a water load was installed in the system
to absorb the reflected power, a three-stub tuner was used to adjust the matching impedance
into the drying cavity. The power generated from the magnetron could be continuously adjusted
using an Akter SM445 power controller. Both the incideni and the reflected power were
measured using two HP power meters so that the power absorbed by the drying sample was
accurately determined.
Diced Red Delicious apples (Matus domestica Borkh ) with initial moisture content of 22.4
9c
(wb) were used in drying tests. The spouted bed superficial air velocity was 1.9 m/s in all the
tests. This velocity was able to provide stable particle circulation during drying to ensure
uniform heating. Forty grams of diced apples were used in drying. Moisture loss was monitored
by periodically weighing the sample on an electric balance. The average moisture content of
samples was determined using the vacuum oven method (AOAC. 1990). The drying
temperature at the core of the dice was determined by measuring the inner temperature of ten
randomly chosen apple pieces with a type T thermocouple (response time ().8s) at pre­
designated time intervals. The pressure was measured using fresh apples with a fiber optical
pressure probe, which has a resolution of I kPa. The probe was carefully inserted into the
center of a fresh cut apple dice sealed with vacuum grease to prevent leakage of vapor. A date
logging system was used to record the data.
96
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Table 2. Input parameters used in numerical investigation.
P a ra m e te r
U n it
V a lu e
P a ra m e te r
0 .2 9
Pf
k g
n r
KMX)
EC
2 9 5
P.
k g
n
1 6 5 0
k P a
1 0 1 .3
Ppb
k g
n r"
7 1 0
Ro
m
0 .0 0 2 5
Pv-
k g
m "
1 .0 2 9
W,
k g
0 .0 3
D.
m
0.082
p
r absorb
W
2 0 0
Ho
m
0.09
K,
m
0 .1 2 2
7
d e g r e e
34.4
Xo
T,
P M l =
P
p v-
P V—
R'
EC
3 4 3
U
P a
9 2 4 3
Pa-
k g
J
m '3
m o r-E C 1
M,
k g
m
M,
k g
m o l" 1
o l1
ECo
0 .0 0 9 4
8 .3 1 4
N
0 .0 1 8
TL
U n it
m
k g
r
s ';
m '1 s ' 1
m
'
V a lu e
1 .9
l o i x nr*
3.Ox u r ::
15
s
2 9
97
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 5 0 0
Direction
coupler
Circulator
Magnetron
H
t
Power
controller
1
•
1oooo
!
Three-stub
tuner
O O
i
cm
Power
meter
/'
Temperature
controller
Microwave
cavrtv
Computer
Samples in
spouted bed
Portable
a
\ i r pump
Figure 6.2450 MHz microwave and spouted bed combined drying system.
98
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
MODEL VALIDATION
A num erical test was conducted using different time steps and mesh sizes to examine
convergence of the modeL With time step of 2. L and 0.5 second, almost identical model
predictions were produced for moisture, temperature, and pressure. The mesh size effect was
examined by dividing the sphere into 10. 15. 30. and 45 elements. The mesh convergence was
verified with refined mesh sizes. Detailed analysis is presented in Appendix A
Model predictions and experimental results are compared in Figure 7 and 8 for diced
apples with initial moisture content of 22.4% (wb). Four replicates were conducted and drying
conditions were controlled at microwave power density of 4 W/g (wb) and hot air temperature
of 7()°C. The model simulation of moisture content followed an exponential decay curve that
characterized the drying in the falling rate period for hygroscopic materials (Figure 7). The
prediction underestimated the moisture loss at the beginning of the drying while overestimated
at low moisture range. This is probably due to the error in the experimentally determined
effective moisture diffusivity. As mentioned in the previous section, the effective moisture
diffusivity defined in Eq. (35) lumps the effect of both the bound water and the free water
transport. It was determined in a separate drying experiment that the internal vapor generation
was negligible. This condition was achieved by using hot air to dry the sample at moderate
temperatures. However, in these drying tests, the final moisture content did not reach lower
than 10% (wb). The diffusivity at low moisture was. hence, externally extrapolated.
Uncertainties and errors might have been introduced in this extrapolation. On the other hand, in
our previous study (Feng et aL. 1999a). we reported that the interaction of microwaves and
water molecules not only yielded a high internal gas pressure to provide an additional driving
force for moisture transport, but also excited the water molecules by increasing its activation
energy. Such an increase in the activation energy resulted in an increase in the effective
moisture diffusivity. This increase could not be measured with the hot air drying test.
Therefore, the underestimation of moisture loss at the beginning might be the result of a lower
effective moisture diffusivity obtained using hot air drying method. The equilibrium moisture
content limited the drying at low moisture. Hence, the derivation between prediction and
experiment may also be due to the error in sorption isotherm relations, e.g. Egs. 39 and 40. used
in this study.
99
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.20
■
3
0.15 ■
1
0.10
■
0.05
0.00
0
3
10
15
20
25
30
Drying Time (rain)
Figure 7. Comparison of moisture content for MWSB drying at microwave power level of 4
W/g and hot-air temperature of 70°C
The center temperatures of diced apples from experiment and prediction are compared in
Figure 8. The experimental values were from ten pieces of randomly selected diced apples.
Predicted temperatures agree well with measurements. In the beginning of the drying, both the
hot air and the microwave energy heated the apple dice from outside and inside, respectively.
This resulted in a rapid increase in temperature. When the apple dice surface temperature
surpassed the air temperature, the air started to cool the dice. The center temperature continued
to increase as a result of microwave heating until it reached about 82°C when a balance was
established between the energy supply from the microwave and heat loss due to surface cooling
and evaporative loss of moisture. A temperature leveling was observed. This is a unique
characteristic in the microwave and spouted bed (MWSB) combined drying. It prevents the
product from overheating and charring. In the transition zone between the phase I and II. a
slight overestimation from model prediction is observed. It may be due to an underestimation in
100
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
moisture content in the corresponding moisture curve. The higher residual moisture would
result in a higher microwave heat generation and hence a higher temperature. By comparing
Figure 7 and 8. one may observe that, at phase H. the temperature prediction should have
slightly overestimated the true value if the moisture prediction was- in agreement with the
experiment.
100
90 -r
80
u
p
5
Air Temperature
60 ■
50 -1
40
Prediction
Experimental
30 •
20
■}
10 4
0
10
15
20
25
30
Drying Tune (min)
Figure 8. Comparison of temperatures for MWSB drying at microwave power level of 4 W/g
and hot-air temperature of 70°C.
Pressure readings from the fiber optical probe are compared with model prediction in
Figure 9. In the pressure measurements, cylindrical fresh diced apples and a higher power level
of 8 W/g were used. Fresh diced apples and higher power level were used because: (I) the
evaporated apple dices were not large enough to secure a pressure determination and (2) at
power level of 4 W/g (wb). the pressure produced from evaporated diced apple of 22.4 % (wb)
moisture content was too low to be detected by the pressure probe we used, which has
resolution of I kPa. We experienced difficulty in sealing the probe during MWSB drying. In
order not to damage the fragile probe tip, a needle was used to first bore a hole into the dice and
101
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the fiber optical probe was inserted into the dice through this hole. The hole was then sealed
with vacuum grease. Thus, the probe was only loosely held in the dice. During the drying,
because of the up-blowing air. a good seal was not secured. This can be seen from Figure 9 as
indicated by a sharp decrease in pressure reading when it reached an- overpressure of 3 kPa.
After that peak, the pressure reading fell to zero most likely due to a failure of the seal. This is
not shown in the figure. Otherwise we should expect a smooth decrease from the peak. Because
the resolution of the probe was I kPa. only stepwise readings were obtained. Some detailed
changes may have been buried in the stepwise readings. Considering the sealing problem in the
experiment, the model pressure prediction is regarded as satisfactory.
a
•ji
CDOO
03000000(000 O
1o
Experiment
Prediction
3
4
ooooooo
1
2
Drying Time (min)
Figure 9. Pressure comparison for MWSB drying at microwave power level of 8 W/g and hotair temperature of 70°C.
102
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
RESULTS AND DISCUSSION
Figures 10 and 11 show the predictive moisture profile for MWSB drying at microwave
power density of 4 W/g (wb) and hot air temperature of 70°C. During the first 30 seconds or so
of drying, since the moisture content was relatively high and the residual free water constituted
a relatively large portion in the total moisture, a surface moisture accumulation effect was
observed, especially at 10 and 20 seconds (Figure 10). At about 10s. the surface moisture
reached a maximum value accompanied by a subsurface minimum. The model materials, the
evaporated diced apples, were a semi-finished product before we used them in our tests. They
were produced by drying fresh apples to a moisture of 20 to 25% (wb) using convective hot air
drying. During this pre-drying, a migration of soluble solids with the moisture to the dice
surface occurred. When the soluble solids moved to the surface and the moisture was removed,
re-crystallization might have taken place. As a result, a relatively dense and impermeable
surface might be formed. When applying MWSB drying to these diced apples, the
concentration and gas pressure gradients pushed internal moisture toward the surface. This
moisture had to break the surface barrier to reach the surroundings, probably by dissolving the
solids or just enlarging the small residual capillaries. This would cause a moisture build up at
the surface at the beginning of the drying. As soon as the passway for moisture transport was
well established, this surface moisture accumulation vanished. The high surface mass transfer
facilitated by the spouted bed technique enabled the moisture to be removed at a speed
sufficiently high to eliminate the moisture accumulation inside the dice. Hence, a moisture
profile similar to conventional hot air drying can be observed after I minute of drying. The
surface moisture accumulation or even liquid pumping in microwave drying or heating has
been well observed in previous studies. Constant et aL (1996) have demonstrated, both
numerically and experimentally, the liquid pumping phenomenon at high power microwave
drying of a non-hygroscopic material. Ni et aL (1999) studied microwave heating of porous
material at high power density and predicted a similar surface liquid pumping. Compared to
their studies with highly saturated materials, the present study showed that even with low
saturation hygroscopic material, the evaporated diced apples, surface moisture accumulation
can still occur under certain conditions.
Figure II shows the changes of moisture content at 16 nodes used in the simulation. The
moisture at the surface node experienced a short increase followed by a sharp decrease until it
103
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reached the equilibrium moisture content determined by sorption isotherms. The purpose of
such a moisture profile is to manifest the moisture gradient. Obviously, the moisture gradient is
m inim um
at both initial and final stages of the drying. It is of interest to compare this moisture
gradient change with the average moisture loss curve in Figure 7. It seems that the rapid
moisture loss at the initial stage must be due to a mechanism other than diffusion, which is
driven by the moisture concentration gradient. This justified the introduction of the capillary
flow mechanism in the MWSB drying model developed in this study.
0.30
£
025
10 s
20 s
30 s
020
I min
4 nun
0.15
3 min
0.10
10 min
0.05
20 min
0.00
0.0
1.0
2.0
2.5
Location (mm)
Figure 10. Moisture profile for MWSB drying at microwave power level of 4 W/g and hot-air
temperature of 70°C.
104
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0.30
0.25
0.20
■
0.15 ■
Center
* 0.10 ■
0.05 ■ Surface
0.00 -i------------.----------- .----------- .------------.----------0
5
10
15
20
25
Drying Time (min)
Figure 11. Changes of moisture at different nodes for MWSB drying at microwave power level
of 4 W/g and hot-air temperature of 70°C
The temperature profiles in the diced apples are shown in Figures 12 and 13. In the first
minute, the dice temperature increases rapidly probably because the hot air heated the dice
externally while microwave energy heated the dice volumetrically. A relatively flat temperature
curve can be observed in this period. It is worth mentioning that during the first 20 seconds, we
can observe a slight temperature increase at the surface and subsurface nodes. This
corresponded well with the surface moisture accumulation observed in the moisture profiles
(Figure 10). The higher moisture content at the surface resulted in a higher absorption of
microwave energy, and therefore, a higher temperature. When the surface temperature
surpassed the air temperature after about one minute of drying, a temperature gradient was
established. Comparing with Figure 10, we can see that this temperature gradient went in the
same direction as the moisture gradient, hence helping to enhance the drying. As moisture
content decreased, internal heat generation due to microwave heating was less intensive. As a
result, the temperature distribution over the sample radius tended to be relatively flat when
approaching the end of the drying. The relatively small temperature gradient in MWSB drying
105
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could be expected if we examine the Biot number. For the apple dice we used, the Biot number
was 0.4. mainly due to the small particle size. It suggests that the surface resistance to heat
transfer is more pronounced than the internal resistance.
The pressure build-up during MWSB drying can be seen in Figure 14. An internal pressure
increase can be observed in the early stages of the drying. After one minute, the pressure profile
was relatively flat. After that, pressure began to catch up with the increase in temperature until
it reached a maximum at about 3 to 5 minute of drying. About 50% of the initial moisture was
removed in this period as can be seen in Figure 7. The ability of residual moisture to generate
vapor pressure in accordance with the sorption relation decreased. A reduction in pressure can
be observed hereafter. At the 13th minute, the internal pressure begun to approach the external
pressure.
9 0
10 min
20 mm
8 0
I
-
7 0
2
6 0
4
3
3
c .
m in
3 0
m in
5 min
s
5 0
3
4 0
2 0 s
3 0
10 s
20
0 .0
0 .5
1 .0
1 .5
L o c a tio n
2 .0
1 5
(m m )
Figure 12. Temperature profile for MWSB drying at microwave power level of 4 W/g and hotair temperature of 70°C.
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
g . 50 ■
~
40
30
20
-
0
200
400
600
800
1000
1200
Time (s)
Figure 13. Time evolution of temperature for different nodes for MWSB drying at microwave
power level of 4 W/g and hot-air temperature of 70°C.
CONCLUSIONS
A comprehensive heat and mass transfer model for MWSB drying was developed in this
study. A total gas equation was introduced to highlight the influence of internal vapor
generation, which characterized the MWSB drying, on the drying behavior. The model
prediction compared favorably with experiments for average moisture content and temperature.
The pressure readings from fiber optical probe measurements compared adequately with model
prediction.
The study demonstrated that for the low and medium moisture diced apples, a surface
moisture accumulation phenomenon occurred at the beginning of the drying, which is very
similar to that often observed in high moisture microwave drying. This surface moisture
increase was also accompanied by a less noticeable temperature increase at the surface. A
temperature leveling effect was predicted and was in agreement with the experiment- This
unique feature in MWSB drying paves the road for applying this technique to a variety of
107
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
applications. The internal pressure built up in MWSB drying relied on both the moisture
content and the temperature.
nun
1 nun
7 nun
10 min
W
Z
5*J
I min
o
13 min
0.0
0-5
1.0
10
Location (mm)
Figure 14. Pressure profile for MWSB drying at microwave power level of 4 W/g and hot-air
temperature of 70°C.
NOTATION
C
capacity coefficient
Cp specific heat. J-kg'1 K"1
dp particle diameter, m
D
kinetic coefficient: material derivative
D1V binary air-vapor diffusivity, m2-s ‘
Db bound water diffusivity. m2-s"‘
Dc diameter of the spouted bed column, m
f
resistance tensor to gaseous diffusion through porous media
F
heat or mass flux at boundaries, J-m^-s'1or kg-m'2-s'1
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
£
gravitational acceleration, m-s'2
h
enthalpy. J-kg'1: surface heat transfer coefficient. W-m"2 K"1
hm mass transfer coefficient, m-s"1
Ahv latent heat. J-kg"1
H sample thickness, m
Ho initial bed height, m
j
diffusive mass flux, kg-m"2-s"1
kr relative permeability
K
intrinsic permeability, m2
m mass, kg
til moisture evaporation rate. kg-m"3-s"1
M molar mass, kg-mo I"1
M total moisture evaporation rate, kg-m '-s"1
n
mass flux, kg-m"2 s"1: a vector normal to the surface (outwardly)
N
total node number
P
pressure. Pa: microwave power. W
Pc capillary pressure. Pa
q
R
heat flux. J-m"2-s l
sample radius, m"1
R' universal gas constant. J-mol"1 K"1
s
saturation
t
time, s
T
average temperature. K
TL iteration limit for time. s l
u
superficial average velocity, m-s"1
U spouted bed air superficial velocity, m-s"1
X
moisture content (dry basis), kg H20/kg solid
X' moisture content (wet basis), kg H20/kg wet material
w
mass, kg
Greek symbols
109
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
finite difference element thickness, m
E
porosity, tolerance limit on iteration scheme
£'
porosity defined in Eq. (36): dielectric constant.
E"
loss factor.
Y
angle of conical base in the spouted bed. degree
<P shape factor = l/sphericity
heat source, W-(kg solid)'3
A.
thermal conductivity. W-m'1-EC'1: wave length, m
d
dynamic viscosity, kg-m'1-s'1
P
density, kg-m'’
P< solid density (solid weight / solid volume), kg-m'5
f
T
shear stress tensor, kg-m'2
parameter defined in Eq (12-34)
Subscripts and superscripts
0
at saturated condition or free space: initial condition (refers to fresh sample)
a
air
atm atmospheric pressure
b
bound water, bulk density
c
velocity or temperature scales
eff effective
f
free water
a
gas = air + vapor
i
space step in finite difference scheme
i
liquid = free water +- bound water
max maximum values
P
P
particle
s
solid, or relating to surface
T
temperature
pressure
110
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
v
vapor
w total moisture = free water +• bound water + vapor
X
moisture
oo surrounding
Dimensionless groups
n
' I
\
U'
A
U
Parucle
Archimedes
number
Particle Reynolds Number
*
Ar-
Re =
Pa—)
:----------
S ^ p P a —ippb
UJpPa.-
REFERENCES
Adu. B. and Otten. L. (1996) Modeling microwave heating characteristics of granular
hygroscopic solids. J. Microwave Power and Electromagnetic Energy. 3 1: 35-42.
Bird. R. B.. Stewart. W. E. and Lightfoot. E. N. (I960) Transport Phenomena. John Wilry &
Sons. New York.
Bories. S. A. (1991) Fundamentals of drying of capillary-porous bodies, in Convective Heat
and Mass Transfer in Porous Media. S. Kakac et aL (eds.). BCluwer Academic Publishers.
Dordrecht.
Bruin. S. and Luyben. EC. Ch. A. M. (1980) Drying of Food Materials. In Advances in Drying.
/. A.S. Mujumdar. (ed.). Hemisphere Publishing. New York.
Chen. P. and Pei. D. C. T. (1989) A mathematical model of drying processes. Int. J. Heat Mass
Transfer. 32: 297-310.
Chen. P. and Schmidt. P. S. (1990) An integral model for drying of hygroscopic and
nonhygroscopic materials with dielectric heating. Drying Technol., 8:907-930.
Constant. T.. Perre. P. and Moyne. C. (1992) Microwave drying of light concrete: from
transport mechanisms to explanation of energy saving. In Drying '92, A. S. Mujumdar (ed.).
Elesevier Science Publishers. 617-626.
Constant. T.. Moyne. C. and Perre. P. (1996) Drying with internal heat generation: theoretical
aspects and application to microwave heating. AIChE J.. 42:359-368.
Ill
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Donsi. G.. Ferrari. G. and Nigro. R. (1996) Experimental determination of thermal conductivity
of apple and potato at different moisture contents. J. Food Eng.. 30: 263-268.
Feng. H. and Tang. J. (1998) Microwave finish drying of diced apples in a spouted bed. J. Food
Sci.. 63: 679-683.
Feng. H.. Tang. J. and Cavalieri. R. (1999a) Combined microwave and spouted bed drying of
diced apples: Effect of drying conditions on drying kinetics and product temperature. Drying
TechnoL. 17: 1981-1998.
Feng, H. (1999b) Microwave Drying of Particulate Foods in a Spouted Bed. Ph.D.
Dissertation. Washington State university.
Garcia. R.. LeaL F. and Rolz. C. (1988) Drying of bananas using microwave and air ovens. Int.
J. Food Sci. & TechnoL 23: 81-90.
Goedeken. D.L. and Tong. C.H.( 1993) Permeability measurements of porous food materials. J.
Food Sci.. 58: 1329-1331.
Gong. L. (1992) A Theoretical. Numerical and Experimental Study o f Heat and Mass Transfer
in Wood during Drying. Ph.D. Dissertation. Washington State university.
Jansen. W. and van der Wekken. B. f 1991) Modeling of dielectrically assisted drying. J.
Microwave Power and Electromagnetic Energy. 26: 227-236.
Jolly. P. and Turner. I. (1989) Microwave drying of porous media. In Proceedings o f the
Fourth Australasian Heat and Mass Transfer Conference. University of Canterbury.
Christchurch. New Zealand. 331-342.
Krokida. M. K. and Maroulis. Z. B. (1999) Effect of microwave drying on some quality
properties of dehydrated products. Drying TechnoL. 17:449-466.
Lewicki. P.O. and Lenart. A. (1995) Osmotic dehydration of fruits and vegetables. In
Handbook o f Industrial Drying, A. S. Mujumdar (ed.), Marcel Dekker. Inc.. New York. 691713.
Lian. G.. C. S.. Harris. R. Evans and Warboys. M. (1997) Coupled Heat and Moisture Transfer
During Microwave Vacuum Crying, J. Microwave Power and Electromagnetic Energy. 32.
34-44.
Le Pourhiet. A., Bories, S. and Bialod, D. (1982) Drying simulation of hygroscopic media applications with use of microwaves. In Proceedings o f the Third International Drying
Symposium, 429-437.
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Markowski. A.S. (1992) Drying characteristics in a let-spouted bed dryer. The Canadian J.
Chem. Eng.. 70: 938-944.
Metaxas. A.C.. Meradith. R.J. (1988) Industrial Microwave Heating. Peter Peregrinus Ltd..
Stevenage. Herts. UK.
Mohsenin, N. N. (1986) Physical Properties of Plant and Animal Materials Gordon and
Breach Publishers. Amsterdam. The Netherlands.
Moyne. C. and Perre. P. (1991) Processes relation to drying: Part L theoretical model. Drying
TechnoL 9: 1135-1152.
Mullin. J. (1995) Microwave processing. In New Methods o f Food Preservation. G. W. Gould.
(ed.). Blackie Academic & ProfessionaL London. 112-134.
NL H.. Datta. A. K. and Torrance. K. W. (1999) Moisture transport in intensive microwave
heating of biomaterials: a multiphase porous media model. Int. J. Heat and Mass Transfer.
42: 1501-1512.
Niesteruk. R. (1996) Changes of thermal properties of fruits and vegetables during drying.
Drying TechnoL 14:415-422.
Ozosik. M. N. (1994) Finite Difference Methods in Heat Transfer. CRC Press. Boca Raton.
Plumb. 0. A.. Couey, L. M. and Shearer. D. (1986) Contact drying of wood veneer. Drying
TechnoL 4: 387-413.
Prabhanjan. D.G.. Ramaswamy. H.S. and Raghavan. G.S.V. (1995) Microwave-assisted
convective air drying of thin layer carrots. J. Food Eng. 25: 283-293.
Roman. G. N.. Urbicain. M. J. and Rotstein. E. (1982) Moisture equilibrium in apples at several
temperatures: experimental data and theoretical considerations. J. Food Sci.. 47: 1484-1489.
Rotstein. E. (1986) Advances in transport phenomena and thermodynamics in the drying of
cellular food systems, In Drying*86. A. S. Mujumdar (ed.), Vol. I, I-l I. Hemisphere.
Washington. DC.
Stanish . M. A.. Schajer, G. S. and Kayiham F. (1986) A mathematical model of drying for
hygrascopic porous media. AIChE J.. 32: 1301-1311.
Torringa. E. M., van Dijk, E. J. and Bartels, P. S. (1996) Microwave puffing of vegetables:
modeling and measurements. Proceedings o f 31st Microwave Power Symposium. Int.
Microwave Power Inst.
113
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Turner. I. W. and Jolly. P. G. (1991a) Combined microwave and conventional drying of a
porous material. Drying TechnoL. 9: 1209-1269.
Turner. I. W. (1991b), The Modeling of Combined Microwave and Convective Drying of a
Wet Porous Material. Ph.D. Thesis. University of Queensland.
Turner. I. W.. Puiggali, J. R. and Jomaa. W. (1998) A numerical investigation of combined
microwave and convective drying of a hygroscopic porous material: A study based on pine
wood. Trans. IChemE.. 76: Part A. 193-209.
Wei. C. K.. Davis. H. T.. Davis. E. A. and Gorden. J. (1985) Heat and mass transfer in water­
laden sandstone: microwave heating. AIChE J.. 31: 842-848.
Whitaker. S. (1977) Simultaneous Heat. Mass. Momentum Transfer in Porous Media: A
Theory of Drying/' In Adv. In Heat Transfer.. Academic. New York. 13: 119-203.
APPENDIX A
I pf KK- dP. \\
l - £ p. Pf
It
I Pf Kk4 dPc
D(=l - £ P, Pf \ dT r_
Dk=~
D> =- 1 P '
I ” * P, Pf
I - £ ' Db eR'T ( dP ^
l - £ p r PM ,
k
** * V
I ~£ Dh
l - e p t Mv
eR'T'dP)
PM, dT
Dp =0
MM,
£)‘ - D^P.
n
_
x (1 - e ) p t KT{PsMa +(ilfv - M a)Pv) a x
MM,
(I-e )p , R'T{PSMX+ (Af. - M X)P^) dT
I
D’„=(I- e ) p t
P M . K kn
D„MMA
BTT fit
R'T{PgMa H M „ - M J P v)
114
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M t [ (1 - e ) p t P„
£J l Z ^ x ,
1 /?' [ p f + p b T
Pf +Pb
I dP
TdXL
M
d[PJT)
Crr=(pC,)a, + i / l . 1 f e - f i z £ k x ,
dT
Pf +Pb
Dtx —&Jivi}—s)p' Dx
Djt =
0 ~ £ )Pr ®T
+
Dtb =AJi. (l-e)o.D'r,
P
1 3 -P
*v
e M„
Cpx —
R'
V
eM,
i-1 g
Cpr —■
£
r
1 -g
Pt
g Pf +Pb ,
I- I-g
g
/
X,
P'
Pf +Pb
f />,
r:
P,
P/+P*
1 3PV
rax.
a(/>, /r )
ar
I - - - g P ’ X,
g Pr+Pt
M,
' a/> i
R T Pt Ma -HMt - M a)Pt [dX„ k
Dx = - ( ! - E ) p , D x = -D JV— ;
P<Ma
(dP^)
At.
D* = - a - e ) p rD±=- Dm —
R'T Pt Ma +{MV- M a)Pv dT A Y .
r
I D
R'T
p%
M ,
P M ,
“* R'T PfMj + {M V- M , )PV
D'x = X aD x : D r ^ T ^ - T ^ D r :
D'f =(PnBX - P ^ J D ,
= X o,D tx : Djy = (r max - T ^ D jt '. D'tp =(Pmax - P aXM)Drp
D ' x = X , D xa : D'x =(Tuax —Tq )DX: D'P =(P!mx ~Pim )D*
c = I - 1—
g
Pr
X,
Pr+Pi
115
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Chapter 4
DETERMINATION OF MOISTURE DIFFUSIVITY OF RED DELICIOUS APPLE
TISSUES BY THERMOGRAVEV1ETRIC ANALYSIS
H. Feng. J. Tang & St. John Dixon-Warren
Department of Biological Systems Engineering
Washington State University. Pullman. WA 99164-6120
ABSTRACT
Moisture diffusivity is an important parameter needed in the analysis, design and optimization of
drying processes for food and other materials. Published data on moisture diffusivities of food
materials are scarce and. sometimes, inconsistent due to a lack of a precise and repeatable
experimental technique. Most experimental data are limited to low and moderate drying
temperature (< 70°O. whereas in the food industry drying condition of up to 100°C is usually
used in the falling rate period to speed up the drying processes. In this study, the effective
moisture diffusivities of Red Delicious apple tissues were determined from drying curves
produced with a Perkin Elmer thermogravimetric analyzer, using the slope method. The
experiments were conducted at four temperatures 60. 80. 100 and 120°C. Two well-defined
falling rate periods were observed. The effective moisture diffusivity. for the four temperature
levels ranged from 3.2 x 10"' to 7.9 x 10"® nT/s for the first falling rate period and 3.8 x 10 s to
4.7 x 10'9 m7s for the second falling rate period. The temperature dependence of the effective
diffusivity can be described with an Arrhenius-type equation.
116
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Introduction
Moisture diffusivity is one of the key parameters in the analysis, design, and
optimization of food drying operations. Published data on moisture diffusivity related to drying
of fruits and vegetables are scare and. sometimes, inconsistent. The reason may arise from the
wide variation of the composition and microstructure of the food materials (Khraishen et aL.
1997). The experimental measurement techniques and the analysis methods used to obtain
diffusivity coefficient may also cause discrepancies (Kiranoudis et aL. 1993). For a specific
food, the moisture diffusivity changes with many factors including processing temperature,
moisture content, pretreatment (Saravacos and Raouzeos, 1984), physical structure (Vagenas
and Karathanos. 1993). and the physical state of food polymers (Achanta and Okas. 1996).
Different experimental techniques were developed by researchers for analyzing moisture
transport within a food stuff, including the drying method, the permeability method, the
moisture profile method (Pel and Brocken. 1996). and the sorption kinetics method (Karathanos
et aL. 1990). The drying method is the most widely used (Moyne et aL. 1987; Zogzas and
Maroulis, 1996).
Several methods have been developed to estimate diffusion coefficient from data
obtained using the drying method. In general, the drying data for the falling periods are used
during which the internal resistance is dominant and moisture migration can be approximated
by the Fick's second law. The Fickian equation is then solved either analytically or numerically
depending if the diffusivity coefficient is considered as a constant. For a constant diffusivity.
the slope method derived from the series solution to the Fickian equation provides a simple
means to obtain the diffusivity coefficient. In the analysis in which the moisture diffusivity is
considered to be a function of moisture content, more complicated methods are used. It is a
common, but questionable, practice in the literature to estimate concentration dependent
moisture diffusivity using the series solution derived from the Fick’s second law of diffusion
which is based on constant diffusivity assumption. The finite difference method and the finite
element method are more elaborate means to estimate moisture dependent diffusivity. These
two methods divide the analysis domain into discrete sub-domains and use linear equations to
approximate the partial differential equations for mass transfer within the sub-domains
(MaCarthy and Perez, 1991; De Elvira. 1993). Marinos-Kouris and Maroulis (1995) proposed a
117
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numerical solution-regression method to fit drying data to the Fick’s equation. This method was
referred as a generalized method (Kiranoudis et al„ 1993). The Regular Regime Method is
another approach for estimating diffusion coefficient using the drying data (Schoeber and
Thijssen. 1977. Tong and Lund. 1990). With this method, an experimental drying curve is
transformed into a characteristic function, the dependence of diffusivity coefficient with
moisture content can be determined accordingly (Okazaki et aL, 1995). Generally, the methods
used to correlate the diffusion coefficient to moisture content have to use such experimentally
determined physical parameters as the surface mass transfer coefficient, the specific heat, the
equilibrium parameters (sorption isotherm), and the specific volume. Including those
parameters may bring errors to the final results. Those errors may be propagated and amplified
through mathematical manipulation, thus making it difficult to justify the accuracy of the
obtained diffusion coefficients.
Literature values on moisture diffusivity are difficult to compare. This is because the
experiments conducted by one research group can not be repeated by others because of the
differences in the sample materials, the treatment methods, the experimental methods and
conditions, as well as different analysis methods to arrive at the diffusivity data. This has been
demonstrated by the collaborative experiments of COST 90bis (Moyne et aL. 1987). One
solution to this problem may be the development of a standard experiment technique and a
simple analysis method to conduct a routine analysis.
In spite of many studies on moisture diffusivities. there still is a lack of information on
moisture diffusivity that can be directly used to analysis the industrial operations. For example,
in industrial drying of selected fruits, products are exposed to high temperatures (between 80 to
I I0°O in the falling rate region to reduce the drying time. Almost all experiments, however,
aimed to estimate the moisture diffusivity of fruits and vegetables were conducted at
temperatures lower than 80°C. It is well known that the moisture diffusivity used for
engineering purpose is an overall parameter which lumps many different effects into a single
quantity. At high temperatures, some factors which are not important at low temperature may
become important. Although the Arrhenius-type of dependency of the moisture diffusivity on
temperature has been well documented for many food products at temperatures between 20 to
60°C (Tang and Sokhansanj, 1993: Khraishen et aL, 1997), it is of interest to examine the
influence of high temperature, because the vapor diffusion will become more important.
118
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The objective of this research was to determine the moisture diffusivity of Red
Delicious apples at high temperatures using the thermogravimetric analysis technique (TGA) to
obtain the drying data, and to use slope method to estimate the diffusivity.
Materials and Methods
Red Delicious apples (Malus domesnca Borkh.) were supplied by Tree Top Inc.. Selah.
Washington. The apples were stored at 4°C for more than three months before the tests. Apples
with similar size were chosen and kept at room temperature over night before the experiments.
The initial moisture content was determined by the vacuum oven method (70°C. 6hrs). One
cylindrical sample of 3.7 mm in diameter was taken from each apple using a core borer at a
right angle to the stem-calyx axis. An 8-mm length specimen was made from this cylinder by
cutting, vertical to the cylinder axis, I mm off from the skin end. and the rest off from the core
end. Selection of apples and the location where cylindrical sample was taken were randomized.
The two ends of each cylinder were sealed to ensure only radial moisture migration during
drying. Three sealing media Duro Super Glue-5 (Loctite Corporation. Rocky Hill. CT. USA).
Devcon 5-minute superfast epoxy (ITW Devcon. Denvers. MA. USA), and vacuum grease
(Dow Coming Corporation. Midland. ML USA) were tested. The criteria for selecting
appropriate sealing material are: it should stand the temperature, be of negligible permeability,
and have minimum effect on the bulk properties of the samples. The Duro Super Glue-5 has
been found to have shortest solidifying time. The drawback is that it absorbs some water to
catalyze the solidifying reaction which introduces errors in the moisture calculations. Vacuum
grease showed less weight change during the heating. However, when apple sample surface has
free water, it is difficult to apply it to the sample surface. Finally, epoxy was chosen as the
sealing media. The weight loss for a 0.015g epoxy sample during a ten-minute heating test was
less than 0.3%.
A Perkin-Elmer PC series TGA 7 thermogravimeter was used to obtain the drying
curves. It has a standard furnace, a purging gas system..and a micro-balance (Figure I). The
electric furnace can operate from ambient to 1000 °C with a heating rates from 0.1 to 200
°C/min. Temperature was monitored by a built-in jacked chromel-alumel thermocouple in close
proximity to the sample. The microbalance has a maximum sensitivity of 0.1 micrograms with
119
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a balance accuracy of better than 0 .1 percent of the readings. The sample holder has a capacity
of up to 50 microliters. The resolution for temperature measurement is 0.1°C. The purpose of
the purging gas in this test was to remove moisture from the sample holder, transport heat from
the furnace to the sample, and provide a protection for both the apple samples and the
microbalance. Ultra-pure nitrogen was used as the purging gas with a flowrate of 40 to 100
cubic centimeters per minute. The nitrogen purging created an oxygen free environment which
prevents the oxidation and non-emzymatic reaction.
The advantage of using thermogravimetry (TGA) to obtain the moisture diffusivity lies
in that it is a standard analytical instrument with an accurate weighing system and repeatable
drying environment. The results from difference researchers can be compared as the same
experimental conditions for TGAs from different manufacturers can be easily achieved.
Microbalance
Purging gas
Controller
Computer
Furnace
Sample
Figure I. Schematic diagram for the Thermogravimetric Analyzer used in this study
The drying tests were conducted at four temperatures 60. 80. 100. and 120°C. One
sample was used in each test and the tests were conducted in triplicate. The heating rate during
the tests was selected to be O.I°C/min, such that the temperature raising during a ten minutes
period was l°C. For a given test temperature, say 60°C, the initial and final temperature for a
120
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ten-minute heating period was set as 59.5 and 60.5°C. respectively, with an average of 60°C.
The preheating rate to bring the sample from room temperature to the test temperature was
200°C/min in all tests. For cases where test duration was longer than ten minutes, the tenminute heating can be repeated as long as the time interval for saving data and restarting the
data logging between the heating periods was recorded.
Sample weight (about 80mg) was taken at the moment when it was put in the sample
holder. Whenever a sample is cut from an apple, a weight loss occurs. The measured sample
weight loss rate when it is exposed to air was about 0.6 mg/min at room temperature. A fourpoint weight checking was performed using a Sartorius A200S analytic balance to monitor the
sample weight changes during the tests. First weighing was done when the sample was cut. The
second recording was made when epoxy was applied to estimate the weight of epoxy added to
the sample. The third checking was conducted at the time when the sample was to transfer to
the TGA. The fourth was made after the TGA test. The micro-balance of the TGA started
recording the sample weight immediately after the sample was placed in the sample holder. The
differences between the balance and TGA readings were within I% at the beginning of the
TGA tests and 2% at the end of the test.
The weight calibration was made using a 100-mg standard before a test. An on-line
weight calibration was also conducted with the purging gas on to take into consideration of the
drag effect. The weight reading calibration is needed as long as the purging gas rate or the
handdown wire of the TGA is changed.
The slope method
It has been established that drying of porous materials in the falling rate period when
the internal resistance is dominant can be proximated by Fick’s second law no mater what
mechanisms is involved (Zogzas and Maroulis. 1996). For an isotropic long cylindrical
geometry, the Fick’s second law can be expressed as
£ £ = i i - (rD i £ )
dt r dr
dr
d i p , X ) ^ l d r D <9(p.Z)
dt
r dr
dr
121
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(I)
where C is the local moisture concentration (kg/m3), t is the time (s). ps is the local
concentration of drying solids (kg solid/m'’). X is the moisture content (kg water/kg solid) and
D is the moisture diffusivity (m2/s). With constant D and ps. Eg. ( I ) can be further reduced to:
dX
dt
d . dX
( 2)
where Deff is the effective moisture diffusivity. Under the assumptions of one-dimensional
moisture movement, no volume change, uniform initial moisture distribution throughout the
sample, and negligible external resistance, the analytical solution of Eg. (2) is as follows
(Crank. 1975):
• _ X{t) —X e
4
X =
x* - X, = ^«t=l F exp
(3)
Rz
where X(t) and Xe are the average and the equilibrium moisture content (kg water/kg solids).
b„, n= l,2.... are the roots for Bessel function of first kind of zero order, and Rc is the average
radius of the cylinder (m) during a duration of drying test under consideration. Further
simplification is often made by using only the first term of Eg. (3). which leads to the widely
used slope method expression:
x
X(t)-Xr
4
= -------= r=-exp
x0-x.
(4)
b\
Reduction from Eq. (3) to (4) requires special precaution, because significant errors
may be introduced by using only one term of the series solution. It is important to determine the
conditions under which the infinite terms in the analytical solution can be reduced to the first
term with a reasonable accuracy. Pabis and Henderson (1961) proposed that when the drying
time for a slab is greater than l.2L2/(irD), where L is the thickness of the slab, the first term in
122
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equation (3) will predominate. A commonly used criterion for applying equation (4) is X* < 0.6
(Perry etal.. 1984; Zogzas and Maroulis. 1996).
An iterative technique was developed in this study to determine number of terms
needed for the convergence of Eq. (3) at different moisture ratio X*and drying time t. The
procedure is illustrated in Figure 2. For the nth term of Eq. (3). Newton - Raphson iteration was
used to obtain a converged
In order to estimate the number of terms in Eq. (3) needed for
a diffusivity
begin
R ., X * ( 0 .I 5
a n d
K 0 .8 3
to
to
6
0 .8 ) .
h r)
use Newton-Raphson method to solve
for Dn and Dn+t for n o r n+l terms from eqn. (3)
no
n + I => n
y e s
term =n
end
Figure 2. How diagram for the convergence analysis of the series
solution of the Hck’s second law
123
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with acceptable error, the diffusivity from the nth term expression of equation (3) was
compared with the diffusivity of a n+l term expression. If the relative error (Defrtn> - Deffm^nV
is less than 1%. the iteration was stopped and the n term expression was used as the
calculation formula for diffusivity estimation. The result of analysis is given in Figure 3. From
Figure 3. it can be seen that the terms needed for a converged Deff with a relative error of less
than 1% change with dimensionless moisture ratio X* = ( X(t) - X^)/(X0 - X,.). Since four terms
are needed at X* = 0.6. the commonly used criterion of X* < 0.6 for using the first term to
estimate the moisture diffusivity does not satisfy the conditions of this research. The condition
for satisfying the slope method is X* < 0.3. It is interesting to note that the drying time does not
have a direct influence on the convergence of equation (3) at least in the time frame designated
in the numerical test (0.83 to 6hrs)
Figure 3. The terms needed for a converged moisture diffusivity with a relative error
of less than I%
124
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Results and Discussions
The data recorded by TGA are plotted in the form of percentage weight loss vs. heating
time. Moisture contents vs. drying time curves were developed accordingly. A typical drying
curve is characterized by two falling rate periods with no apparent constant rate period (Figure
4). The second falling rate region exhibits a parabolic type profile which may correspond to a
quasistatic surface mass flow condition (Moyne et al.. 1987). A drying rate curve of this kind
suggests that the internal resistance is the major rate limit during the drying (Khraishen et aL.
1997). Roman et aL (1979) in a desorption test with single-piece apple of I to 3 mm thickness
produced similar water desorption curves. The drying curves reported by Sankat et aL. 1 1996)
for banana slices, and Pezzutti and Crapiste (1997) for garlic were also consisted of two
different drying rate regions.
The semi-log dimensionless moisture ratio -ln(( X (t)-Xe)/(Xo-Xe)) vs. drying time plot
is shown in Figure 5. Two well-defined falling rate periods, each corresponding to an
approximately constant slope, can be distinguished. It is especially true for the lower
temperatures (60 and 80 °C). In the case of a constant slope drying curve, a constant diffusivity
can be determined (Adu and Otten. 1996). A linear regression was used to estimate the
effective diffusivity for each section. Because the slope method is applicable when the
dimensionless moisture ratio X* < 0.3. only the data satisfying this condition was used to
produce the slope for the 1st falling rate period. The diffusivity coefficient in the 1st falling rate
period is about one magnitude higher than the one in 2nd falling rate period. For the four
temperature levels, the average Defr ranges from 3.2 x 10‘7 to 7.9 x 10'8 nr/s for 1st falling rate
period while 3.8 x IO'8 to 4.7 x IO'9 m2/s for 2nd falling rate period. The literature values of
diffusivity data for fruits and vegetable drying with two sections are compared in Table I with
the data obtained in our study. It is obvious that in some cases the moisture diffusivity in the 1st
falling rate period is substantially higher than that of the 2nd falling rate period, as indicated by
the work of Pezzutti and Crapiste (1997) and Simal et aL (1996). While the difference of the
diffusivities for potato reported by Khraishen at al. (1997) was less significant.
125
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6
0J5
0.25
4
0.20
drying rate
0.10
0.05
moisture content
0.00
o
0
3
10
15
25
20
30
35
40
45
Drying time (min)
ti
5. Moisture content and drying rate as functions of drying time at 100 °C
s
7
-In( X-Xc)/( X«-Xc)
6
4
too ° c
80 °C
60 °C
1st falling
rate period
i
2nd falling
rate period
0
0
20
40
60
80
D ry in g tim e (m in )
Figure 4. Semi-log drying curves for four temperatures
126
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Drying rale UIX/ill)
Moisture conicnl (db)
0.30
Table I. Diffusivity values for the 1st and 2nd falling rate period.
Deft rrT/s
De,f m 7s
M aterial and
Ist falling rate period
2nd falling rate period
M ethod
Khnushen et a l
40 - 60 °C
40 —60 “C
hot air dried
(199T>
(3 .1 6 -6 .1 7 ) x l 0 ',Q
(2 3 3 -7 .0 6 ) x 10'10
potato
Pezzutti and
3 7 -6 2 .2 °C
45 - 75 °C
hot air dned
Crapiste (1997)
(1 3 4 - 3.45) x LO’10
(3.37-5.85) x 1 0 “
garlic
Simal et a l
so -g o ^ c
30 - 90 “C
hot air dned
(1996)
(1 .6 0 - 2.17) x 10-’
638 x 10'10 - 5.94 x 10 n
grape
Lomauro et a l.
25 JC
25 °C
sorption of freeze-
I 1985)
7.4 x 10‘,:
Roman er al..
30 JC
30 “C
(1979)
15 7 x 10'10
4.92 x 10 11
present work
6 0 - 120 “C
6 0 - 120 °C
TGA dried
7.9xt0'8- 3.2xI0'7
4.7xI0'4- 3 .8xl0'8
apple
Reference
1.4 x [O'12
dried turnip
apple desorption
Figures 6 and 7 show the diffusivity data for the 1st and 2nd falling rate period,
respectively. As expected, a steady increase in moisture transport ability with increasing
temperature was observed for both drying periods. Temperature dependence of the effective
diffusivity followed the Arrhenius type relation:
(D „)i : =1.19x10-' « p ( - « 2 |j d )
r 1 = 058
(5>
700 t 9
( D .„ ) ^ = 8 2 J x I 0 - e x p l- - ^ F )
r; = 058
,6)
where R is the ideal gas constant in fcJ/mol-K and T is the absolute temperature in K. The
activation energy values obtained from Eq (5) and (6) are 63.6 kJ/mol for the 1st falling rate
period and 78.8 kJ/mol for the 2nd falling rate period. Singh et a l (1984) reported activation
energy of 44 to 89 kJ/mol for 0.0 to 13 MC (dB) and Luyben et a l (1980) reported 51 to 110
kJ/mol for MC (db) range of 0.05 to 2.0. The effect of temperature on effective diffusivity for
two
127
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2 n d
fa llin g
ra te
p e r io d
Effective diffusivity n r / s
10-°
V Z Z fo
1 s t fa llin g
ra te
p e r io d
IO-7
10^
IO’1*
40
60
80
100
120
140
Heating temperature °C
Figure 6. Moisture diffusivity in Red Delicious apples in the wet zone and dry zone
periods of drying at four temperatures
-12
-14
Ist falling rate period
-16
~
-18
-20
2nd falling rate period
-22
o .(
0.0026
0.0028
0.0030
0.0032
l/T (1/ k)
Figure . Arrhenius-type temperature dependence of the moisture diffiistvitv in Red
Delicious apples
128
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falling rate periods is shown in Figure 7. The Arrhenius-type correlation is also applicable to
diffusivities at temperature levels above 100°C. Boiling point elevation at low moisture content
may be responsible for this phenomenon. It is reasonable to postulate that a combined liquid
and vapor transport mechanism instead of vapor diffusion is still prevailing at these
temperatures.
The radius reduction of apple samples during the drying is correlated to the moisture
content change by a linear equation:
R,0 ~ R = ~ 0.023 + 0268(X 0 - X)
r z = 053
(7)
where Rco is the initial radius, and Rc is the measured radius by talcing a measurement
periodically of the apple cylinder samples. Equation (7) indicates that the shrinkage of apple
samples is proportional to the moisture loss. Similar relationship was reported by Sjoholm and
Gekas (1995) for apple slab shrinkage during drying.
Literature data on the moisture diffusivity of apples have been summarized by Gekas
(1992). Zogzas et al. (1994). and Zogzas et al. (1996). A comparison of the diffusivity
coefficients of present work with literature is tabulated in Table 2. The moisture diffusivities
from previous works probably only focused on the 2nd falling rate period based on the
magnitude of the diffusivity values and the tested moisture content ranges. As mentioned
before, the moisture diffusivity is influenced by factors as the moisture content, the
pretreatment, the processing temperature, the experimental technique, and the analysis method.
It is difficult to compare values from different research groups when those factors are not
identical. Therefore, Table 2 only serves as a reference to indicate the magnitude of the data.
For high temperature diffusivities. no directly comparable data are available. Figure 8 provides
a comparison using the literature data obtained with the drying curve method and analyzed with
the slope method or simplified solution for the Fickian equation. The 95% confidence line for
the regression covered all the data except that of Zogzas and Maroulis (1996), demonstrating
the rationality of the result.
It is of interest to examine the transition period between the 1st and the 2nd falling rate
periods. During this transition, there was possible a change from porous tissue structure to an
129
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T ab le I, A p p le diffusivity data
T e m p e r a tu r e
nc
66
30
66
70
71
30
3 0 -7 0
15-45
25
3 0 -7 0
24
5 0 -8 0
60
80
100
120
D„,i x 10**
mVs
6,4
0,005-0.009
0,02-0.07
0,09-0,7
l.l
3.617
1.6
0 .0 4 9 '
0,257-’
0 .0 8 -3 .5
0 ,0 0 4 -0 .1 7 3
0 .0 0 4
0 ,0 1 -0 .3
8,3
0 ,7 4 -0 .9 5
0 .0 2 -2 .3 5
1 .19-2,97
0 ,4 6 -3 ,6 6
4 .7 '( 7 9 .6 ’)
1 1 .|'( I 2 5 .( ) 3>
I6 .K '(2 5 3 .0 >)
3 8 ,l '( 3 l 8 .( ) J)
A p p le
C u l tiv a r
—
M C ( d .b .)
g /g
—
M c In to sh
0 ,1 2
M c In to sh
G ra n n y S m ith
P re tr e a lm e n t
—
first falling
rate p e rio d
air-d ried
p u ll-d rie d
fre ez e-d ried
h o t-air d rie d
sul filed
h o t-a ir d ried
G ra n n y S m ith
G ra n n y S m ith
—
—
--
—
—
0 .0 3 -1 .5
< 0 .1 3
--freeze d ried
—
A n a ly s is
m e th o d
the slo p e m eth o d
S a m p le
g e o m e tr y
--
so rp tio n
k in e tic s
se rie s so lu tio n
ol P ic k 's
law '
2'"'
slab
Saravacos (1967)
2nUlaw
slab
slab
Uabuzn and Simon 11970)
Roslcin v ia l. (1974)
—
d ry in g m eth o d
—
so rp tio n
kin etics
d ry in g m eth o d
d ry in g m eth o d
so rp tio n
k in e tic s
slo p e m eth o d
slab
Alzam ora (1980)
Rom an v ia l. (1979)
re g u la r reg im e
re g u la r reg im e
first 6 0 te rm s in the
s e rie s so lu tio n o f
P ic k 's 2 ml law
sp h ere
slah
l.uybcn vi al. (1980)
Singh vi a U 1984)
slab
l.o m a u ro v ia l. (1985)
d ry in g m eth o d
R ed d e lic io u s
1st fallin g
rale p erio d :
0 3 5 .-6 .0
2nd falling
rule p erio d :
0 .0 1 -0 .0 3 5
P ic k 's
Saravacos ami Charm
(1962)*
—
d ry in g m eth o d
d ry in g m eth o d
R ed d e lic io u s
R e fe re n c e
E x p e r im e n ta l
te c h n iq u e
d ry in g m eth o d
(hcrm ogrnvim etric a n a ly sis
I: 2nd falling rate period; 2: 1st falling rate period; * values cited from Gekas (1092)
M otarjemi (1988)*
th e fin ite d iffe re n c e
m e th o d for d ry in g
e q u a tio n s
m o d el
m o d el 2
slo p e eq u a tio n
P ag e eq u a tio n
the slo p e m eth o d
slab
M cCarthy ami Perez
(1991)
c y lin d e r
Zogzas and
M uroulis(|996)
cy lin d e r
present work
1
\r. io-r
c u rre n t study (d ry zo n e)
r»
>v
95% confidence tine
M cCarthy and P erez (1 9 9 1)
S aravacos and
>
R ostein e t al. (1 9 7 4 )
Zogzas and Maroulis I I996i
0.0024
1143.7°C)
0.0026
( 11 t .6JC)
0.0028
(S4.I°C)
0.0030
(60.3°C)
0.0032
(39.5°C)
0.0034
<2I.I°C>
0.0036
t4.8°C)
I/T ( I/K)
Figure 8. Comparison of the moisture diffusivities from this study with the literature values for
apples. The 95% confidence bands are for the means of all the data shown in the graph
7
4 .0
6
transition
zone
so 3.5
W
O
4 *
- In
3
so
a 3‘° ' 1
2
co
2
sample radius
~d
3
§ 15
C/1
I
moisture content
0
0
10
20
30
40
50
Drying time (min)
Figure 9. Moisture content, drying rate and sample radius in different drying regions
131
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increasingly non-permeable structure. The shrinkage might have caused a denser and
tougher structure which might increased the resistance to internal moisture movement
(Sankat et al.. 1996). The sugar in a glassy state might also caused a decrease in diffusion
(Rahaman and Lamb, 1991: Xiong etal.. 1991).
The higher values of moisture diffusivity found in our work, compared to the
literature data, may be experienced by the drying conditions in the TGA apparatus. The
rapid heating may have caused considerable expansion (puffing) of the small samples,
resulting in rapid evaporation and vapor diffusion.
Case-hardening is another possible explanation for the occurrence of 1st and 2nd
falling rate periods. It was noticed in the present work that the shrinkage nearly stopped
when a layer of crust was formed. It was at this point that a transition from 1st to 2nd
falling rate period occurred. Figure 9 includes the drying curve, a curve based on the
slope method, together with the shrinkage measurement to demonstrate transition regions.
Case hardening is a common phenomenon during drying of food polymers (Achanta and
Okos. 1996). The formation of the crust has been related to the glass transition
temperature Tg of the food polymer. Achanta and Okos (1996) postulated that during the
rapid drying the moisture loss at the surface can not be compensated by the internal
moisture so that the surface moisture content drops to such a value that a transition of
rubbery to glassy occurred.
Conclusion
The moisture diffusivity coefficients of Red Delicious apple tissues at 60.80. 100
and 120°C were obtained using a thermogravimetric analysis technique. The slope
method was used to analyze the drying data. It was found that under the experimental
conditions of the present work, the criterion for applying the slope method is when the
dimensionless moisture ratio X* < 0.3. The temperature dependence of the moisture
diffusivity can be described by an Arrhenius-type equation. The shrinkage during the
drying was found to be proportional to the moisture loss. Two well-defined drying
periods ( Ist and 2nd falling rate periods) with different drying rate were identified for all
the tests. The average diffusivity De{f, for the four temperature levels tested ranges from
132
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3.2 x IO'7 to 7.9 x 10"8 m2/s for the 1st falling rate period and 3.8 x 10'8 to 4.7 x lO'1*nr/s
for the 2nd falling rate period. The diffusivity obtained compared well with the literature.
Acknowledgment
We acknowledge the financial support from the IMPACT Center of Washington
State University and the Washington State Agricultural Research Center. We thank
Leonard Henscheid for assistance with the TGA. and Tree Top Inc. for donation of
evaporated diced apples.
References
t. Achanta.S.. Okos.M.R.. 1996. Predicting the quality of dehydrated foods and
biopolymers- Research needs and opportunities. Drying Technol.. 14(6) pp. 13291368.
2. AduJ3.. Otten.L.. 1996. Diffusivity characteristics of white beans during microwave
drying. Agric. Engng. Res.. 64 pp. 61-70.
3. Aizamora.S.M.. ChirifeJ.. ViollazJ>.. VaccarezzaX.M.. 1980. Heat and mass transfer
during air drying of avocado, in Development in Drying. Mujumdar. A.S. (ed).
Science Press N. J.. pp. 247-254.
4. CrankJ.. 1975. The Mathematics of Diffusion. 2nd ed.. Oxford University Press.
Oxford.
5. De Elvira.C.. 1993. The use of alternating direction implicit methods to model
diffusion phenomena in elliptic products. /. Food Eng.. 19 pp. 159-170.
6. Gekas.V.. 1992. Transport Phenomena o f Foods and Biological Materials. CRC
Press.
7. Karathanos.V.T.. Villalobos.G.. Saravacos.GJD.. 1990. Comparison of two methods
of estimation of the effective moisture diffusivity from drying data. J. Food Sci..
55(1) pp. 218-231.
8. Khraishen,M.A.M.. Cooper.T.J.R.. Magee.T.R.A.. 1997. Transport mechanisms of
moisture during air drying processes. Trans. IChemE. 75 C pp. 34-40.
133
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9. Kiranoudis.C.T.,
MarouIis.Z.B..
Marinos-KourisJ)..
Saravacos.
G.D..
1993.
Estimation of the effective moisture diffusivity from drying data. Application to some
vegetables. 6th International Congress on Engineering and Food. 1993 May. Chiba.
Japan.
10. Labuza.T.P.. SimonXB.. 1970. Surface tension effect during dehydration. I Air
drying of apple slices. Food Technol.. 24 pp. 712-715.
11. Lomauro.CJ.. Bakshi.A.S.. Labuza.T.P., 1985. Moisture transfer properties of dry
and semimoist foods, J. Food Sci.. 50 pp. 397-400.
12. Luyben.K.C.A.M.. OtiemanJJ.. Bruin.S.. 1980. Concentration dependent diffusion
coefficients derived from experimental drying curves, in Drying'80. Vol. 2.
Mujumdar. A.S. (ed.). Hemisphere Publishing Corporation, pp. 233-243.
13. Marinos-KourisJ).. MarouIis.Z.B.. 1995. Transport properties in the drying of solids,
in Handbook o f Industrial Drying, Mujumdar A.S.(ed.), Marcel Dekker. New York,
pp. 113-159.
14. McCarthyXJJ.. Perez.E.. 1991. Model for transient moisture profile of a drying apple
slab using the data obtained with magnetic resonance imaging, Biotechnol. Prog.. 7
pp. 540-543.
15. Moyne C.. Roques M.. Wolf. W.. 1987. A collaborative experiment on drying beds of
glass spheres, in Physical Properties o f Foods-2. R. Jowitt et a/(eds). Elsevier.
London, pp. 27-54.
16. OkazakLM.. ImakomaJI.. Yoshida.M.. Legros.M.. 1995. Principle and applications
of drying characteristic functions. Drying Technol.. 13(5-7) pp. 1113-1131.
17. Pabis,S., Henderson.SXI.. 1961. Grain drying theory, II A critical analysis of the
drying curve for shelled maize. J. Agric. Eng. Res., 6(3) pp. 272-277.
18. PelX.. BrockenJH., 1996, Determination of moisture diffusivity in porous media
using moisture concentration profiles. Int. J. Heat & Mass. Transfer. 39 pp. 12731280.
19. Perry.R.H.. GreenJD.W.. MaloneyJ.O..
1984, Perry's
Chemical Engineers’
Handbook. McGraw Hill, New York, pp. 15-32-15-45.
20. Pezzutti^A., Crapiste,GJI.. 1997. Sorptional equilibrium and drying characteristics of
garlic, J. Food Eng.. 31 pp. 113-123.
134
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
21. RahmanJvLD.S.. LambJ.. 1991. Air drying behavior of fresh and osmotically
dehydrated pineapple. /. Food Process Eng.. 14 pp. 163-171.
22. Roman.G.. RosteinjE.. Urbicain.MJ.. 1979. Kinetics of water vapor desorption from
apples. /. Food Sci.. 44( I) pp. 193-197.
23. RosteiniE.. Laurai\A.. De Cemborain.M.E.. 1974. Analytical prediction of drying
performance in nonconventional shapes. J. Food Sci.. 39 pp. 627-631.
24. Sankat.C.K.. Castaigne,F.. Maharaj.R.. 1996. The sir drying behavior of fresh and
osmotically dehydrated banana slices. Int. J. Food Sci. and Technol.. 31 pp. 123-135.
25. Saravacos.G.D.. Charm.S.E.. 1962. A study of the mechanism of fruit and vegetable
dehydration. Food Technol.. Jan. pp. 78-81.
26. Saravacos.GJD.. 1967. Effect of the drying method on the water sorption of
dehydrated apple and potato. J. Food Sci.. 32 pp. 81-84.
27. Saravacos.G.D.. Raouzeos.G. S.. 1984. Diffusivity of moisture in air-drving of starch,
in Engineering and Food. Vol. I. McKenna. B. M. (ed.). Elsevier Applied Science
Publishers. New York. pp. 499-507.
28. Schoeber.WJ.A.H.. Thijssen.H.A.C.. 1977. A short-cut method for the calculation of
drying rates for slabs with concentration-dependent diffusion coefficient. AIChE
Symposium Series, 73( 163) pp. 12-24.
29. Simal.S.. MuIet.A.. Catala.P.J.. CanellasJ.. Rossello.C.. 1996. Moving boundary
model for simulating moisture movement in grapes. J. Food Sci.. 61( 1) pp. 157-160.
30. Singh.R.K.. Lund.D.B.. BuelowJ^.H.. 1984. An experimental technique using regular
regime theory to determine moisture diffusivity. In Engineering and Food. Vol. I.
McKenna. B. M. (ed.). Elsevier Applied Science Publishers. New York. pp. 415-423.
31. Sjoholm, I.. Gekas. V.. 1995. Apple shrinkage upon drying. /. Food Eng.. 25( I ) pp.
123-130.
32. TangJ.. Sokhansanj.S.. 1993. Moisture diffusivity in laird lentil seed components.
Transaction o f ASAE. 36(6) pp. 1791-1798.
33. Tong.C.H.. LundJXB.. 1990. Effective moisture diffusivity in porous materials as a
function of temperature and moisture content. Biotechnol. Prog.. 6 pp. 67-75.
34. Vagenas.G.K.. Karathanos.V.T.. 1993. Prediction of the effective moisture diffusivity
in gelatinized food systems. J. Food Eng.. 18 pp. 159-179
135
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35. XiongJC.. Narsimhan.G.. Okas.M.R.. 1991. Effect of composition and pore structure
on binding energy and effective diffusivity of moisture in porous food. J. Food Eng..
15(3) pp. 187-208.
36. Zogzas.N.P.. MarouIis.Z.B.. Marinos-KourisJX 1994. Moisture-diffusivity methods
of experimental determination. A review. Drying Technol.. 12(3) pp. 483-515.
37. ZogzasJs.P. and Maroulis.Z.B.. 1996. Effective moisture diffusivity estimation from
drying data. A comparison between various methods of analysis. Drying Technol..
14(7&8) pp. 1543-1573.
38. Zogzas.N.P.. Maroulis,Z.B.. Marinos-KourisX).. 1996. Moisture diffusivity data
compilation in foodstuffs. Drying Technol.. 14( 10) pp. 2225-2253.
136
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Chapters
DETERMINATION OF DIELECTRIC PROPERTIES OF APPLE TISSUES AS A
FUNCTION OF MOISTURE CONTENT AT TWO TEMPERATURES
ABSTRACT
In this study the dielectric constant e' and loss factor e" of Red Delicious (Maius domestica
Borkh) apple tissues were measured as a function of moisture content (4 to 87.5%. wb) at two
temperatures (22°C and 60°C). The measurements were conducted using the open-ended
coaxial line probe technique. The influence of sample size and sample thickness on the
measurement accuracy was analyzed. The dielectric relaxation spectra over a frequency range
of 45 MHz to 3 GHz was analyzed to delineate the influence of different dispersion
mechanisms on the dielectric behavior of samples at different moisture contents and
temperatures. The results indicated that when moisture was relatively high (-70%. wb). free
water dispersion and ionic conduction were mainly responsible for the loss mechanism. At
medium moisture (-23%. wb). ionic conduction played a major role, affecting dielectric
properties. At low moisture content (-4%. wb), bound water was the major dispersion
mechanism. A reduction in moisture depressed dielectric properties. A transition region was
found in e" curves that corresponded to the transition from bound water to free water. When
free water relaxation was less important, an increase in temperature resulted in an increase in
dielectric properties. However, at higher moisture content, the temperature response was
determined by the contributions of free water, ionic conduction, and bound water. This
response was difficult to predict. The results of this study compared well with Mudgett et al’s
(1980) work. Penetration depth increased as moisture decreased. A polynomial equation was
used to correlate both the moisture and the temperature effects on dielectric properties.
137
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INTRODUCTION
Microwave heating is a rapid heating technique. It has found industrial applications in
cooking, tempering, baking, reheating, curing, freeze-drying, and dehydration of food products.
The heat generation and temperature distribution in a food product when exposed to microwave
radiation can be quantified by knowledge of its complex permittivity (e = £' - je"). The real
component of the complex permittivity, known as the dielectric constant, e'. is related to energy
storage and the imaginary component, the ioss factor, e", is related to . energy dissipation. Both
properties affect the penetration depth of microwaves in foods. In order to understand the
interaction between microwaves and food products and to predict both the heating pattern and
heating history, a knowledge of dielectric properties as influenced by product composition,
temperature, and moisture is indispensable.
Many efforts have been made to understand the influence of food composition,
temperature, and moisture content on dielectric properties at microwave and RF frequencies.
Sun et al. (1995). analyzed literature data in studying the effects of moisture, temperature, and
ash content on dielectric properties for a wide range of fruits, vegetables, meats, and fish at
temperature of 5 to 65 °C and frequencies of 2.400 to 2.500 MHz. They concluded that for
selected meats both the dielectric constant and the loss factor increased with moisture and salt
content. The dielectric constant decreased when temperature increased. They also pointed out
that the loss factor increased with temperature when salt content was high, whereas it decreased
if salt content was low. In their study, protein, carbohydrates, and fat did not significantly
contribute to changes in dielectric properties. Tong et al. (1994) used the cavity perturbation
technique to study the temperature dependency of pea puree at 915 MHz and 2450 MHz at
temperatures between 25 and I25°C. At 915 MHz. the loss factor increased with temperature,
while at 2.450 MHz it decreased with increased temperature until reached a minimum at
temperature between 25 to 75 °C. In a study aimed at using microwaves to surface treat cottage
cheese to prolong shelf life, Herve et al. (1998) measured dielectric properties of cottage cheese
using an open-ended coaxial probe technique at 915 MHz and 2.450 MHz and four
temperatures. Fat content of the cottage cheese was found to play an important role in
controlling the penetration depth.
138
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Comprehensive reviews conducted by Nelson (1973), Kent (1987), and Datta et al.
(1995) provided good sources for dielectric properties for a wide range of food and agricultural
materials. Some of the data compiled in these reviews were measured at different temperatures.
Only a few recent studies were aimed at examining the effects of both temperature and
moisture. Kim et al (1998) performed experiments to measure dielectric properties of flourwater mixture at radio frequency (27 MHz) over a moisture range of 2 to 100%. They
examined the effects of moisture, density, and temperature on dielectric properties using a
parallel plate capacitance technique. They observed an increase in dielectric constant when
moisture and temperature were increased. For the loss factor, however, the response was
complicated as indicated by a moisture and temperature interaction term in the temperature-loss
factor correction. Goedeken et al (1997) conducted a comprehensive study to examine the
influence of temperature (25 to 95°C), moisture (10 to 44%. wb). salt, and specific volume of
pregelatinized bread on dielectric properties, using a transmission line technique at 2.450 MHz.
They found that both z' and z" increased with respect to moisture content. Dielectric constant
was observed to increase when temperature increased from 20 to 65°C then became nearly
constant from 60 to 95°C. The loss factor increased linearly from 25 to 95°C and decreased
when no salt was present.
For fruits and vegetables, dielectric property data relating to temperature and moisture
dependency are scarce and no research has been documented in the literature on the effect of
both moisture content and temperature on their dielectric properties. The application of
microwave energy, on the other hand, is associated with significant temperature and moisture
changes. The object of this research was to determine the moisture content dependency of apple
tissues at room and elevated temperatures. The open-ended coaxial probe technique was used
for this purpose. This technique was selected for the following reasons: I) it provides simplicity
and flexibility in both operation and data processing. 2) the instrumentation is commercially
available: 3) it can cover a wide frequency range in a single measurement; 4) it can provide
adequate accuracy for thermal calculations (Engelder and Buffler, 1991).
139
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MATERIALS AND METHODS
Apple samples
Fresh and evaporated Red Delicious (Malus domestica Borkh) apples were used in the
experiments. The fresh apples were bought from a local grocery and had average moisture
content of 87.5 % (wb). The evaporated diced apples were supplied by TreeTop Inc. (Selah.
WA). They were dried from freshly diced apples of 12.7 x 9.5 x 6.4 mm (1/2 x 3/8 x 1/4 inch)
to 22.4% (wb) in commercial hot air dryers. Both the fresh and evaporated apples were stored
at 4°C before experiments. The fresh apples were used to prepare samples with moisture
contents of 23.8 to 87.5% (wb) while the evaporated apple was used to prepare samples with
moistures below 22.4% (wb).
Sample moisture content control and measurement
Reduction of moisture content for apple samples was achieved by dehydration. For
diced evaporated apples, a microwave and spouted bed combined dryer described in Feng and
Tang (1998) was used. The drying conditions were controlled at a hot air temperature of 70°C
and microwave power density of 2.3 W/g (wb). Fresh apples were sliced and then dried in an
UOP-8 tray dryer (Armfield LTD.. Hampshine. England). The hot air temperature was 80°C
and inlet air relative humidity was 40%. The dried samples were sealed in glass jars to
condition at room temperature for about 24 hours before moisture determination. The weight
change during drying was monitored using a Satorius electric balance (3000g ± 0.01g). The
moisture of samples were determined by drying at 70°C and 13.3 kPa for 7 hours according to a
standard vacuum oven method (AOAC. 1990).
Temperature control and calibration
Two temperatures. 22°C and 60°C. were selected for the dielectric property
measurements. Temperatures higher than 60°C were found to yield an unacceptable change in
structure. The upper temperature in our studies, therefore, was selected as 60°C. For
measurements at 60°C. a NCPCO® Model 630-7 air oven (National Appliance Co.. Portland.
OR) was used to condition the probe. A transparent Perspex sheet of 9.5-mm thickness was
used as the oven door during the measurement. A hole of 90 mm (3.5") diameter was cut into
140
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the plate to allow handling of the sample in the oven during the measurement. The hole was
sealed with a rubber sheet to reduce heat loss when an operators hand placed the sample under
the probe. This plate provided good visibility for sample handling. After moisture reduction
TVt
and conditioning, apple samples sealed in glass jars were submerged in a Digi-Bath ‘ water
bath (Laboratory Devices Inc.. Hollston. MA) to preheat to 60°C. Preheated samples were
quickly removed from the water bath to an air oven for the measurement. Calibration of the
dielectric property measuring system was conducted using the standard air. short, and triple­
distilled water procedure at each moisture and temperature. At 60°C. both the short and the
distilled water were preheated in the air oven, hence, both the calibration and the measurement
were conducted at the same temperature.
Sample size and thickness effect
The effects of sample size and thickness on the accuracy of the dielectric property
determination are best understood by examining the principle of the open-ended coaxial probe.
A schematic of this probe is shown in Fig. I. It consists of an inner conductor and an outer
conductor separated by a Teflon spacer. The inner conductor had a radius of a. The outer
conductor had an inner radius of b and an outer radius of c (Fig. I). The change in the phase of
reflection coefficient at a defined reference plane, which is located at the interface between the
test dielectric and the probe, was measured by a network analyzer. Effects of sample size and
thickness have been studied by analyzing the electric field and energy absorption distribution at
the probe tip (Swicord and Davis. 1981: Anderson et al.. 1986). Anderson et al. showed that a
maximum field intensity occurred at radial distance of 1.2a while another small peak occurred
at 0.98b. The magnitude of the field outside the outer conductor inner radius b was less than
6% of the maximum field. Hence, they concluded that beyond the outer conductor outer radius
c. the field intensity was negligible. This suggests that sample sizes larger than the outer
conductor outer diameter 2c should have negligible effects on the dielectric measurement. An
analysis conducted by Swicord and Davis (1981) also resulted in similar electric field
distribution. They showed that 90% of the energy from the probe was absorbed in lossy
material within a hemisphere with radius of b. The experiments conducted by Seaman et al
(1989) confirmed the confined aperture field distribution. The probe used in this study has a
141
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dimension of a = 0.45 mm, b = 1.4 mm. and c = 2.4 mm. Therefore, a sample size greater than
2c = 4.8 mm was considered to cause negligible error.
The open-ended coaxial probe technique requires a sample thickness large enough to
simulate a slab which is electrically semi-infinite in size (Stuchly and Stuchly. 1980). Previous
studies have shown that a sample with a thickness equal to the outer conductor inner diameter
2b can be considered as a semi-infinite large body (Fan et al.. 1990). This was supported by
observation of Anderson et al. (1986) with the dielectric measurements of water sample of
finite thickness. They observed that little field extended beyond six times the inner conductor
radius, a. Seaman and Seals (1991) suggested that for low loss fruit skin, the effective thickness
was 2 to 5mm for a probe with outer conductor inner diameter 2b = 2.2 mm. It is. therefore,
reasonable for us to assume that a sample thickness of 2c = 4.8 mm is enough for a
measurement with negligible error. An experiment was conducted with evaporated diced apple
to further ascertain the effect of thickness. Two extreme conditions were considered: a dice
backed by metal and a dice backed by plastic foam which represented air. These arrangements
represented two extreme conditions in the dielectric measurements (Anderson et al.. 1986). The
diced apples were dried with the microwave and spouted bed combined dryer and had a
moisture content of about 4% (wb). Three measurements were conducted for each arrangement.
The results from dielectric properties at 2.450 MHz are given in Table I. Statistically, no
significant difference was found between two treatments and the means from metal and foam
backings had small relative errors (<5%). This indicated that with a single piece of evaporated
diced apple, which had a thickness of 3.3(±0.7) mm. the maximum error caused by the
thickness effect was less than 5%.
Table I. Comparison between measurements with metal base and foam base.
Frequency
(MHz)
Dielectric
Properties
2450
€
£"
Foam
backing
(mean)
1.425
0.032
Metai
backing
(mean)
1300
0.040
Relative
Error %
ANOVA
5
2
Not significant
Not significant
142
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sample
Open-ended
coaxial line probe
\
|
J ^
2b
Teflon
.»/•
*/•*> *> '
B */•*••^ •>•%•>•s•%<
_ 4 H y > tV V .^ a.y V ^ t V
I t* V ^ » * V A * V > * V A * S '
I*%•/• ••• »s*s • s • s • %•••• s «
I•/* • •*•/• t *
/•^y» *s •*••> • s <
<?<?<?<?<?<•<•/?/?<••
?<•<?<?<;<•<•<?<•<•■
.<
»s»%
• s • *»•/• • %•/» ••••/• 1
/?<?<?<?<?<?<?<?/?<•■
Figure I. Th open-ended coaxial line probe configuration
Dielectric property measurement
A HP 85070B open-ended coaxial probe (Hewlett Packard. Fullerton. CA) was used in
the dielectric property determination. A HP 8752C vector network analyzer was used to
measure the change in reflection coefficient from the probe, which is related to the permittivity
of the sample (Tran et al. 1984). The dielectric measurements were conducted for samples with
three moisture content ranges: fresh apples (87.5% wb), dried slices from fresh apples (23.8 to
80.7% wb). and dried dices from evaporated diced apples (3.8 to 22.4%. wb). A different
procedure was used for measurement of the samples with different moisture contents and
geometries.
(I) For fresh samples, measurements were made by cutting apple into halves and directly
placing them in contact with the probe. Five measurements were made. The mean and the
standard deviation were reported.
143
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(2) For slices dried from fresh apples, five slices were measured at each moisture content by
direct contact with the probe. Five readings were taken from each slice. The means and
standard deviations were reported. The thickness effect was considered negligible since dried
slices had a thickness of 8.0 to I L.5 mm when moisture was reduced to 23.8% (wb). Slices
shrank as moisture was removed, which resulted in a convex surface at both sides of a slice. To
lessen the shrinkage, comers of a slice were cut diagonally to a depth of about 3-5 mm before
drying to release shrinking strain. During the dielectric measurement, a small amount of
pressure was applied manually to eliminate the air gap and ensure good contact of the sample
with the probe. Since dried slices were not perfectly flat and had a crumpled surface, the
pressure helped to diminish the effect of these surface defects.
(3) For diced apple, measurements were made on a single apple dice backed by an dice-cake.
compressed from dices of apples at about same moisture content using a Carver Laboratory
Press (Fred S. Carver Inc., Sumit. NJ). Since the press was manually operated, there was some
variation in the thickness of the cakes. Cakes hence had a thickness of 9.8-12.2 mm. At low
moisture content, two surfaces of a dice were gently trimmed using a sharp blade to provide a
good contact with both the probe and the cake. At each moisture content. 13-16 pieces of dice
were used for dielectric property measurements. The mean and the standard deviation were
reported. Evaporated diced apple had a size of 9.2 (±1.0) x 5.8(±0.9) x 3.3(±0.7) mm. The
contact area of the dice with the probe was large enough compared to 2c = 4.8 mm. The
thickness of a single dice plus a cake was 13.1 to 15.5 mm and was much greater than 2c = 4.8
mm. Hence, the errors in a dice-cake backed single dice measurement caused by the size and
the thickness effects can be ignored.
RESULTS AND DISCUSSIONS
Dielectric relaxation spectra (DRS)
Dielectric relaxation spectrum analysis is an effective method to study the properties of
water in food products by analyzing the frequency dependency of the dielectric properties. It
has been used to study the hydration of some foods and food components (Tsoubel et al.. 1995:
Lu et al., 1998). In RF and microwave frequencies, dielectric properties of foods responsed to
frequency change according to three major mechanisms; namely, the p, 5. and y dispersions.
144
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The p dispersion corresponds to interfacial polarization (Maxwell-Wagner dispersion) which
usually occurs around 0.1 MHz. The 8 dispersion is caused by bound water dipole reorientation
which centers at about 300 MHz. The y dispersion is due to the reorientation of free water
dipoles and its peak is located at about 20 GHz (Lu et al, 1998; and Kuang and Nelson. 1998;
Tang. 1999). A schematic presentation of the dispersions was given by Tang (1999) (Fig. 2). It
is clear that the dielectric-frequency interaction of a food system will be determined by the
combination of different dispersion mechanisms that dominate certain frequencies.
The dielectric relaxation spectra of Red Delicious apples at three moisture contents and
two temperatures are shown in Fig. 3. In Engs. 3a-c. comparisons were made among samples at
60aC for different moisture contents. Figs. 3d-f show a similar comparison at 22°C. Because of
the difficulty in obtaining sample moisture from different drying batches, dielectric properties
were compared at close moisture contents.
Ionic
conductivity
Effect of increasing
“*■ temperature
Free water (y)
Maxwell-Wagner
Effect (p)
0.1 MHz
100 MHz
Effect of
increasing
temperature
20,000 MHz
Log ( f )
Figure 2. Dielectric dispersion of bound water, free water, and ionic conduction (Tang, 1999).
145
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
At high moisture content, e.g.. Fig. 3a and 3d. a gradual reduction in e' and a U-shape in
e" can be observed. This agrees with previous studies for fresh fruits and vegetables (Seaman
and Seals. 1991: Nelson et al.. 1994; Ikediala et al., 1999). The gradual reduction in e' might
have been caused by the transition from the static dielectric constant £* to the e_ (the low
boundary of the dielectric constant). In a single dispersion system (pure water), this transition is
sharp while in multi-dispersion systems, such as foods, the combination of the bound water 15)
relaxation, free water (y) relaxation, and ionic dispersion make the transition less obvious. The
U-shape frequency response in e" can be best explained by the superposition of ionic
conduction and free water dispersion at the frequency of our interest (45 MHz to 3 GHz) (Ftg.
2). Nelson et al. (1994) measured dielectric properties of three apple caltivars at 23°C and
observed that the minimum value for the U-shape in e" occurred at about I GHz. Ikediala et al.
(1999) presented a curve for Red Delicious with similar frequency corresponding to the
minimum e" value. The minimum e" in our study was observed at IGHz (Fig. 3d) at 22°C. It
shifted to about 2 GHz at 60°C (Fig. 3a). This shift can be related to the temperature response
of both the free water dispersion and the ionic conduction. To examine the temperature effect
of the free water dispersion, we first looked at the response of pure water to temperature
change. For Debye type relaxation (pure water), the relaxation time t and the viscosity of the
water can be related by (Tang. 1999).
t =V
3v
kT
and
—
v oe e RT
(I)
146
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
40
30
(a)
?
3 O oc®afflaa o
e'
(d)
=
a = 0 °0:=a5ste
20
V
20
30
V
0
25
in
60“C
MC = 69%
Jr?^*xsss5SS&
22°C
MC = 70%
£->
”
e” 0
14
20
(b)
°
12
10
(e)
15
15
3
5
c
10
*
5
0
8
° =0
_
6"
v ^^VAMWd3ii555S5/1
MC = 22%
8
6
4
22°C
MC = 24%
7
7
0
6
3.0
(c)
5
4
c
v
(0
o
0
e’
C O C < ^ I\
2.5
.
o
c
„ r
8’
= cnotrrrrtft'wr:
3
2.0
1.5
1.0
60°C
MC = 4%
le+7
7
_
/ ^
£"
le+8
le+9
Frequency (Hz)
22°C
MC —4%
le+7
~
_
£”
^^^53335555557
le+8
0.5
0.0
le+9
Frequency (Hz)
Figure 3. Dielectric relaxation spectra of Red Delicious apples at three moisture contents and
two temperatures - comparison between e' and e".
147
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I 'u r m c iih ilily
10
where t is relaxation time, v is viscosity. Ea is activation energy. R is universal gas constant. V
is the volume, and k is a constant. From Eq. (I), when temperature increases, viscosity
decreases and relaxation time decreases. The critical frequency for the relaxation peak is at fc =
1/ t. Hence, an increase in temperature shifted the peak of the dipole relaxation to a higher
frequency (Fig. 2). Another contribution was the shift of ionic conduction to higher frequencies
as temperature increased, again due to the reduction in viscosity which led to increased ionic
conductivity. The combination of these two effects resulted in the shift of the minimum in e" to
a higher frequency.
As moisture decreases, s' and e" responded to frequency change in a more complex
manner. The monotonic decrease in e' with frequency continued when moisture was lowered to
- 2 3 (wb) (Fig. 3b and 3e). The U-shape for e". however, was not present at this moisture
level. It is likely that, at this low moisture content, the free water relaxation peak was depressed
due to depletion of free water. Instead, a gradual decrease in e" with frequency was observed,
probably due to the greater influence of ionic relaxation. This trend continued at low moisture
content 4% (wb) (Fig. 3c and 3f). At this stage, bound water might be the main relaxation
mechanism. It is interesting to notice the peak in e" at 60°C and 4% (wb) (Fig. 3c) centered at
about 1.5 GHz. Harvey and Hoekstra (1972) observed a peak at 4 GHz and one at 0.3 GHz. for
second-layer and monolayer water, respectively, in low to mediate moisture lysozyme. For the
same reason, the second-layer water in dried apples might be responsible for the peak in s" at
1.5 GHz at 60°C. This peak was not observed at 22°C (Fig. 3f). This suggests that the bound
water at additional-layer might have higher mobility at 60°C. The peak seems to have no effect
on the loss factor e" (Fig. 3c). The low values of e" might have obscured the change and made
it undetectable.
The effects of temperature change on dielectric properties of apples at different
moisture contents are presented in Fig. 4. There are four factors at frequencies of our interest
(45 MHz to 3 GHz) that could affect the temperature response of dielectric properties. Those
factors include the ionic conduction, the free water dispersion, and the bound water dispersion,
as shown in Fig 2. When temperature increases they all shift toward higher frequencies.
Another factor is the negative response of e s and
to temperature increasing. Kaatze (1989)
148
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
developed the following expressions for the temperature dependency of e* and e_ of pure
water.
£ _ i q U * > ■ « < » -1 w w r-rn is))
(2 )
= 5.77 - 0.0274x (T - 273.15)
36
o
° o
33
MC = 69%
©0
I
(d)
MC = 69%
25
32
20
O
V
31
30
o
v
29
15
o
60°C
22°C
10
MC = 70%
28
5
21
18
X
S
cy
30
o
(b)
o
15
21
o
18
(e)
MC = 24%
°Q
15
°CH.
MC = 24%
12
V
9
0
V
6
MC=22%
t7
MC = 22%
o
(f)
3
6
(c)
MC = 4%
v
0 _
u O C fi-n iiiim iii)
v v v^^35j5jsSac7
!2
9
6
- 4
°
■ 3
° °ooc& S3!\ i
v
MC = 4%
. 2
MC=4%
o
MC = 4% v
le+7
le+8
le+9
le+7
Frequency (Hz)
I
° OQQctoa?mTmn
^ ^ ^©^^3035533557
le+8
0
le+9
Frequency (Hz)
Figure 4. Dielectric relaxation spectra of Red Delicious apples at three moisture contents and
two temperatures-comparison between two temperatures.
L49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.oss I’iicior r"
34
(a)
35
o
A reduction in es and e_ as temperature increases will lower the value of e' and depress
the magnitude of the free water e" peak (Ryynanen. 1995). The shift of free water peak
decreased the dielectric property values while the shift of bound water from low frequency to
relatively high frequency increased the values. Ionic relaxation always increased the values of
both e' and
e".
Observed increases in dielectric properties with temperatures at 22% and 4%
twbxFig. 4b-c. 4e-f). therefore, demonstrated a dominant ionic relaxation mechanism at these
two moisture contents. The increase of the salt concentration as moisture decrease may partially
contribute to this increase at intermediate moisture content (22%. wb) (Mudgett. 1990). The
relatively straight and declining curves at 22% and 4% (wb) also indicated negligible effect of
free water. At moisture content of 70% (wb). the temperature effect was complicated as
indicated by the intersection of curves at two temperatures. This was caused by contributions of
the multi-dispersion mechanisms and is hard to predict.
Moisture content effect
The dielectric constant and loss factor vs. moisture content at two temperatures are
presented in Fig. 5 for 915 MHz and 2450 MHz. In general, both values decreased with
increasing moisture content at these two frequencies. This phenomenon was due to the change
in state of water in apples when moisture was removed. The water in a food can be divided into
three groups (Okos et al.. 1992): Group A is the bound water which is tightly bound to
polysaccharides in the form of H-bond and is called monolayer water: Group B is the water
held in small capillaries, which is known as multi-layer water, and is less tightly bonded: Group
C water is held in intercellular space, or large capillaries which behaviors like free water. The
group B water is usually considered a continuous transition from free water to bound water
when moisture decreases. The effect of the state of water in food on the dielectric behavior is
two fold. First, it determines the ease for the water dipole to respond to the electromagnetic
field change. A transition from free water to bound water translates to a decrease in the
rotational ability of the dipoles and hence a decrease in the dielectric property values (Fig. 5).
On the other hand, this transition will also decrease the ionic activity by reducing the amount of
water to form the ionic solution. Karel (1975) pointed out that the amount of bound water in
foods ranged from 50 to 100 grams of water / kg of dry solids, which corresponds to a moisture
150
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
content of 4.8 to 9.1 % on wet basis. This suggests that when water content is lower than 9.1%
(wb), only bound water remains. At slightly higher moisture, the percentage of free water
increased and the availability of the water to form a solution with salt increased (Mudgett et al..
1980). As a result, ionic conductivity increased. This may be responsible for the sharp increase
in loss factor e" when moisture reached about 25% (wb) (Fig. 5b and 5d).
60
50
12
40
10
8
30
6
20
a
2
to
2450 MHz
CD
2450 MHz
0
60
0
14
•j
50
12
40
10
8
30
6
20
4
2
10
915 MHz
915 MHz
o
0
to
20
30 40 50 60 70
80 90 0
Moisture Content (wb). %
10 20
30 40 50 60 70
80 90
Moisture Content (wb). %
Figure 5. Dielectric properties of Red Delicious apples as influenced by moisture content.
151
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
Other proposals have been suggested to elucidate the positive response of dielectric
properties to moisture change. Since bound water has a static dielectric constant (ej close to
that of ice (Ryynanen. 1995), it is predictable that an increase in the percentage of bound water
will lower the dielectric values. The increasingly dense concentration of sugar in the water
solution in apples when moisture content decreases will cause dielectric property to decrease,
too. This can be proven by tests conducted by Roebuck et al. (1972) with glucose and sucrose
solution. They observed a decrease in both z' and z" when sugar concentration is lower than
50% (wb) at 3 GHz. Organic solids, which have dielectric properties similar to ice (Ryynanen.
1995), will take up more volume as moisture decreases and will also depress the dielectric
relaxation. The incremental increase air space definitely contributed to the low values of both z'
and e". Both e' and z" decreased significantly with decreasing moisture content between 80 and
87.5 % (wb) (Fig. 5). This may be caused by the increase of void ratio when surface water is
removed.
Comparison with literature
Comparison of the measured dielectric properties with previous measurements was
difficult because no data existed in the literature that related dielectric properties in apples to
moisture content prior to this study. Dielectric property data of apples reported by Tran et al.
(1984). Seaman and Seals (1991), and Nelson et al. (1994) studied the frequency response of
fresh apples at room temperature. Dielectric properties of fresh apples at temperatures up to
55°C were measured by Ikediaia et al. (1999) using the open-ended coaxial probe technique.
They observed a slight decrease in both e'and e" with increasing temperature. Some early
measurements were made for potato and carrots at elevated temperatures and a specific
frequency other than what is used today in industry (Bengtsson and Risman. 1971. Ohlsson et
al.. 1974). Mudgett et al. (1980) studied the moisture effect on dielectric behavior of freezedried potato. They used a standing wave measurement system and measurements were
conducted over a wide moisture range (-3% to 80.3%, wb) at 3GHz and 25°C. Our results
compared well with their results at comparable moisture contents (Fig. 6). Discrepancies were
observed at high moisture contents. This may be attributed to the significant difference between
the intercellular space of potatoes and apples, which is an indication of the air space in the
152
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
products. Apples have an intercellular space of 20 to 27% (Khan and Vincent. 1990). while
potatoes have a value of less than 1% (Hudson. 1975). The air trapped in the intercellular space
reduced the dielectric properties of apples. The differences in sugar content, salt content,
frequency, temperature, and measurement technique may also contribute to the difference
between the dielectric properties of two products. For example, the ash content, which is an
indicator for the total salts, is 0.26% for apples while for potatoes it is as high as 0.89%
(Anonymous. 1984). The higher salt content, frequency, and temperature could also be
responsible for the higher values in measured dielectric properties of potatoes.
Penetration depth
Fig. 7 shows the microwave penetration depth (dp) calculated from the measured
dielectric properties using the following equation:
/
dp =
where
/ \0 5
■> \ 0
i+ f£
5 -1-05
-1
(3)
is the wavelength of the free-space. which equals to 122.7 mm at 2.450 MHz and
327.7mm at 915 MHz. The penetration depth of pure water at room temperature is 122.5mm at
915 MHz and 16.8mm at 2.45GHz (Tang. 1999). The penetration depth of microwaves in fresh
Red Delicious (87.5%. wb) was comparable with water at 2,450 MHz at 22°C. However, the
value at 915 MHz was lower than the penetration depth in water. In measuring dielectric
properties at 60°C, we experienced difficulties in heating high moisture apples to elevated
temperatures while at the same time maintaining the structure. The tests at 60°C were then only
made on dehydrated apples with a moisture of up to 68.7 % (wb) (Fig. 7b). At high moisture
contents, moisture had little effect on penetration depth at two frequencies and the tested
temperatures until the moisture content was reduced to about 30%. Below this moisture
content, microwave penetration depth increased sharply with decreasing moisture. This
moisture corresponded well to the sharp change in dielectric properties in Fig. 5. A similar
change in the penetration depth with moisture was also reported by Goedeken et al. (1997) for
153
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
pregelatinized bread. In general, penetration depth increased as both temperature and the
moisture decreased.
v
60
Potato (3GHz. 25°Q
Apple (2.45GHz. 22°Q
50
15
40
u
u
V
V
30
20
10
0
0
20
M
40
o is tu r e
60
C o n te n t (w b ).
20
80
%
40
M
o is tu r e
60
80
C o n te n t ( w b ) .
100
9c
Figure 6. Comparison of dielectric properties with literature data.
800
160
9 I 5 M
2 4 5 0
19 600
H
M
140
z
H z
!
120
500
-3
100
400
300
|
22°C
60°C
200
40
LOO
0
10
20
M
30
o is tu r e
40
50
60
70
80
90 0
C o n te n t (w b ). %
10
20
M
30
o is tu r e
40
50
60
C o n te n t ( w b ) ,
%
Figure 7. Penetration depth as a function of moisture content at two temperatures.
154
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
80
Penetration depth (mm)
700
-
Model prediction of dielectric properties
We needed to develop a correlation between dielectric properties and changes of temperature
and moisture for computer simulation models. However, for fruits and vegetables, a lack of
experimental data and the difficulties in measurements at elevated temperatures and low
moistures have hindered such an effort. Measured values of e' and e" at 915 MHz and 2450
MHz are tabulated in Table 2 and Table 3. These values were correlated to moisture for 60°C.
The equations obtained are as the follows
e ' = a, + a , X + a 3 X 1
(4)
e '= b x + b ,X + b , X 1'
(5)
where ai to a? and bt to b? arelisted in Table 4.The quadraticequationwas selected
for its
simplicity and accuracy. The r s are all close to 0.99(Table 4). Eqs. (4) and (5) canbe used for
isotherm heating applications. Because the dielectric data at 22°C exhibited a transition region
(Fig. 5). it is more appropriate to use a two-sectional equation to fit the data.
Table 2. Dielectric properties of Red Delicious at 60°C and eight moisture contents.
9 1 5
M C (w b )
?c
£ '
M
S td .
2 4 5 0
H z ( 6 0 ° O
e "
D e v .a
S td .
e '
S td .
M
H z
( 6 0 ° O
e "
D e v .
D e v .
S td .
D e v .
6 8 .7
3 2 .7 7
4 .0 6
9 .1 1
0 .9 9
3 0 .8 4
3 .6 1
7 .5 4
0 .8 6
5 3 .6
2 8 .4 5
5 .4 4
8 .5 4
2 .6 2
2 6 .0 3
5 3 8
7 .2 0
1 .4 8
3 4 .6
2 2 .4 8
4 .2 8
6 .8 2
1 .7 6
1 9 .6 5
4 .0 3
6 .5 9
1 .2 6
2 2 .4
1 4 .4 4
4 .9 8
4 .5 0
1 .2 9
1 1 .8 6
4 .6 0
4 .4 5
1 .4 2
1 2 .7
7 .3 5
2 _ 3 4
2 .1 0
0 .9 6
6 .2 3
1 .7 9
1 .7 4
0 .8 8
1 1 .0
5 .3 4
0 .7 9
1 .6 9
0 .3 5
4 .4 5
0 3 9
1 .3 7
0 .2 S
5 .9 3
4 .1 4
0 .8 2
1 .0 0
0 .2 5
3 .6 8
0 .7 1
0 .7 2
0 .1 8
3 .8
3 .6 1
0 .6 0
0 .6 8
0 .1 0
3 .5 6
0 .4 9
0 .4 7
0 .1 3
a: standard deviation.
155
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3. Dielectric properties of Red Delicious at 22°C and fourteen moisture contents.
M
9 1 5
C (w b )
%
e'
M
S td .
2 4 5 0
H z ( 2 2 ° C )
e"
e'
S td .
S td .
H z
( 2 2 ° Q
E"
S td .
D e v .
D e v .
D e v .
M
D e v .
8 7 .5
5 6 .0
0 .9 0
8 .0
0 .4 0
5 4 3
1 .2 0
1 1 .2
0 .5 0
8 0 .7
4 3 .0 3
5 .0 2
6 .9 6
1 .0 3
4 0 .9 8
4 .7 5
9 .2 5
1 .1 7
7 9 .6
3 8 .2 2
3 .9 1
6 .0 6
0 .9 3
3 6 .2 5
3 .8 1
8 .5 6
0 .9 0
7 8 .0
3 8 .9 7
6 .6 4
6 .2 7
1 .11
3 7 .0 6
6 .1 5
8 .4 9
1 .4 1
6 9 .7
3 3 .0 3
3 .6 8
6 .6 6
1 .0 7
3 0 3 2
3 3 9
8 3 3
1 .0 6
5 5 .1
2 6 .9 2
2 3 8
6 .8 7
0 .9 4
2 3 .0 9
2 .0 7
8 .4 5
0 .8 5
4 6 .6
2 2 .2 4
2 .0 1
6 .7 1
0 .9 5
1 8 .3 8
1 .7 7
7 .8 3
0 .8 4
3 6 .4
1 6 .2 1
2 .6 2
6 .1 0
0 .9 2
1 2 .2 7
2 .1 2
6 .2 2
1 .0 8
3 0 .3
1 4 .3 9
5 .9 4
5 .9 4
0 .9 7
1 0 .7 4
1 .6 1
5 .5 2
0 .9 5
2 3 .8
5 .6 5
0 3 1
2 .1 0
0 .3 0
4 3 2
0 .3 6
1 .5 8
0 .2 0
1 9 .0
3 .7 0
0 .3 1
0 .8 1
0 .1 2
3 .3 0
0 .2 5
0 .6 5
0 .0 9
1 4 .1
2 .8 0
0 .2 4
0 .3 3
0 .0 6
2 .6 3
0 .2 2
0 .2 9
0 .0 4
9 .2
2 .2 4
0 .2 3
0 .1 7
0 .0 3
2 .2 1
0 .2 2
0 .1 4
0 .0 3
3 .8
t.6 9 5
0 .1 7 5
0 .0 8 6
0 .0 4 3
1 .7 1 0
0 .1 8 2
0 .0 6 6
0 .0 3 9
In order to correlate data with both the temperature and the moisture, a weighted linear
extrapolation from data at 22°C and 60°C was made to generate dielectric data at 100°C. 100°C
was selected as the upper temperature in the correlation because at atmospheric conditions most
microwave heating applications are at temperatures lower than water boiling point because of
the evaporation cooling effect. The weight was selected between 0.3 to 0.5 because a weight
greater than 0.5 will yield a peak on e" curves at medium moisture contents that could even
exceed e" values at high moisture content. A correlation for the loss factor, using a weight of
0.5 to generate data at 100°C. is given by:
e'=a.
T + a,T2 + ax X +a*XT
( 6)
+a6X T 1+aTX 1+ai X 1T+a9X :'
156
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where T is temperature in K and X is moisture content in dry basis. Since a transition region
existed in z" curves at moisture of about 25% (wb) (Fig. 5), the curve fitting in Eq. (6) is only
for moisture range of 4 to 30.0 % (wb) at temperature range of 22 to 100°C. Coefficient at to a?
are:
a! = -23.5999: a2 = 0.158233: a3 = -0.000256978: a* = -1.87998: a5 = 0.00768435: a* = -5.6363
x IO'6: a7 = 0.0289568: as = -7.66337 x 10‘5: a? = -4.09947 x IO'5. The r for Eq. (6) is 0.97. Eq.
(6) can be used in thermal calculation dealing with both temperature and moisture changes.
Table 4. Coefficients in Eqs (4) and (5).
Dielectric
Frequency
property
(MHz)
U|
az
a;
r"
915
-0.0839
0.7775
-0.0042
0.99
2450
-0.3360
0.6171
-0.0023
0.99
b,
bz
b-.
915
-0.7377
0.2768
-0.0019
0.99
2450
-1.0611
0.2915
-0.0024
0.98
CONCLUSIONS
The dielectric properties of Red Delicious apples were measured with the open-ended coaxial
line technique at 22°C over moisture content of 4 to 87.5 % (wb). and 60°C over a moisture
content of 4 to 68.7 % (wb). The dielectric relaxation spectra was analyzed to explain the
moisture and temperature effects over a frequency range from 45 MHz to 3 GHz. Water content
and ionic conductivity had different effects on the loss mechanism at different moisture and
temperature levels. When moisture was relatively high (-70%, wb), both free water dispersion
and ionic conduction were important in determining the dielectric behavior. At intermediate
moisture (-23%. wb), the ionic conduction determined the frequency response of the dialectic
properties. At low moisture content (-4%, wb). the bound water was the main dispersion
mechanism. Moisture reduction resulted in a decrease in dielectric properties. A transition
region was found in e"' curves that corresponded to the transition from bound water to free
water. An increase in temperature at low moisture contents resulted in increased dielectric
157
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
properties. At high moisture contents, the temperature response was determined by the
contributions of free water, ionic conduction, and bound water and was difficult to predict. The
result of this study compared well with work of Mudgett et al (1980). The penetration depth
increased as moisture was removed from the sample. The data were correlated with a
polynomial equation to predict both the moisture and temperature effect.
ACKNOWLEDGEMENTS
Financial support from Washington State University IMPACT Center and Northwest Center for
Small Fruits Research are gratefully acknowledged. We acknowledge TreeTop. Selah. WA. for
donating evaporated apples.
REFERENCES
1. Anderson. L. S.. Gajda. G. B. and Stuchly. S. S.. 1986. Analysis of an open-ended coaxial
line sensor in layered dielectrics. IEEE Trans. Instrum. Meas.. IM-35( I), pp. 13-18.
2. Anonymous. 1984. Composition o f Foods, in Agriculture Handbook 8-9 & 8-11. USDA.
Human Nutrition Information Service.
3. AOAC. 1990. Official Methods o f Analysis. 15th ed. Association of Official Analytical
Chemists. Washington. DC.
4. Bengtsson. N. E. and Risman. P. O.. 1971. Dielectric properties of foods at 3 GHz as
determined by a cavity perturbation technique. II. Dielectric measurements. J. Microwave
Power. 6. pp. 107-123.
5. Datta. A. K.. Sun. E. and Solis. A.. 1995. Food Dielectric Property Data and Their
Composition-Based Prediction. In Engineering Properties o f Foods. Rao. M. A. and Riviz.
S. S. H.. (eds.). Marcel Dekker. Inc.. New York.
6. Engelder. D. S. and Buffler. C. R.. 1991. Measuring dielectric properties of food products at
microwave frequencies. Microwave World. 12(2). pp. 6-15.
7. Fan. S.. Staebell. EC. and Misra. D.. 1990. Static analysis of an open-ended coaxial line
terminated by layered media. IEEE Trans. Instrum. Meas., 39(2). pp. 435-437.
8. Feng H. and Tang. J.. 1998. Microwave finish drying of diced apples in a spouted bed. J.
Food Set, 63(4). pp. 679-683.
158
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9. Goedeken. D. L., Tong. C. H. and Virtanen. A. J.. 1997. Dielectric properties of a
pregelatinized bread system at 2450 MHz as a function of temperature, moisture, salt and
specific volume. J. FoodSci.. 62( I), pp. 145-149.
10. Harvey. S. C. and Hoekstra. P.. 1972. Dielectric relaxation spectra of water adsorbed on
Ivsozyme. 7. Phy. Chem., 76(21), pp. 2987-2994.
11. Herve. A-G. Tang. J.. Luedecke. L. and Feng, H.. 1998. Dielectric properties of cottage
cheese and surface treatment using microwaves. J. Food Eng.. 37. pp. 389-410.
12. Hudson. D. E.. 1975. The relationship of cell size, intercellular space, and specific gravity
to bruise depth in potatoes. Am. Potato J.. 52, pp. 9-14.
13. Ikediala. J. N.. Tang. J.. Drake. S. R. and Neven. L. G.. 1999. Dielectric properties of apple
cultivars and codling moth larvae. Trans. ASAE.
14. Kaatze. U.. 1989. Complex permittivity of water as a function of frequency and
temperature. J. Chem. Data. 34. pp. 371-374.
15. Kara!. M.. 1975. Physiocochemical modification of the state of water in foods. In Water
Relations in Foods. Duckworth. R. B. (ed.). Academic Press. New York.
16. Kent. M.. 1987. Electric and Dielectric Properties o f Food Materials. Science and
Technology Publishers. England.
17. Khan. A. A. and Vincent. J. F. V.. 1990. Anisotropy of apple parenchyma. /. Sci. Food
Agric.. 52. pp. 455-466.
18. Kim. Y. -R.. Morgan. M. T.. Okas. M. R. and Stroshine. R. L.. 1998. Measurement and
prediction of dielectric properties of biscuit dough at 27 MHz. J. Microwave Power and
Electromagnetic Energy. 33(3), pp. 184-194.
19. Kuang, W. and Nelson, S. O.. 1998. Low-frequency dielectric properties of biological
tissues: A review with some new insights. Trans. ASAE.. 41( I), pp. 173-184.
20. Lu. Y.. Fujii. M. and Kanai. H.. 1998. Dielectric analysis of hen egg white with
denaturation and in cool storage. Int. J. Food Set Tech.. 33, pp. 393-399.
21.Mudgett. R. E., Goldblith, S. A.. Wang, D. L C. and Westphal, W. B.. 1980, Dielectric
behavior of a semi-solid food at low, intermediate and high moisture contents, J.
Microwave Power, 15(1), pp. 27-36.
159
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
22. Mudgett. R. E.. 1990. Development in Microwave Food Processing, in Biotechnology and
Food Process Engineering, Schwartzberg. H. G. & Rao. M. A. (eds.). Marcel Dekker. Inc..
New York.
23. Nelson, S. O., 1973. Electric properties of agricultural products - a critical review. Trans.
ASAE, 16(2), pp. 384-400.
24. Nelson. S.. Forbus. Jr.. W. and Lawrence. K... 1994. Permittivities of fresh frutts and
vegetables at 0.2 to 20 GHz. J. Microwave and Power and Electromagnetic Energy. 29(2).
pp. 81-93.
25. Ohlsson. T.. Bengtsson. N. E. and Risman, P. O., 1974. The frequency and temperature
dependency of dielectric food data as determined by a cavity perturbation technique. J.
Microwave Power. 9. pp. 129-145.
26. Okos. M.R.. Narsimhan. G., Singh. R.K. and Weitnauer. A.C.. 1992. Food Dehydration. In
Handbook o f Food Engineering. D.R. Heldman and Lund. D.B.. (eds). (Marcel Dekker.
Inc.. New York), pp. 437-562.
27. Roebuck. B. D.. Goldblith. S. A. and Westphal. W. B.. 1972. Dielectric properties of
carbohydrate-water mixture at microwave frequencies. J. Food Sci.. 37. pp. 199-204.
28. Ryynanen. S.. 1995. The electromagnetic properties of food materials: A review of the
basic principles. / . Food Eng.. 26. pp. 409-429.
29. Seaman. R. L.. Burdette. E. C. and DeHaan. R. L.. 1989. Open-ended coaxial device for
applying RF/microwave fields to very small biological preparations. IEEE Trans.
Microwave Theory Tech.. MTT-37. pp. 102-111.
30. Seaman, R. and Seals. J.. 1991. Fruits pulp and skin dielectric properties for 150 MHz to
6400 MHz. J. Microwave and Power and Electromagnetic Energy. 26(2), pp. 72-81.
3l.Stuchly. M. A. and Stuchly. S. S.. 1980. Coaxial line reflection methods for measuring
dielectric properties of biological substances at radio and microwave frequencies - A
review. IEEE Trans. Instrum. Meas.. IM-29(3). pp. 176-183.
32. Sun, E.. Datta. A. and Loba. S.. 1995. Composition-based prediction of dielectric properties
of foods. J. Microwave Power and Electromagnetic Energy, 30(4), pp. 205-212.
33. Swicord, M. and Davis, C. C., 1981. Energy absorption from small radiating coaxial probes
in lossy media, IEEE Trans. Microwave Theory Tech., MTT-29( II), pp. 1202-1208.
34. Tang, J., 1999, Factors affecting dielectric properties of foods, manuscript.
160
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35. Tong, C. H.. Lentz. R. R. and Rossen. J. I
1994. Dielectric properties of pea puree at 915
MHz and 2450 MHz as a function of temperature. J. Food ScL, 59( I). pp. 121-134.
36. Tran. V. N.. Stuchly. S. S. and Kraszewski. A.. 1984. Dielectric properties of selected
vegetables and fruits 0.1 - 10.0 GHz. J. Microwave Power. 19(4), pp. 251-258.
37. Tsoubel. M. N.. Davis. E. A. and Gordon, J.. 1995. Dielectric properties and water mobility
for heated mixture of starch, milk protein, and water. Cereal Chemistry. 72. pp. 64-69.
161
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Chapter 6
MICROWAVE FINISH DRYING OF DICED APPLES IN A
SPOUTED BED
H. Feng and J. Tang
Department of Biological Systems Engineering,
Washington State University. Pullman. WA 99164-6120
ABSTRACT
A microwave heating and spouted bed (MWSB) combined technique was developed to improve
heating uniformity during microwave drying. This technique was evaluated with experiments
using a laboratory system in which evaporated diced apples of about 31% (dry basis) moisture
content was dried to about 5% (dry basis) at 70°C air temperature and four levels of microwave
power density (0 to 8.0 W/g, dry basis). Heating uniformity was examined by measuring the
center temperature of apple dices after different drying times. Drying characteristics with the
MWSB technique was compared with spouted bed (SB) drying method. With the MWSB
combined method, temperature uniformity in diced apples was greatly improved (< 4°C at 6.4
W/g. dry basis) as compared to that with a stationary bed during microwave drying. The
products had less discoloration, higher rehydration rates as compared to conventional hot air
drying or spouted bed drying. Drying time could be reduced by over 80% comparing with SB
drying without microwave heating.
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INTRODUCTION
Preservation of fruits and vegetables by removing moisture to a shelf stable level using
hot air has long been used since ancient times. A major disadvantage of hot air drying is lowenergy efficiency and lengthy drying time during the falling rate drying period. This is mainly
caused by rapid reduction of surface moisture and consequent material shrinkage, which often
results in reduced heat and moisture transfer.
Prolonged exposure to elevated drying
temperatures may result in substantial degradation in quality attributes, such as color, nutrients,
and flavor. Severe shrinkage also reduces bulk density and rehydration capacity.
Combining hot air with microwave energy has shown advantages over traditional hot-air
drying. Microwave heating is characterized by rapid volumetric heating. When applied to
drying, it results in a high thermal efficiency, a shorter drying time and. sometimes, an
improvement in product quality (Garcia et al., 1988: Prabhanjan et al.. 1995: Torringa et al..
1996). An inherent problem associated with microwave drying is the non-uniformity in heating
caused by an uneven spatial distribution of electromagnetic field inside the drying cavity.
During drying processes, non-uniform heating may cause partial scorching in high sugar
products. Various field-averaging methods have been developed to achieve heating uniformity.
With these methods, a product is in constant movement within the microwave cavity so that
different parts of the product will receive a microwave radiation of about the average of the
spatial electromagnetic field intensity over a period of time. This can be accomplished either
mechanical (Allan. 1967: Huxsoll and Morgan. 1968: Torringa et al. 1996) or pneumatic
agitation (Salek-Mery, 1986: Kudra. 1989).
Fluidization provides pneumatic agitation for particles in the drying bed.
It also
facilitates heat and mass transfer due to a constantly renewed boundary layer at the particle
surface. Salek-Mery (1986) used fluidization and microwave combination technique as an
intermediate stage of a fluidization system for grain. The drying rate was increased by 50%
compared to conventional hot air drying. The enhancement of drying was also observed by
Kudra (1989) for microwave drying of wheat and alumna in a fluidized bed. He also reported a
uniform temperature distribution was found within the samples. Coarse food particles such as
diced apples are difficult to fluidize. especially when their moisture content is relatively high
163
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and surface is relatively sticky. Spouted bed is a specially designed bed for fluidizing coarse
particles that are not suitable for a conventional fluidized bed. A spouted bed consists of a
downward moving bed in the peripheral section with an upward moving “spurt” like dilute
phase (Figure I) in the central section (Mathur and Epstein, 1974). A spouted bed has not been
reported in combination with microwave heating in food drying applications.
The objectives of this study were to improve the microwave heating uniformity by
incorporating a spouted bed in a laboratory system and to evaluate the quality and drying
characteristics when drying diced apples. The feasibility of the microwave and spouted bed
(MWSB) combined technique for uniform drying was tested on apples because high sugar
content makes dehydrated apples extremely sensitive to scorching and nonuniform heating
would cause obvious discoloration.
MATERIALS AND METHODS
Evaporated diced apples
Evaporated diced Red Delicious. Golden Delicious and Granny Smith apples (Malus domestica
Borkh) with a moisture content ranging from 29.5% to 31.2% (db) were supplied by Tree Top
Inc. (Seiah. WA). Diced apples have been pretreated with sulfite to prevent browning. The
size of the fresh dices for all three varieties was 12.7 x 9.5 x 6.4 mm (1/2 x 3/8 x 1/4 inch).
Moisture content, color and bulk density of the dices were measured before drying tests. The
samples were placed in sealed plastic bags and stored at 4°C before the finishing drying tests.
Laboratory drying system
An experimental dryer was developed for the drying tests (Figure I). The system consisted of a
microwave power source, cavity, hot-air source, spouted bed. and water load. The microwave
generator operated at 2,450 MHz. The generator output power was regulated between 0 and 1.4
kW by an Alter SM445 power controller (Casselberry. FL). The multimode microwave drying
cavity had a dimension of 393 x 279 x 167 mm. The spouted
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Microwave power controller
Stirrer
Spouted bed
Microwave cavity
Computer
Magnetron
Sample
3
By-pass
Temperature
controller
Water load
Water pump
Heater
T
Electric balance
Sink
2
Blower
D —Dew point temperature:
F —Flowrate:
T —Temperature:
V - Velocity:
Figure 1. Schematic diagram of microwave and spouted bed (MWSB) drying system.
bed was constructed with microwave-transparent perspex. It consisted of a cylindrical section
and a 3 1 degree conical base. The bottom of the cone was made of a plastic screen to hold the
particulate samples and provided a pass for the hot air. The spouted bed was supported by a
metal plate and a metal screen with holes small enough to cut-off the microwave leaking. The
metal plate was supported by three plastic legs standing on an electrical balance. This
arrangement provided the flexibility to weigh samples either on-line or off-line. A blower (Fuji
Electric Co.. Ltd. Tokyo. Japan) provided an air velocity of up to 8 m/s in the spouted bed.
Before entering the spouted bed. the air was pre-heated by a 1.7 kW electric heater. The air
temperature was controlled by a SET-TEMP® digital controller (Laboratory Devices. Inc..
Holliston. MA).
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A water load was placed to protect the magnetron from overheating. It consisted of a
AC-2CP-MB water pump (MFG.. Inc.. Glenview. IL). a FLO-Sensor flowmeter (MaMillan.
Copperas Coup. TX), and two temperature sensors. The inlet and outlet temperature difference
of the water was monitored by Labview data logging system (National Instruments. Austin.
TX). The power absorbed by the water load was calculated accordingly.
The microwave power output from the generator was calibrated following the two-liter
method recommended by the International Microwave Power Institute (Anonymous. 1989). The
power absorbed by the samples during drying was calculated as the difference between the
power absorption by the water load and the total magnetron power output.
Drying tests
Drying tests for Red Delicious were conducted at microwave power levels equivalent to 4.9.6.4
and 8.0 watt per gram of dried evaporated apple dices. Evaporated Golden Delicious and
Granny Smith were dried with a microwave power intensity of 6.4 W/g (dry basis). The hot air
was controlled at 70°C with a superficial velocity of 1.9 m/s in the spouted bed. This velocity is
determined by dividing air flowrate by the cross-sectional area of the large end of the spouted
bed. It was the minimum requirement for the particles of 31.2% moisture content (db) to be
spouted and agitated. Samples of 40g were used for all the tests and sample weight changes
during drying were monitored by removing the spouted bed and weighing on a Satorius electric
balance (3000g ± O.Olg). For quality evaluation, control tests using the spouted bed hot-air
drying without microwave heating were conducted under the same air conditions. After the
drying tests, samples were kept in airtight containers until the measurement of color, bulk
density and rehydration capacity within 2 weeks after the drying. All drying tests, except the
spouted bed hot-air drying of Red Delicious and Granny Smith apples, were repeated three
times and average values were reported and plotted
Heating uniformity
Heating uniformity within a sample during drying with the MWSB method was examined by
measuring core temperature of individual apple piece. Red Delicious was dried at a microwave
power level of 4.9 W/g and with a hot air of 70°C and l.9m/s. The core temperature of 10
166
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randomly chosen apple pieces was measured at different drying times using a TMQSS-020U
thermocouple (Omega Engineering, Inc.. Stamford. C D with a response time of 0.8 second.
The temperature readings were taken by inserting the thermocouple into the core part of each
randomly chosen piece. For each drying time, temperature measurements were completed
within 1.5 min and the temperature drop during this period was less than 3°C. For comparison,
similar measurements were made in a stationary bed during microwave drying with hot air
flowing horizontally through the surface of a deep bed of diced apple. The color of the
dehydrated apple dices also observed as an indicator of the heating uniformity, because uneven
heating would cause scorching and hence obvious nonuniform color.
Moisture content
The initial and final moisture content were determined using the vacuum oven method at 70°C
and 13.3 KPa (AOAC. 1990). The means of three measurements were reported. The moisture
contents in between were extrapolated from weight readings and initial and final moisture
contents.
Rehydration capacity
Rehydration capacity (R.C.) is defined as the ratio of the moisture regained when submerged in
water to the moisture removed during the drying (Loch-Bonazzi et al. 1992). A dehydrated
sample (5g) was weighed and submerged in boiling water for 2 minutes. The sample was
immediately drained on a metal sieve for 5 minutes and reweighed. The rehydration capacity is
given by:
Dr,
regained moisture(g)
initialmoisture(g)—residual moisture(g)
K L — --------------------------------------------------------------------------------------
The amount of initial and residual moisture of the samples was determined from the moisture
content of fresh apple and the moisture content of dried products, respectively. The regained
moisture was calculated from the sample weight difference before and after the rehydration.
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The dehydration measurements were conducted 3 times for all tests and the means were
reported.
Bulk density
Samples (5g, containing 67 ± 5 pieces) were used to measure the bulk density. The weight of
samples was taken with an analytical balance (± 0.0Ig). The volume of the samples was
determined by water displacement method. Measurements were made three times.
Color
Sample color was measured using a Minolta Chroma CR-200 color meter (Minolta Camera CO.
LTD. Japan). For fresh apples, three measurements were conducted at randomly chosen
locations of sliced apples, and the mean was reported. For evaporated or dehydrated apple
dices. 40g sample was wrapped with transparent Saran Wrap (Dow Brands L.P.. Indianapolis.
IN) into a square shape. Measurements were made at five different locations of the pack. For
each location. 5 measurements were made and the average was used.
The color readings were expressed by the ICI chromaticity coordinates (L*a*b*) system.
Color difference from the fresh apples AE. as defined the following, was used to describe the
color change during drying:
( 2)
where subscript "o” refers to the color reading of fresh apple flesh. L*. a* and b* indicate
brightness, redness and yellowness, respectively. Fresh apple tissue was used as the reference.
The larger the AE. the greater the color change from the reference color of the fresh apple flesh.
RESULTS AND DISCUSSIONS
Moisture and temperature history of a typical MWSB drying test is shown in Figure 2.
For this test, the sample temperature passed the air temperature of 70°C in 2 min after the start
168
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of the drying. After that point, the temperature gradually reached a plateau about 14°C higher
than the ambient air, and then slightly decreased towards the end of drying.
30
100
\
Temperature
--5-
-
*
80 U
I
ti
Spouted bed air temperature
\
r
<o
£
rr
------ W
25
in
/■■■»
Cl
,
20 =
r 15
\
£
u
p
40
4)
h 10 5
Moisture
i
-----O
0
r 5
0
0
10
15
20
Drying time (min)
Figure 2. A comparison of center temperature variation among 10 Red Delicious apple dices
randomly taken from the spouted bed after 2.5 minutes of drying with MWSB (6.4 W/g and hot
air of 70°O and from a stationary bed with MW and flow hot-air drying (hot air of 70°O.
To explain the temperature change, a thermal energy balance equation could be written
for the sample:
E n ergy
W
E n ergy
/
> +
E n e r g y in
l
E ,
' E n e rg y o u t'
,
\
F
( 3)
0
where. Eg (>0) is the energy input due to microwave heating, Er is the thermal energy input due
to air-particle heat transfer, and Eq is energy loss due to moisture evaporation. A positive energy
169
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
accumulation would lead to an increase in sample temperature. Ei could be positive or negative,
depending upon the direction of heat transfer. Moisture level decreased throughout the drying
processes, thus, Eo was always greater than zero.
Eg in Eq. (3) is related to the local electromagnetic field intensity and effective loss
factor e" (Goldblith. 1967):
E g = 5.56 x l(T* x f e ' E 2
(4 )
where. Eg = the conversion of microwave energy into thermal energy per unit volume (W/cm')
f = frequency (GHz)
e" =
relative dielectric loss factor
E = electric field (V/cm)
The heating curse in Figure 2 can be partitioned into three stages. In stage I. sample
temperature was less than the air temperature. Sample was, therefore, heated by a heat transfer
from the hot air (E[>0) and microwave heating (Eg>0). The microwave heating in this stage
should be relatively intensive due to the high loss factor of the moist sample. As a result,
sample temperature increased rapidly and surpassed the air temperature in 2 min. although there
was heat loss due to moist evaporation. In stage II. temperature of sample was higher than
ambient air. therefore, the air helped to removed heat from the sample (Ei<0). But the sample
center temperature continued to increase ( AE >0). due to intensive microwave heating, and then
reached a plateau. In stage m. the sample temperature remained stable ( AE =0). The energy due
to microwave heating was balanced by evaporative cooling and a heat transfer from the sample
to the ambient air. In this stage, the positive temperature gradient from sample center towards
surface was in sharp contrast with that when dried with hot air. This positive temperature
gradient in a MWSB system maintained a positive vapor pressure and helped to speed up the
drying process.
A slight temperature reduction occurred towards the end of the MWSB drying. It is
likely that the material loss facto ( e" ) as dramatically reduced as the diced apples lost most of
moisture. A moisture leveling effect resulted in a reduction in absorption of MW energy
170
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(Metaxas and Meredith, 1988). Thus, the sample temperatures were slightly reduced due to the
more predominant combined effect of evaporative cooling and heat transfer from sample to the
air. Similar temperature reduction was reported by Adu and Otten (1993) in soybean microwave
drying tests.
Temperature distribution among sample particles during the drying process, as indicated
by the error bars in Figure 2. was very uniform. A comparison was made (Figure 3) of center
temperature variation in 10 apples pieces after 2.5 min of drying with the MWSB method and
the stationary bed microwave drying method. With the MWSB method, the measured
maximum temperature variation was ±4°C about the average temperature. However, this
variation was reduced to ±I.4°C toward the end of a 25-minute drying period. With a stationary
bed and a horizontal flow of hot air at 70°C. however. MW drying caused severe localized
heating. For example, the center temperature of one piece was I93°C. while another was at
65.5°C. Some apple pieces were charred, while others were still very moist.
It can be concluded that the spouted bed in microwave heating served two purposes: I)
it provided a pneumatic agitation to help avoid uneven microwave heating: 2) it reduced
possible overheating because high air velocity and effective mixing in spouted bed increased
particle-air heat and mass transfer.
171
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10
MWSB drying
Feniperuliirc deviation
U
T( average) =74.29 C
r o
100
-10
MW & parallel flow hot-air drying
75 50 25 -
T( average) = 101.32 °C
0
-25 -i
.« ■ !
0
TE^T"
I
3
w
4
5
6
7
8
9
10
U
Sampling sequence
Ftgure 3. Temperature history and average moisture content of diced Red Delicious apple
during microwave drying at 6.4 W/g (db) and 70°C hot air temperature.
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Golden Delicious (MWSB)
Granny Smith (MWSB)
Red Delicious (MWSB)
Golden Delicious (Hot-air)
Granny Smith (Hot-air)
Red Delicious (Hot-air)
jC.
S
u
25 -
0 0
20
40
60
80
100
120
140
160
Drying time (min)
Figure 4. Drying curves of three apple cultivars dried with MWSB (6.4 W/g and hot air of
70°C) and SB (70°C hot air).
The drying curves of the three apple cultivars were compared (Figure 4). These curves
exhibited typical exponential decay, indicating an internal controlled mass transfer (Tulasidas et
al. 1993). To produced crunchy dehydrated texture in dehydrated apples, it is desirable to have a
final moisture of about 5% (db). The time to dry evaporated Golden Delicious apple dices from
33.7% (db) to 5.0% (db) was 147 min when using spouted bed alone with a stream of air at
70°C and l.9m/s. The drying time was reduced to 17.5 min when microwave energy of 8.0 W/g
(db) was included. It was an 88% reduction in drying time. Similar reduction in drying time was
recorded for diced Red Delicious and Granny Smith apples by the MWSB method.
The influence of microwave power density is illustrated in Figure 5 for diced Red
Delicious apple. As expected, the moisture transport was enhanced as power density increases.
The drying time required to dry an evaporated sample from 41.8 to.5% (db) to 5.0% (db) was
173
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reduced from 28 minutes at a power density of 4.9 W/g to 10 minutes at a power density of 8.0
W/g.
The reproducibility of the drying data was evaluated by standard deviations of final
moisture contents from replicated drying tests as shown in Table I. The low standard deviations
indicate a good reproducibility of the drying curves. Drying characteristics were slightly
different among the 3 cultivars (Figure 4). Since the evaporated apples had been obtained from
a commercial supplier, there was insufficient data and sample history to explain any
differences.
Table I. Standard deviations of the final moisture contents from different drying processes
E v a p o r a te d
C u ltiv a r
M
M W
C (% )
M
4 .9
R e d
D e lic io u s
G o ld e n
D e lic io u s
G r a n n y
■* m e a n
S m ith
o f th re e
2 9 .5 ± 0 . 8 1
5 .9
W
±
/g
6 .4
re p lic a te s
±
s ta n d a r d
d ry in g
S B
C (% )
W
/g
6 . 2 ± 0 . 2 '*
0 .9 1
3 3 .7 ± 1 .8 9
2 9 .9 ± 0 . 1 1
S B
5 .0 ± 0 .8 *
M C (% )
8 .0
5 .6 ±
W
/g
I .O '*
6 .5 b "
5 .3 ± 0 . 3 a
5 4 . 0 ± 0 . 2 '*
d e v ia tio n :b o n e te s t w a s
d ry in g
c o n d u c te d
174
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6 .0 b
.c
£
M
W
S B
( 4 .9
w /g . d b )
M
W
S B
( 6 .4
w /g . d b )
M
W
S B
( 8 .0
w /g . d b )
S B
0
20
40
60
80
(0
w /g )
100
120
140
160
Drying time (min)
Figure 5. Drying curve of Red Delicious dried with MWSB method with different microwave
power levels.
The lightness of three apple cultivars processed with different methods is listed in Table
2. Preferred colors are those closest to the original color of fresh apple fleshes. In this study, the
evaporated diced apple was the starting point. Some discoloration had been experienced for the
evaporated apples as indicated by a reduction in the L* value. MWSB drying caused further
slight darkening. Color degradation of the product resulted from SB drying was slightly more
than that by MWSB drying. Commercial hot-air dried products exhibited the greatest reduction
in the lightness.
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Table 2. Lightness for apple dices dried with different methods as compared with fresh apple
fleshes.
Lightness (L)
Red Delicious
Golden Delicious
Granny Smith
Flesh
82.13 ± IJZ3a
8238 ±0.78
79.06 ± 1.04
Evaporated dices
8033 ± 3.69 (23%)b
80.37 ± 3.22 (2.4%)
78.81 ±5.08(03%)
MW&SB dried dices
76.17 ±2.33 (7.3%)
76.94 ±437 (6.6%)
77.61 ±331 (1.8%)
SB dried dices
73.43 ± 1.91 (9.4%)
76.63 ±335 (7.0%)
72.04 ±4.48i 8 9%)
commercial hot-air
70.40 ±6.17 (14.3%)
73.41 ±231 (10.9%)
69.48 ±2.59 (12.1%)
dried dices
d mean ± standard deviation;brelative changes in lightness with respect to fresh apple fleshes
The total color change AEs. which takes into account the changes in redness and
yellowness, was also compared (Figure 6). MWSB drying caused little color changes from that
of the evaporated apple dices. SB dried products also experienced less discoloration than the
commercial hot-air dried samples. The development of discoloration of the evaporated diced
apples during the finish drying may be related to the nonenzymatic browning (Salunkhe et al.
1991). The heat sensitive polyphenoloxidase activity had probably been prohibited during the
preliminary drying (Kostaropoulos and Saravacos. 1995) which reduced the moisture content of
fresh apple to that of the evaporated apples (25 - 33%. db). The presence of glucose, fructose,
and malic acid in apples would
176
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20
Red Delicious
&
16
12
Golden Delicious
o
a
T
8
§
4
0
U
Granny Smith
Evaporated MW & SB
SB
Hot-air
commercial
Figure 6. Color comparison of apples dried with different methods
promote browning reaction when heat was applied. Drying temperature and time are important
parameters for the development of browning during apple drying (Tulasidas et al. 1995). The
less color degradation of MWSB dried dice may. therefore, be due to the substantial reduction
in drying time. This may also be true for the SB drying because of high heat and mass transfer
(Mathur and Epstein. 1974) that facilitate higher drying rate as compared with conventional
hot-air drying methods. Less discoloration in graphs after microwave drying was reported by
Tulasidas et al (1995).
The rehydration characteristics of a dried product are widely used as a quality index.
(McMinn and Magee. 1997). They indicate the physical and chemical changes during drying as
influenced by processing conditions, sample pretreatment and sample composition. The
rehydration capacity for three cultivars dried with different methods are compared (Figure 7).
The MWSB dried products generally had higher rehydration rates than the other two methods.
The rehydration capacity of Red Delicious apple dried with MWSB method had the maximum
value (0.71 ±0.02). This was a 20% increase comparing with the commercial hot-air dried
177
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apples. None of the dried products regained the initial moisture. Irreversible physio-chemical
changes might have occurred during the drying which would cause the reduction in water
holding capacity of the structural matrix. Pendlington and Ward (1965) studied structure
changes of hot-air and freeze dried carrot* parsnip and turnip by a histological examination.
They postulated that the migration of soluble solids during hot-air drying was also important in
the physical changes. The solutes leaking from damaged cells migrated to the surface to form a
crust and resulted in a relatively close surface structure. Possibly the internal microwave
heating facilitated a predominant vapor migration from the interior of the material as compared
to a more predominant transfer of sugar solution during conventional drying. This difference in
vapor and sugar transfer, combined with high internal pressure, would likely result in a more
porous structure compared with conventional hot-air drying products. The higher rehydration
capacity of microwave dried products might be the result of such enhanced porous structure.
Results from the density measurements (Figure 8) confirmed that densities of MWSB
dried products were lower than hot-air dried products because of the internal heating and vapor
generation as expected. However, the difference was not substantial for
0.8
Red Delicious
0.7 J
'u3
C.
a
Golden Delicious
tr>‘•.ar--
Q£
0.7 0.6
Granny Smith
-
MW & SB
SB
Hot-air
commercial
Figure 7. Rehydration capacity of apples dried with different methods
178
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Red Delicious
Golden Dehcious
700 -
- 700
Granny Smith
600 500 MW & SB
Hot-air
commercial
Figure 8. Density of apples dried with different methods
Red Delicious and Granny Smith. For Golden Delicious, a slightly higher density than
commercial product was measured. Microwave dried products have been reported to possess a
higher porosity because of the puffing effect caused by internal vapor generation (Torringa et
al.. 1996). During the course of MWSB drying in present study, noticeable puffing was
observed, but products shrank towards the end of drying. Further research is needed to
investigate drying conditions that would minimize such shrinkage after microwave puffing.
CONCLUSIONS
The microwave and spouted bed combined method provide much more uniform heating
within the microwave cavity as indicated by more uniform temperature distribution among
sample particles during the drying and even color in final products. The drying time needed to
reduce moisture from evaporated apples to the low moisture dehydrated apples (=5%) was
greatly shortened. The MWSB dried products exhibited least discoloration compared with
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spouted bed or commercially dried products. The MWSB dried products had better
reconstitution characteristics. An improvement in density was also achieved for Red Delicious
and Granny Smith cultivars by MWSB drying.
ACKNOWLEDGEMENT
We acknowledge financial support from the WSU IMPACT Center and NCSFR. We also thank
Tree-Top. Inc. for donating evaporated apple sample.
REFERENCES
Adu. B. and Otten. L.. 1993. Simultaneous microwave heat and mass transfer characteristics of
porous hygroscopic solids. J. Microwave Power. 28:41-46.
Allan. G. G.. 1967. Microwave moving-bed dryers: a feasibility study. J. Microwave Power. 3:
21-29.
Anonymous. 1989. A procedure for power output measurement of consumer microwave ovens.
Microwave World. 10(5): 15.
AOAC. 1990. Official Methods of Analysis. I5,h ed. Association of Official Analytical
Chemists. Washington. DC.
Garcia. R.. Leal. F. and Rolz. C. 1988. Drying of bananas using microwave and air ovens. Int. J.
Food Sci. & Technol. 23:81-90.
Goldblith. S.A. 1967. Basic principles of microwaves and recent developments. Adv. Food Res.
15:277-301.
Huxsoll. C.C. and Morgan JR.. A.I. 1968. Microwave dehydration of potatoes and apples.
Processing Eng. 22:47-52.
Kostaropoulos. A.E. and Saravacos. G.D. 1995. Microwave pre-treatment for sun-dried raisins.
J. Food Sci. 60:344-347.
Kudra. T. 1989. Dielectric drying of particulate materials in a fluidized state. Drying Technol.
7(1): 17-34.
180
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Loch-Bonazzi. C. L.. Wolff. E. and Gilbert. H. 1992. Quality of dehydrated cultivated
mushrooms (Agaricus bisporus): A comparison between different drying and freeze-drying
processes. Lebensm. -Wiss. U. -Technol. 25: 334-339.
Mathur. K.B. and Epstein. M. 1974. Spouted Beds. Academic Press. Inc.. New York.
McMinn. W.A.M. and Magee. T.R.A. 1997. Quality and physical structure of a dehydrated
starch-based system. Drying Technol. 15: 1961-1971.
Metaxas. A.C.. Meradith. R J. 1988. Industrial Microwave Heating. Peter Peregrinus Ltd..
Pendlington. S. and Ward. J.P. 1962. Histological examination of some air-dried and freezedried vegetables in Proceedings of the First International Congress of Food Science and
Technology. (IV) Manufacture and Distribution of Foods. Lames Muil Leitch (ed.). p. 5565. Gordon and Breach Dcience Publishers. New York.
Prabhanjan. D.G.. Ramaswamy. H.S. and Raghavan. G.S.V. 1995. Microwave-assisted
convective air drying of thin layer carrots. J. Food Eng. 25:283-293.
Ryynane. S. and Ohlsson. T. 1996. Microwave heating uniformity of ready meals as affected by
placement, composition, and geometry. J. Food Sci. 61:620-624.
Salek-Mery. J. 1986. Heat and Mass Transfer Studies in Fluidized Beds Combined with
Microwaves for the Dehydration of Food Materials. Ph.D. dissertation. Univ. of Dlinois at
Urbana-Champaign.
Salunkhe. D.K.. Bolin. H.R. and Reddy. N.R. 1991. Storage. Processing, and Nutritional
Quality of Fruits and Vegetables. 2. CRC Press. Boca Raton. Florida.
Torringa. E. M.. van Dijk. E. J. and Bartels. P. S. 1996. Microwave puffing of vegetables:
modelling and measurements. Proceedings of 31st Microwave Power Symposium. Int.
Microwave Power Inst.
Tulasidas. T. N.. Raghavan. G. S. V. and A. S. Mujumdar. 1993. Microwave and convective
drying of grape., Trans, of ASAE. 36(6): 1861-1865.
Tulasidas. T. N.. Raghavan. G. S. V. and A. S. Mujumdar. 1995. Microwave drying of grapes in
a single mode cavity at 2450 MHz-H: quality and energy aspects. Drying Technol. 13: 19731992.
181
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Chapter 7
COMBINED MICROWAVE AND SPOUTED BED DRYING OF DICED APPLES:
EFFECT OF DRYING CONDITIONS ON DRYING KINETICS AND PRODUCT
TEMPERATURE
H.
Feng, J. Tang and R. P. Cavalieri
Department of Biological Systems Engineering
Washington State University, Pullman. WA 99164-6120. USA
ABSTRACT
The influence of microwave power (0 to 8.0 W/g, dry basis) and hot air temperature
(25°C to 95 °C) on drying rate and product temperature of diced apples (from 31% to 5%
moisture content, dry basis) in a laboratory microwave and spouted-bed combined dryer was
investigated. Product temperature initially increased sharply to a plateau about 12 to 15°C
above the spouted bed air temperature at a microwave input power 6.4 W/g. This temperature
remained almost constant thereafter. Uniform microwave heating was achieved as evidenced by
uniform product color and product temperature. Drying rates increased with increasing spoutedbed air temperature or microwave power level. But higher microwave power caused more
darkening of the product. Drying of the diced apples in the microwave and spouted bed drying
system exhibited two falling rates periods. The influence of air temperature on effective
moisture diffusivity followed an Arrhenius type equation. The activation energies were 23.7
kJ/mol and 26.7 kJ/mol for the first and second falling rate periods, respectively.
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INTRODUCTION
In large commercial drying operations, diced apples are usually dried in two steps: I )
from fresh to about 31% moisture content (dry basis) to produce so-called evaporated apples
that can be used in pie filling or in other bakery products: and, 2) from 31% to about 5% (dry
basis) to produce low moisture diced apples used in breakfast cereals. Hot-air drying in the first
stage is very effective. In the second stage, however, hot air drying is much less efficient as the
drying enters the falling rate period, and the drying is lengthy. The low drying rates are caused
mainly by a large resistance to moisture transfer within products and in part by reduced thermal
conductivity in the porous structures of partially dehydrated products. Microwave energy
couples directly to the moisture in the core of partially dehydrated biomaterial. The resulting
volumetric heating can be used to evaporate internal moisture and create favorable pressure
gradient for liquid and vapor transfer. leading to a significant reduction in drying time. An
inherent drawback of microwave heating that potentially affects product quality is a nonuniform product temperature distribution due to uneven spatial distribution of the
electromagnetic field inside the drying cavity. Improving heating uniformity is. therefore,
essential to the successful application of microwave technology to various food processes.
In an earlier study. Feng and Tang (1998) investigated the possibility of combining
microwave heating with a spouted bed to achieve uniform heating to dry diced apples. A
spouted bed is a special fluidization technique suitable for handling Group D particles in the
Geldart classification of particles (Geldart. 1973). Group D particles are coarse panicles that
can not be fluidized well in ordinary fluidized beds. Many particulate food and agricultural
products fall into this category. A major distinction between a spouted bed and an ordinary
fluidized bed lies in the particle flow pattern (Figure I). In an ordinary fluidized bed. particles
experience a localized oscillatory and somewhat random movement. In a spouted bed, the
particles move through a macroscopic circulation that exhibits upward "spouts" and a
downward annulus (Mathur and Epstein. 1974). The trajectory of an individual particle forms a
three-dimensional pattern in the spouted bed over a certain period, but the position of the
particle at any moment is random. This particle circulation provided uniform heating in the
microwave field and resulted in improved quality in heat sensitive diced apples. The diced
183
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apples experienced a much smaller temperature variation and less discoloration than when
microwave dried in a stationary bed. The diced apples also had lower bulk density and higher
reconstitution capacity compared to traditional drying methods (Feng and Tang. 1998). The
main objective of this work was to further investigate the influence of operational parameters,
such as microwave power level and hot air conditions, on the drying kinetics and temperature
changes of diced apples in a microwave and spouted bed (MWSB) dryer.
MATERIALS AND METHODS
In this study, we selected evaporated diced Red Delicious apples (Malus domestica
Borkh) as the model food to evaluate the drying system because of their sensitivity to thermal
damage. The commercially evaporated apples had an initial moisture content of 31% on a dry
basts or 23.8% on a wet basis, and a bulk density of 688 kg/nr. The diced apple had an
irregular curved hexahedral geometry after slight shrinkage in the previous drying. An average
equivalent diameter of 5 mm was found for the diced apple by equating the dice to a sphere of
same volume. Based on the modified Geldart’s particle classification chart <Figure 2). the diced
apples were spoutable particles (Group D).
The drying tests were conducted in a laboratory MWSB dryer (Figure 3). The dryer
consisted of a spouted bed with a hot air supply system, a microwave power controller, a water
load, and a microwave cavity. Dimensions of the spouted bed were: column inside diameter
80mm. bed height 80mm. and cone angle 31°. Details of the system were provided in Feng and
Tang (1998). The microwave generator power rating was calibrated following the 2-Liter
method recommended by the International Microwave Power Institute (Anon.. 1989). The
nominal microwave power was then estimated as the difference between the calibrated power
of the microwave generator and the power absorbed by the circulating water load.
Four air temperatures. 25.45.70. and 95°C. were used in the experiments. The air to the
heater was supplied at 20°C and 40% relative humidity. The minimum spouting velocity was
determined by the modified Mathur-Gishler equation (Mathur and Epstein. 1974):
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Spouted bed
Ordinary fluidized bed
O ° Oo ° °
o
o ° °o
O 0 o oo
° o - ° o f 0 00=
V
■
^
A ir
Figure I. Comparison of particle flow patterns in a fluidized bed and a spouted bed.
Density difference, kg / m
10000
Group-D (spoutable).
"Transition
zone 'v
Group-B
(sand-like)
1000
Group-C
(cohesive)
Group-A
(aeratable)
Diced apples
100
0.0
0.1
t.O
dp*mm
Figure 2. Modified Geldart classification chart for particles.
185
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Microwave power controller
Stirrer
Spouted bed
Microwave cavitv
Computer
Magnetron
Sample
By-pass
Temperature
controller
Water load
Water pump
Heater
T 2
Electric balance
Sink
Blower
D —Dew point temperature:
F - Flowrate:
T —Temperature:
V - Velocity:
Figure 3. Schematic diagram of microwave and spouted bed (MWSB) drying system.
r.D
1/5
r 2gH(pb - p j '
f
D>]
f d' l
I dJ
.
P'*
>
where
tj
= 1.4 is an empirical correction factor taking into account the sticky surface of the
diced apples. Based on Eq. ( I), the superficial air velocity, in the cylindrical part of the spouted
bed. was set as 1.9 m/s throughout the tests. This velocity provided a stable circulating flow
pattern in the spouted bed during the drying tests. The drying experiments were carried out at
one of four microwave power levels. 0.0.4.9.6.4. and 8.0 W/g, defined as nominal microwave
186
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power per unit dry mass of the diced apples. Forty grams of the evaporated diced apples were
used for each test. Moisture loss during drying was monitored by periodically weighing the
sample on an electric balance.
The moisture content of diced apples was determined using the vacuum oven method
(70°C and 13.3 kPa) recommended by the Association of Official Analytical Chemists for
dehydrated fruits. Product temperature was determined by measuring the inner temperature of
ten randomly chosen apple pieces with a type T thermocouple (response time O.S s) at pre­
designated time intervals.
The color of dried apples was measured with a Minolta Chroma CR-200 color meter to
detect the degree of both localized and overall discoloration occurred during drying. For
comparison, color of evaporated, fresh and commercially dried apples was also measured. The
dried apples were wrapped with a Saran Wrap transparent film (Dow Brands L. P..
Indianapolis. IN) into a square shape. Color measurements were made at five locations on the
square package to ensure an overall color evaluation. Quantitative evaluations were made by
examining the total color change. AE. defined by:
( 2)
where, subscript "o" denotes the color of apple fresh immediately after cut. The value of AE
indicates color change of the dried sample from fresh and is represented by the distance in the
CIE L*a*b* color space between the points that represent the dried sample and the fresh. A
darkness factor b*/a* was also used to quantify possible discoloration.
RESULTS AND DISCUSSION
Temperature variation
Temperature changes in diced apples at four different spouted-bed air temperatures are
shown in Figure 4. The temperature variations about the mean among ten randomly taken diced
apple pieces were less than 3.5°C in all tests. The sample temperature increased in the initial
drying period to reach a plateau. This was in sharp contrast with observations made by many
187
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researchers that, in conventional hot-air assisted microwave drying (microwave heating plus
thin-layer or deep bed drying), drying was not uniform and the product temperature experiences
a monotonic increase when moisture content was low (Beke et aL. 1997). Nonuniform heating
and high product temperature could cause severe thermal damage to product quality. Our
MWSB drying system provided a unique temperature leveling effect after a short warming
period. This temperature leveling phenomenon might have been due to convective cooling by
the air when apple temperature rose above the air temperature coupled with evaporative cooling
at the product surface (Lu et aL, 1998). The high surface heat and mass transfer rates facilitated
by the intensive pneumatic agitation in the spouted bed ensured heat removal at a rate high
enough to balance heat internally generated by microwave energy. The plateau temperatures
were about 12°C to 15°C above the spouted bed air temperatures when the microwave power
level was set at 6.4 W/g. It is. therefore, possible to control the product temperature during a
MWSB drying by regulating the spouted-bed air temperature at a fixed microwave power level.
This is of special importance for temperature sensitive biomaterials.
120
Air temp = 95°C
Air temp = 70°C
too -
Air temp = 45°C
Air temp = 25°C
w
60
20
-
0
to
20
30
D r y in g
40
50
60
70
tim e , m in
Figure 4. Temperature of diced Red Delicious apples in a MWSB dryer at microwave power
level of 6.4 W/g (dry basis).
188
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20
Power = 0.0 W/g
Power = 4.9 W/g
Power = 6 .4 W/g
Power = 8.0 W/g
i- 20
■
0
r 30
20
40
60
80
100 0
Drying time, min
20
40
60
80
100
120
140
160
Drying time, min
Figure 5. Change of moisture content of diced Red Delicious apples during MWSB drying at
(a) microwave power level of 6.4 W/g (dry basis), and (b) air temperature of 70°C.
Increasing spouted-bed air temperature increased the drying rates in diced apples (Figure
5a). As expected, an increase in microwave radiation intensity also significantly increased the
drying rate, as evidenced by a significant reduction in drying time compared to spouted bed
along drying (Figure 5b).
Color evaluation
Table I presents the results of the color measurement for the apple samples. The total
color change. AE, and darkness factor. b*/a*. characterized the overall color quality of the
sample. The commercially dried sample had the most pronounced color degradation (Table I).
The color change (AE) of MWSB dried apples increased from that of evaporated apples as
power level increased. A similar trend was observed for the darkness factor (b*/a*). The
darkness of MWSB dried apples increased slightly (indicated by a lower b*/a* value) but the
darkening was less severe compared to the commercially dried samples. The darkening of
apples can be attributed to non-enzymatic browning (NEB) in the presence of glucose, fructose,
and malic acid. NEB rate generally increases as water is removed during a drying process
because of the increased concentration of reactants. Elevated temperatures used in drying also
189
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Moistur e c o n t e n t , % U l b )
Moistur e c o n t e n t , W t i l h )
Air temp = 25°C
Air temp =45°C
Air temp = 70°C
Air temp = 95°C
expedite the NEB reactions. When further dried to low' moisture contents, the NEB rates are
reduced due to reduced mobility of reactants. The NEB rates, therefore, reach a maximum at
intermediate moisture contents (18% to 25%. dry basis) (Copley and Van Arsdel. 1964). It is
possible that MWSB drying shortened the period when the product passed through the moisture
content range optimal for NEB reactions, and reduced the darkening of the dehydrated product
compared to lengthy conventional hot air drying.
Table I. Color measurement results (L*a*b*). darkness factor b*/a*. and total color difference
AE for diced apples.
Treatment
L*(C V % )
a* (CV %)
b* (CV %)
b*/a*
AE
fresh
83.5 ±0.2-(0.2)"
0.47 ±0.1 (21.3)
22.3 ± 0 .4 ( t .8)
1198
0.00
evaporated
81.8+2.2(2.7)
4.98 ± 0.6 (12.0)
30.9 ± 2 .0 (65)
6.21
5.26
MWSB" (3.7 W/g)
77.4 + 4.2(5.4)
5 5 4 ± 1.3 (23.5)
25.2 ± 2 5 (9.9)
454
6.07
MWSB (4.9 W/g)
76.2 ± 3 .2 (4.2)
5.74 ±0.8 (13.9)
26.0 ± 2 .0 (7.7)
4.53
6.99
MWSB <6.t W/g)
75.2 ± 3.0 (4.0)
5.77 ± 0 5 (8.7)
27.4 ± 1.9 (6.9)
4.76
7.88
commercial
73.4 ± 2 5 (3.4)
S. 15 ± 0.8 (9.8)
30.9 ± 2 .0 (65)
3.79
11.51
a; standard deviation: b: CV values.
c: microwave and spouted bed dried
To examine heating uniformity, the coefficient of variation (CV) was used to compare
the closeness of color readings taken from five different locations within diced apple samples.
CV is defined by the standard deviation as a percentage of the mean:
su
CV = — xlOO%
M-
(3)
The smaller the CV. the closer the color readings from the five locations, and the more uniform
the color of the sample. The CV values for L*. a* and b* are listed in Table 4.1 along with the
color readings. The colors of the fresh, the evaporated and the commercially dried apples were
relatively uniform. The CV for the lightness (L*) of the MWSB-dried samples were close to
that of the commercially dried product. The CV values for redness (a*) and blueness (b*) for
MWSB-dried samples were also close or in the same range as the other treatments (Table t).
190
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This demonstrates a comparable scatter in the color readings among all treatments and.
therefore, an equivalently uniform heating in the MWSB drying.
Drying rate
Particle drying rates, based on the drying data presented in Figures 5a and 5b. are
presented in Figures 6a and 6b. It is obvious that higher temperatures and microwave power
inputs resulted in higher drying rates. All drying took place in the falling rate period with
progressively decreasing drying rates toward the end of drying. In theory, the remaining
moisture in a dehydrated product has increasingly stronger bonds with hydrophilic solid
surfaces as moisture decreases. As a result, the vaporization enthalpy increases continuously as
drying proceeds (Okos et aL. 1992). This, in turn, results in an increasing energy requirement
for moisture removal. In the drying of evaporated apples, microwaves were the sole source of
energy for evaporating water when product temperature surpassed the hot-air temperature. The
conversion of thermal energy from microwaves follows the relationship:
P = 5^6xlO"4fe"E2
(4)
0.09
Power level =
Power level =
Power level =
Power level =
Air temp = 95°C
Air temp = 70°C
Air temp = 45°C
Air temp = 25°C
0.08
0.07
0.06
8.0
6.4
4.9
0.0
W/g
W/g
W/g
W/g
- 0.08
r 0.07
- 0.06
0.05
- 0.05
0.04
r 0.04
0.03
- 0.03
0.02
h 0.02
0 .0 1
- 0.01
0.00
*
3
10
15
20
25
30
Moisture content. %(db)
5
10
15
20
25
30
Moisture content. %(db)
Figure 6. Drying rates of diced Red Delicious apples at (a) microwave power level of 6.4 W/g
(dry basis), and (b) air temperature of 70°C.
191
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0.00
Drying rate, kg HaO/(kg solid - min)
Drying rale, kg I ! , ( ) / ( kg solid - m i n )
0.09
The loss factor of biological materials (e") is positively related to the moisture content of the
materials- From the data documented by Kent (1987), the e" of potatoes was 15.7 at 390%
moisture content (dry basis) and 2.9 at 3% moisture content (dry basis). Therefore the value of
P in Eq. (4) decreases as moisture content decreases. The resulting reduction in microwave
energy conversion leads to reduced drying rates as the drying proceeds. In spite of this,
microwave heating was still very effective in speeding up drying in the low moisture ranges
when compared to hot air drying. For instance, at mediate moisture content (27% dry basis), the
drying rate at power level of 8.0 W/g was about three times higher compared to that of the
spouted bed drying (power level = 0.0 W/g). While at low moisture content (9.7%. dry basis),
an increase of microwave power from 0.0 to 8.0 W/g resulted in a 66-fold increase in drying
rate (Figure 5b). Similar comparison can be made to examine the influence of temperature at a
Ftxed microwave power level (Figure 5a). When air temperature increased from 25 to 95'’C at
microwave power level of 6.4 W/g, the drying rates increased 5.1 times at moisture content of
27% (dry basis) and 44 times at moisture content of 15% (dry basis) respectively.
Moisture transport
Moisture migration during drying in biological materials has been related to different
mechanisms, such as moisture transport driven by capillary force, by moisture or vapor
concentration gradients, by Knudsen flow, and/or by a vaporization-condensation sequence. An
effective moisture diffusivity Deff, which lumps all possible moisture transport mechanisms into
a single measurable parameter, is often used to characterize the drying behavior regardless of
the dominating mechanism (Okos et aL. 1992). Fick’s second law for symmetric diffusion in a
homogeneous sphere, after considering the boundary conditions, can be written as:
ax
a
,a x
3dtT = -rr-T~(
dr r T~>
dr
(5 )
X(r,0) = Xo; X(R,t) = Xe
The solution of Eq. (5) integrated over the radius of the sphere was given by Crank (1975):
192
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The effective diffiisivity. DCff, can be estimated by the Slope Method (Tang and
Sokhansanj. 1993). In the falling rate period and when the moisture ratio ( X - Xe)/(Xo -X,.) is
less than 0.3. the first term in Eq. (6) is predominant and a slope equation can be derived (Feng
and Tang. 1999):
Thus. Deff was evaluated from the slope of a semi-log plot of moisture ratio versus drying time.
The equilibrium moisture content X,. in Eq. (7) was evaluated from the sorption
isotherm equation for apples. The Brunauer-Emmett-Teller (BET) model is one of the best
equations to describe the adsorption of water in the low water activity region (Roman et al..
1982). The BET equation is expressed as:
X
C XmUw
' (l-a w)[l+ (C -l)airl
Roman et al. (1982) investigated the effect of temperature on desorption isotherms of Granny
Smith apples using the gravimetric technique. In order to obtain the equilibrium moisture for
our test conditions, we related the values C and Xm in Roman et al.'s work to temperature by
the following Arrhenius-type equations:
r =0.92
(9)
r =0.92
193
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The equilibrium moisture Xe values at the four spouted bed air conditions, were then
estimated from Eqs. (8) and (9) (Table 2).
Figure 4.6 illustrates the application of the slope method. A two-section curve, as
denoted in Figure 7 by I and II, was observed in all tests. These two sections correspond to the
first and second falling rate regions in the drying of a hygroscopic porous biomaterial, which
has also been reported for the conventional hot air drying of potatoes (Khraishen et al.. 1997).
Temperature dependency of moisture diffusivity is shown in Figure 8a. The influence of
hot air temperature on moisture transport, at microwave level of 6.4 W/g. was expressed by
Arrhenius type equations:
23.700
RT
26.700
) ^ = -8.97 RT
ln(Dfff)„f= - 7 . 8 9 -
r-= 0.99
(
10)
r : =0.85
The activation energy was 23.7 kJ/mol for the first falling rate period and 26.7 kJ/mol for the
second falling rate period. Higher activation energy in the second falling rate period suggests
stronger bonding between the water molecules and the solid material than in the first drying rate
period. The activation energy for the two falling rate periods in the MWSB drying were,
however, lower than the activation energies obtained in conventional hot-air drying methods
reported by Luyben et al. (1980) and Feng and Tang (1999) (44.0—110.0 kJ/mol).
Thermodynamically, activation energy is related to the ease with which the water molecules
pass the energy hurdle when migrating within the product. A lower activation energy translates
to a higher drying rate in a drying process (Adu and Otten, 1996a).
The influence of microwave power level on moisture diffusivity at air temperature of
70°C is shown in Figure 8b and can be described by an exponential function:
(Dcff )ijt = 239x 10-8 exp(0.26P)
r = 0:95
(Oeff )2ad = l-44x lO"9 exp(039P)
r = 051
194
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( 11}
Table 2. Calculated equilibrium moisture, X*, based on Roman et al. (1982) tabulated values of
C and Xmfor apples held at the indicated relative humidity.
Treatment
L*(C V % )
a* (CV %)
b* (CV * )
b“/a*
AE
fresh
83 j ± 0 .2 ' (0.2)1*
0.47 ±0.1 (21.3)
22.3 ± 0.4 (1.8)
12.98
0.00
evaporated
81.8 ± 2 .2 (2.7)
4.98 ± 0 .6 (12.0)
30.9 ±2.0 (6.5)
6.21
5.26
MWSB' (3.7 W/g)
77.4 ±421 (5.4)
5.54 ± 1.3 (23-5)
25.2 ± 2j (9.9)
4.54
6.07
MWSB (4.9 W/g)
76.2 ± 3 .2 (4.2)
5.74 ± 0.8 (13.9)
26.0 ±2.0 (7.7)
4.53
6.99
MWSB to.i W/g)
7 5 .2 r3 .0 (4.0)
5.77 x 0 .5 (8.7)
27.4 x 1.9 (6.9)
4.7b
7.88
commercial
73.4 ± 2 .5 (3.4)
8.15 ± 0.8 (9.8)
30.9 ± 2.0 <6.5l
3.79
11.51
a: standard deviation: b: CV values. 9c : c: microwave and spouted bed dried
2.0
13 -
xi
X_
XI
X
y
I
Air temp = 95°C
Air temp = 70°C
Air temp = 45°C
Air temp = 25°C
0.5 -
0.0
-
0
20
40
60
30
Drying time, min
Figure 7. Two falling rate periods and the application of the slope method at microwave power
level of 6.4 W/g (dry basis).
195
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-12
-12
-13
o
v
-14
First failing rate
Second failing rate
Regression
a
v
(b)
First failing rate
Second falling rate
Regression
-14
-16
-16
-17
-17
-18
-IS
|
-iy 1
-20 4
-20
-21
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
(1 / Temperature) * 1000. l/K
0
I
2
3
4
5
6
Power level. W/g
Figure 8. (a) Influence of hot air temperature on moisture diffusivity at microwave power level
of 6.4 W/g (dry basis); (b) Influence of microwave power level on moisture diffusivity at air
temperature of 70°C.
The above two relationships correspond to the first and second falling rate periods in the drying
of evaporated apples, respectively. For spouted bed drying without microwave heating (power
level = 0.0 W/g). the effective moisture diffusivity values at 70°C for the first and second
falling rate period were 2.60 x IO'8 m2/s and 1.60 x 10*9 m2/s. respectively (Table 3). When
adding 6.4 W/g microwave power to the material in the spouted bed. the diffusivity values in
the first and second falling rate periods were increased 3.0 and 4.3 fold to 7.84 x IO'8 m2/s and
6.79 x 10‘9 m2/s. respectively. This increase in the effective diffusivity resulted in significantly
higher drying rates as shown in Figures 6a and 6b.
The effective moisture diffusivities obtained with the MWSB drying method were
compared to the values documented in the literature (Table 3). At microwave power level of
zero, the diffusivity value for diced apples during MWSB drying is comparable to the literature
values at similar temperatures. Increasing microwave energy raised the effective moisture
diffusivity. The moisture diffusivity was related not only to moisture content and temperature
196
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U (l)
Ln (1),
-15
but also to the physical structure of the product. For porous food products, porosity is one of the
most
Table 3. Effective moisture diffusivities in apples obtained using different drying methods.
Reference
Tem perature
DeffXlO9
D rying
JC
m '/s
m ethod
66
6.4
hot-air
Saravacos and C harm ! 1962:
70
3.617
hot-air
Rosteinera/. (1974)
71
1.6
hot-air
Alzamorai 1980)
50-80
0.74-0.95
hot-air
Zogzas and Maroulisl 1996)
present work
0.02-2.35
1.19-2.97
0.46-3.66
70 (0.0 W/g)‘
l.6-’(26.03)
microwave +
70 (4.9 W/g)
5.2:(54.43)
spouted bed
70 (6.4 W/g)
6.8‘(78.43)
70 (8.0 W/g)
22.2*( 144.43)
I: microwave power level: 2: 2nd failing rate period: 3: 1st falling rate penod:
important structural factors affecting the diffusion of moisture in the food polymer matrix.
Different drying methods (such as freeze drying and puffing) and. often, pretreatment (such as
osmosis) have been found to have an influence on the measured moisture diffusivities (Zogzas
et al.. 1994) since they alter the physical structure of the food in various ways. Internal
vaporization during microwave drying might have promoted, in some degree, the formation of a
more porous structure and. hence, a higher effective moisture diffusivity.
With the effective moisture diffusivity expressed in Eqs. (10) and (11), Eq. (6) can be
used to predict the drying rate and drying time at different hot air temperatures and microwave
power levels in the tested ranges. Adu and Otten ( 1996b) have employed this approach to study
the drying characteristics of white beans in a single-mode microwave cavity and good
agreement with experimental results has been reported.
Because of the internal vaporization in MWSB drying, a lower bulk density in diced
apples, when compared with convective hot-air drying, was achieved (Feng and Tang, 1998).
197
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This serves as a good indicator for less shrinkage during MWSB drying. Shorter and uniform
drying in the MWSB dryer also resulted in better color than conventional methods. In fact,
during the course of MWSB drying we observed significant puffing, but this was followed by
shrinking close to the end of the drying. Further research is needed' to maintain the puffed
structure.
The microwaves directly couple with moisture inside food material to generate heat
needed for moisture evaporation during the MWSB drying. We. therefore, expect a high
efficiency for the energy delivered by the microwave power generator. The hot air flow in the
spouted bed serves as a media to carry away the evaporated moisture and fluidize the panicles.
Optimum energy efficiency may be obtained by selecting proper microwave power and hot air
energy ratio. The substantial reduction in drying time will lower the operational energy
consumption. Overall, we expect higher energy efficiency than a hot air fluidized bed dryer.
Detailed information on energy efficiency of microwave spouted bed dryers will be obtained in
our further study.
The cost for microwave power generation and control system has been reduced
significantly over the last two decades. The microwave generator (magnetron) is now more
durable than before as a result of the improvement in design and the use of circulator to prevent
reflected power from heating the generator. But still adding microwave heating to a drying
system may increase equipment cost. However, since microwave heating can significantly
reduce drying time, increased throughput or reduced equipment size and the added value of the
high quality may well offset the additional cost of adding microwave heating system. The cost
of MWSB drying is likely to be product specific due to the differences in the drying rates for
different products. Since the temperature of the air in the MWSB dryer can control the product
temperature, it is very likely that this technique will be most applicable to producing high value
and heat sensitive particulate products.
CONCLUSIONS
Drying of diced apples in a microwave and spouted bed dryer can be expedited by
increasing either spouted-bed air temperature or microwave power level. Temperature leveling
198
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effect was achieved in the microwave and spouted bed combined drying in the tested
temperature range. The product temperature was I2°C to I5°C above the hot air temperature
when the microwave power was set at 6.4 W/g. The temperature dependency of moisture
diffusivity was quantified by an Arrhenius type equation. Lower activation energy values during
MWSB drying suggests that an increase in the mobility of water molecules can be imparted by
microwave radiation. Selecting proper spouted-bed air temperature and microwave power level
can control final product temperature. Although the technical feasibility of MWSB drying
technique in the R&D stage has been demonstrated in this and a previous study (Feng and Tang.
1998). the economical feasibility remains a topic for further studies.
ACKNOWLEDGEMENTS
The authors acknowledge support from the Washington State Agricultural Research Center.
Washington State University IMPACT Center and Northwest Center for Small Fruits Research.
We acknowledge TreeTop. Selah. WA. for donating evaporated apples.
NOMENCLATURE
a
redness
aw
water activity
b
blueness
C
constant
CV
coefficient of variation
4
equivalent diameter of apple dice, m
D
diameter, m
Dc
column inside diameter, m
Di
inlet inside diameter, m
Deff
effective moisture diffusivity. m2/s
E
Electric field intensity. V/cm
f
frequency, GHz
a
gravimetric acceleration, m/s2
H
bed height, m
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L
lightness
P
microwave power level. W/cm3 or W/g
r
radius, m
R
universal gas constant = 8.314. J/(mol K); radius, m
Sn
standard deviation of the color readings
t
time, s
T
temperature, k
minimum spouting velocity, m/s
X
moisture content, kg H^O /(kg solid)
Xc
equilibrium moisture content, kg H2 0 /(kg solid)
xm
multilayer moisture, kg H2 0 /(kg solid)
X,,
initial moisture content, kg H2 0 /(kg solid)
X
average moisture content, kg H2 0 /(kg solid)
Greek letters
e"
relative dielectric loss factor
n
correction factor
M-
mean of the color readings
Pa
air density, kg/m3
Pb
bulk density of diced apple, kg/nr
REFERENCES
1. Adu. B. and Otten. L.. 1996a. Diffusion characteristics of white beans during microwave
drying. J. Agric. Eng. Res.. 64. pp. 61-70.
2. Adu. B. and Otten. L.. 1996b. Microwave heating and mass transfer characteristics of white
beans./. Agric. Eng. Res., 64. pp. 71-78.
3. Alzamora. S. M.. Chirife. J.. VioIIaz. P. and Vaccarezza. L. M., 1980. Heat and mass
transfer during air drying of avocado. In Development in Drying, Mujumdar. A.S. (ed).
Science Press N. J.. pp. 247-254.
200
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4. Anon.. 1989. A procedure for power output measurement of consumer microwave ovens.
Microwave world. 10. pp. 15.
5. Beke. J.. Mujumdar. A.S. and Giroux. M.. 1997. Some fundamental attributes of com and
potato drying in microwave fields. Drying Technol.. 15(2). pp. 539-554.
6.
Copley. M. J. and Van Arsdel. W. B.. 1964. Food Dehydration. Vol. II. Productsand
Technology. (The AVI Publishing Company. Westport. Connecticut), pp. 9-11.
7.
Crank. J.. 1975. The Mathematics o f Diffusion (2nd ed.). Clarendon Press. Oxford.
8.
Feng. H. and Tang, J.. 1998. Microwave finish drying of diced apples in a spoutedbed. J.
Food Sci.. 64(4), pp.679-683.
9. Feng, H.. Tang, J. and Dixon-Warren. St J., 2000. Determination of moisture diffusivity of
red delicious apple tissues by thermogravimetric analysis. Drying Technol.. 18(5).
10. Geldart. D.. 1973. Types of fluidization. Powder Technol.. 1. pp. 285-290.
11. Kent. M.. 1987. Electrical and Dielectric Properties of Food Materials. Science and
Technology Publishers. London. UK.
12. Khraishen. M.A.M.. Cooper. T.J.R. and Magee. T.R.A.. 1997. Transport mechanisms of
moisture during air drying processes. Trans. IChemE. 75 C. pp.34-40.
13. Lu. L.. Tang. J. and Ran. X.. 1998. Temperature and moisture changes during microwave
drying of sliced food. Drying Technol.. in press.
14. Luyben. K. C. A. M.. Olieman. J. J. and Brain. S.. 1980. Concentration dependent diffusion
coefficients derived from experimental drying curves, in Drying’80. Vol. 2. Mujumdar.
A.S. led.). (Hemisphere Publishing Corporation), pp. 233-243.
15. Mathur. K.B. and Epstein. M. 1974. Spouted Beds. Academic Press. Inc.. New York.
16. Okos. M.R.. Narsimhan. G.. Singh. R.K. and Weitnauer. A.C.. 1992. Food Dehydration. In
Handbook o f Food Engineering. D.R. Heldman and Lund. D.B.. (eds). (Marcel Dekker.
Inc.. New York), pp. 437-562.
17. Roman. G. N.. Urbicain. M. J. and Rotstein. E.. 1982, Moisture equilibrium in apples at
several temperatures: experimental data and theoretical considerations, /. Food Sci.. 47. pp.
1484-1489.
18. Rostein, E.. Laura, P. A. and De Cemborain, M. E.. 1974, Analytical prediction of drying
performance in nonconventional shapes. J. Food Sci.. 39, pp. 627-631.
201
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19. Saravacos. G.D.. Charm. SJE.. 1962. A study of the mechanism of fruit and vegetable
dehydration. Food Technol.. Jan.. pp. 78-81.
20. Tang. J. and Soichansanj. S.. 1993. Moisture diffusivity in laird lentil seed components.
Trans. A S A E 36(6). pp. 1791- 1798.
21. Zogzas. NT.. Maroulis. Z.B.. Marinos-Kouris, D.. 1994. Moisture diffusivity methods of
experimental determination. A review. Drying Technol.. 12:. pp. 483-515.
22. Zogzas. N. P. and Maroulis. Z. B., 1996. Effective moisture diffusivity estimation from
drying data. A comparison between various methods of analysis. Drying Technol.. 14. pp.
1543-1573.
202
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Chapter 8
MICROWAVE AND SPOUTED BED DRYING OF FROZEN BLUEBERRIES: THE
EFFECT OF DRYING AND PRETREATMENT METHODS ON PHYSICAL
PROPERTIES AND RETENTION OF FLAVOR VOLATILES
Hao FengTJuming Tang, Dennis Scott Mattinson, and John Keegan Fellman
Department of Biological Systems Engineering
Washington State University. Pullman. WA 99164-6120
ABSTRACT
Frozen blueberries (Vaccinium corymbosum L cv. ’Elliott’ ) were dried in a microwave and
spouted bed combined dryer (MWSB) at 70°C air temperature and 3.7 W/g microwave power
(wet material). The effect of pretreatment using a 2.5% ethyl oleate and 0.2 NaOH dipping
solution followed by sucrose osmotic treatment was investigated. The drying kinetics of
MWSB drying was compared with spouted bed (SB) drying with dipping treatment, and with
tray drying. The rehydration ratio, the color, and the bulk density of MWSB dried blueberries
were compared with those of freeze, tray, and SB drying. The drying time needed to reduce
blueberry moisture content from 82.5% to 15% (wet basis) using MWSB drying was 1/19 and
1/24 (with and without pretreatment) of the time for tray drying. The MWSB drying resulted in
a low bulk density and more reddish and less blue color compared with other methods. MWSB
dried frozen blueberries exhibited a higher rehydration ratio in short soaking times. Analysis of
flavor volatiles by GC/MS identified ten heat-generated compounds. Microwave heating
generated three unique flavor compounds (2-Butanone. 2-methyl butanal. and 3-methyl
butanal). Freeze-dried frozen blueberries lost several flavor compounds including the typical
blueberry aroma, the 1,8-cineoIe.
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INTRODUCTION
Blueberries are popular in North America because of the unique flavor and nutrition values.
Recent studies document their high antioxidant capacity and the benefits of those antioxidants
in neutralizing the effects of free radicals that damage DNA in human cells (Anon.). The
anthocyanin pigment of blueberries is under study for its links to improved eyesight and
reduction in the incidence of age-related diseases. According to a report from The North
American Blueberry Council. 163,631 million pounds of cultivated blueberries were produced
in 1996 (Anon.). Fresh blueberries are perishable and can only be stored for two weeks under
refrigerated conditions after harvesting (Lim et al., 1995). Dehydration can be used to extend
shelf life at room temperature. Dehydrated blueberries may also impart new functional
attributes to final products. Food processors have found that dried cultivated blueberries can
provide an added eye and taste appeal to cereals, confections, and bakery goods (Duxburg.
1992).
Commercially dried blueberries include dehydrated (moisture level 11-18% wb). freeze
dried (moisture level 2-3% wb). and drum dried powders (moisture level 3-5% wb) (Anon.).
Current commercial dehydration methods are limited by either high production cost (e.g. freeze
drying) or by reduced quality (e.g. sun or hot-air tray drying) because of the long exposure of
blueberries to elevated temperatures. Recent research efforts strive to develop appropriate
drying methods that result in high quality dehydrated blueberries. Dehydration techniques
explored include explosion-puffing (Sullivan et al.. 1982). fluidized bed drying (Kim and
Toledo. 1987). microwave drying (Yang and Atallah. 1985; Venkatachalapathy and Raghavan.
1997). high temperature fluidized bed drying (Kim and Toledo, 1987), and osmotic dehydration
(Kim and Toledo, 1987; Yang et al.. 1987; Venkatachalapathy and Raghavan. 1997;
Ramaswamy and Nsonzi, 1998). The criteria used for evaluating those drying techniques were
physical quality attributes such as the rehydration ratio, bulk density, texture, and color (Nsonzi
and Ramaswamy, 1998). New dehydration methods were reported to yield improved quality
when compared to traditional hot air drying. There are few reports concerning aroma volatile
retention.
204
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The objective of this study was to investigate the drying characteristics of ’Elliott’
blueberries in a microwave and fluidized bed combined (MWSB) dryer and to study the effect
of such drying on both the physical and flavor quality attributes.
MATERIALS AND METHODS
Blueberries
Elliott blueberries (Vaccinium corymbosum £.), a popular highbush cultivar in North
America, grown in northern Idaho and harvested on 5 September 1997. were used in this study.
To preserve the aroma volatiles. the blueberries were processed immediately after the harvest
by individual quick freezing (IQF) and refrigerated at -40 to -22°C. Before the drying
experiments, berries were thawed at 4°C for more than five hours. The moisture content of the
thawed blueberries was 82.5% (wb). The drying quality of ’Elliott’ blueberries was evaluated by
rehydration ratio, bulk density, total color difference, and flavor volatile retention.
Drying methods
Following drying methods or combination of drying methods were used in this study to
reduce moisture content of blueberries to 4 to 13% (wb).
(1) Freeze drying: 400g frozen berries were freeze dried in a Freezemoble 24-Unitop dryer
(Virtis Company. Gardiner. NY) under the following conditions: vacuum. 20 millitorr. heating
plate temperature. 20°C: and condenser temperature, -60°C. Since whole berries were used in
freeze drying, the drying time to reduce moisture content to 5.1% was 48 hours.
(2) Tray drying: 400g thawed berries were air dried in an UOP-8 tray dryer (Armfield LTD..
Hampshine. England) at 70°C to a final moisture content of 5.8% (wb). The moisture loss was
monitored by periodically weighing the tray.
205
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(3) Microwave and spouted bed combined drying (MWSB): Microwave drying was combined
with the spouted bed fluidization technique to improve heating uniformity. A spouted bed was
used to provide pneumatic agitation to the berries to avoid localized overheating due to the nonuniform distribution of the electromagnetic field inside the microwave cavity. A schematic of
the drying apparatus is presented in Figure I. Details of the apparatus are reported elsewhere
(Feng and Tang, 1998a). Thawed blueberries (40g) were dried at a microwave power level of
3.7 W/g (wet material) and air temperature of 70°C. The superficial hot air velocity was 2.1
m/s. The final moisture content of dried berries was 6.9% (wb).
(4) Spouted bed drying (SB) with pretreatment using 2.5% Ethyl oleate and 0.2% NaOH
dipping: In preliminary tests to determine the best dipping method, three treatment solutions
were investigated: 2.5% ethyl oleate & 0.2% NaOH solution. 2% NaOH solution, and hot
water. The first dipping solution was found to yield the best appearance and highest moisture
loss rate. For this treatment, thawed berries were dipped in 2.5% ethyl oleate and 0.2% NaOH
solution at 60°C for 60 seconds. The dipped blueberries were flushed with 40°C hot water and
residual surface water was removed with paper tissue. Spouted bed air temperature was 70°C
and air velocity was 2.1 m/s. Blueberries was dried to a moisture content of 12.9% (wb).
(5) MWSB drying with osmotic pretreatment: After 2.5% ethyl oleate & 0.2% NaOH dipping.
40g thawed and dipped blueberries were soaked in 800g saturated sucrose solution at a
temperature of 50°C for 24 hrs to reduce moisture levels. After the osmotic treatment, berries
were flushed with 40°C hot water to remove surface sugar. The moisture content after osmotic
treatment was 56.6% (wb). The berries were then MWSB dried under the above-mentioned
conditions to a final moisture level of 11.7% (wb).
Rehydration ratio
Rehydration ratio was defined as the total mass of rehydrated blueberries per unit mass of
dry matter after rehydration (Kim and Toledo, 1987). Since dried blueberries are mainly used in
cereal, confections, and bakery goods, a rehydration temperature of 21 °C (room temperature)
was used. Dried blueberries (5g) were immersed in lOOg tap water and held for 2.7.17.32. and
206
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52 min. The blueberries were then drained on a perforated plate by applying a gentle suction till
no water drip could be observed (Prabhanjan et al., 1995). The dry matter was determined by
the vacuum oven method at 70°C and 28 in. Hg (AOAC. 1990). Results reported were the
means of three determinations.
Bulk density
Bulk density of dried blueberries was determined as follows (Zogzas et al.. 1994):
Af + M w
Ph~ V + V -t-V.
<l)
Microwave power controller
Stirrer
Spouted bed
Microwave cavity
Computer
Magnetron
Sample
By-pass
Temperature
controller
Water load
Water pump
Heater
Electric balance
Sink
Blower
D —Dew point temperature:
F —Flowrate;
T —Temperature:
V —Velocity:
Figure I. Schematic diagram of microwave and spouted bed (MW&SB) drying system.
207
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where M and V are mass and volume; subscripts "s". ”w”. and "a" denote solid, water, and air
trapped in the berry, respectively. The bulk density defined in eq. ( I) characterized the internal
physical property of the berry and. therefore, is widely used in evaluating quality of dried fruits
and vegetables (Feng and Tang. 1998b). The mass Ms + Mw was determined by an electronic
balance. The volume of dried blueberries, composed of the volume of solid, water, and air. was
determined by a water displacement method (Lozano et al., 1980). Dried blueberries (5g) were
used for each bulk density measurement and the means of three determinations were reported.
Color
Color measurements were conducted with a Minolta Chroma CR-200 color meter (Minolta
Camera Co. LTD. Japan). CIE L*a*b* color system was used to characterize the color changes
of blueberries dried with different drying and pretreatment methods. The CIE scales measure
the degrees of lightness (L*). redness or greenness (+/- a*), and yellowness or blueness (+/- b*).
Total color change AE was employed, which was calculated by (Feng and Tang. 1998a):
( 2)
where subscript ”0” represents the color reading of thawed blueberries which functions as a
reference for the color comparison. AE represents the distance between the point representing
the thawed blueberries and the point for the blueberries dried with one of the five methods (in
three-dimensional CIE color space). Color readings of dried blueberries were taken by
wrapping a sample of about 40g with transparent Saran Wrap (Dow Brands L. P.. Indianapolis,
IN) into a square packet and measuring color at five different locations on the packet. At each
location, five readings were taken and the average of 25 readings from five locations was taken
as the color of the sample.
Flavor Volatile Analysis:
Dehydrated blueberries were rehydrated at room temperature with deionized water. The
amount of water used to reconstitute the blueberries was calculated based on the moisture
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content of the dried blueberries to reach a solid content of 15.6% (g solid/g HiO) in the
mixture. The rehydrated blueberries were macerated with a blender and the mixture was
centrifuged 12-14 min at 8l60g to obtain the clarified juice. Fifty grams of thawed blueberries
were macerated and then diluted in 100 ml distilled deionized water to obtain a mixture. The
mixture was centrifuged to collect the clarified juice. Flavor volatiles analysis was performed
by using 2.5 ml of juice diluted 1:1 with distilled deionized water and injected into a gas
chromatography system using purge-and-trap cryofocusing techniques. Samples were purged in
a closed system for 5 min with helium, and water vapor was condensed from the sampling
stream by passing the vapors through a cryostat held at -10°C. Samples were injected by
cryofocusing at -90°C using a commercial purge-and-tap injector (Chrompack International
B.V.. Middelburg, Netherlands) modeled after that reported by Badings et al. (1985). The
sample was subsequently injected into a HP-5890 gas chromatographic system, and separations
were achieved using conditions reported by Mattheis et al. (1991). except that the DB-WAX
column diameter was 0.32 mm with 5.0 jiM film thickness. Quantitation was achieved using
flame-ionization detection. Positive identification of volatile molecules was facilitated by
purging the sample onto Tenax traps, then using a Tekmar 6000 cryofocusing thermal trap
desorber (Tekmar Co.. Cincinnati. OH) interfaced to a HP-5890 GC with a HP-5971
Quadrupole Mass Spectrometer. The mass spectrometer was operated in the electron ionization
mode at 70eV. Identification was via Wiley/NIST library match and injection of standard
compounds.
RESULTS AND DISCUSSION
Drying kinetics
Drying curves for blueberries (Figure 2a) exhibit a typical exponential decrease, indicating
an internal controlled moisture transport (Tulasidas er al.. 1993). The drying times needed to
reduce moisture from 82.5% (wb) to 15% (wb) were about 40. 50. 200. and 960 min for the
MWSB drying, MWSB + dipping +• osmosis, SB drying, and tray drying, respectively. A
substantial reduction in drying time was achieved by applying microwave energy in the drying
209
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process. With and without pretreatment. the time needed for microwave drying of blueberries to
a moisture of 15% (wb) was 1/19 and t/24 of the time for the tray drying, respectively.
Fluidization also accelerated the moisture removal as indicated by an almost five fold reduction
in drying time compared with the tray drying. A comparison of drying times of blueberries
dried with different techniques is tabulated in Table I. Drying time and temperature are the key
parameters for the quality degradation of fruits and vegetables during drying (Yang and Atallah.
1985: Strumilio et al.. 1996). Among the newly developed techniques listed in Table I.
microwave and spouted bed combined drying yielded the shortest drying time at a moderate air
temperature (70°C) and, hence may be a very effective alternative to the present commercial
drying methods for blueberries.
TABLE I. BLUEBERRY DRYING TIME COMPARISON
T e m p e ra tu re
R e fe re n c e
0.7
°C
70
present study
15
0.8
70
present study
OD' -r HTFB + FB11
12*
1.2
150 + 60
Kim and Toledo. 1987
HTFB + tunnel drying
I21
2.1
170 + 60
Kim and Toledo. 1987
SB + dipping6
15
3.3
70
present study
tunnel drying
12*
12.5
60
Kim and Toledo. 1987
tray drying
15
16
70
present study
sun drying
1 6 -2 5
72
D ry in g
m e th o d
M
o is tu r e
% (wb)
15
MWSBe +dipping6 + ODc
MWSB
i
» .
»r
D r y in g
tim e
h r
Yang and Atallah. 1985
,
bm .
& 0.2% NaOH.c osmotic drying time excluded. J OD (osmotic dehydration): HTFB (high temperature fluidized
bed. air = 150 & I70°O : FB (fluidized bed).e microwave & spouted bed.
The drying rates for four drying methods are presented in Figure 2(b). In Figure 2(c), an
enlarged drying rate scale was used to show the drying rates of the spouted bed +- dipping and
the tray drying. Drying of blueberries occurred in the falling rate region. Microwave drying rate
was three orders of magnitude higher than SB drying or tray drying- The drying rate for spouted
210
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bed approximated three times the rate of tray drying (Fig. 2b & 2 0 . During the first 5 min in
the MWSB drying, the blueberries burst and liquid bled out. The high drying rate of MWSB
drying was partially due to bursting which provided openings in the berry epidermis thus
allowing moisture to escape. Prevention of rupture and elimination of resulting reduction of the
drying rate, dipping and sucrose osmotic pretreatment were used to reduce moisture to 56.6%
(wb). MWSB drying of osmotically pretreated blueberries was slightly slower than the MWSB
drying. Our data suggest that microwave heating generates a positive pressure and temperature
gradient from sample center to surface thus causing an increase in the drying rate (Torringa et
al.. 1996).
Rehydration
The rehydration ratios for dehydrated blueberry are shown in Figure 3. The effect of drying
method on relative water regaining capacity of blueberries was significantly different when
measured after 2 min and 32 min soaking. The MWSB dried blueberries yielded the highest
rehydration ratio at 2 min while, at 32 min. tray dried samples exhibited the largest water
holding capacity. The higher rehydration capacity of MWSB drying at the beginning of the
reconstitution process may result from the bursting which created openings in the blueberry
skin. The high resistance of blueberriy skin to moisture diffusion has been documented by
Venkatachalapathy and Raghavan (1997). The dried blueberries with cracks on the skin could
absorb water easier and faster at the beginning and. for the same reason, their water holding
capacity would be reduced during long soaking times (Figure 3). It may be advantageous for
dried blueberries to have a high short time reconstitution capacity when used for breakfast
cereals, since they are consumed with milk within the first minutes of mixing. Freeze dried
blueberries do not exibit a higher rehydration capacity compared to tray drying as reported by
Yang and Atallah (1985). This may be the consequence of less epicuticular wax decomposition
when compared to lengthy thermal trav drying. Sugar-infused blueberries exhibited poor
rehydration. It is possible that the sucrose absorbed during osmosis could block the micropores
in the skin or create a higher osmotic pressure inside the dried blueberries when water was
absorbed.
211
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S
1 2
2
a
I
40
60
HO
II O
Drying time (mini
0
200
600
400
800
1000
1200
1400
Drying time (min)
4e-6
(c)
3e-6
2e-6
c
Ie-6
le-5 -
0
I
3
4
M
t
5 0
•>
3
4
=0
a
-j£
W
50
D
o is tu r e c o n te n t. % (d b )
MWSB drying (power = 3.7 W/g. air = 70°C)
MWSB+dipping+Osmosis (power = 3.7 W/g. air = 70"O
SB+dipping (air = 70'’O
Tray dryer drying (air = 70“O
Figure 2. Drying Kinetics of Elliott Blueberries with Different Drying and Pretreatment
Methods
Color
Color measurements of dried blueberries are presented in Table 2. The desirable color is the
one closest to that of the thawed blueberries. The total color change AE values indicated the
212
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
most severe discoloration in the freeze dried blueberries while the MWSB dried sample
exhibited the smallest color degradation, when compared to the thawed blueberries. MWSB
dried blueberries exhibited higher a* and b* values, indicating a more reddish but less blue
color, possibly caused by a leakage of anthocyanin as a result of bursting. The anthocvanin
pigments of blueberries are located in the epidermal and subepidermal cell layers (Sapers and
Phillips. 1985). Above the epidermal cell layers, the outermost epicuticular wax layer and the
underlying cuticle may decrease the perception of anthocyanin pigment colors. The slightly
higher L* value and. therefore, more pale appearance, of freeze dried samples may relate to
0.7
0.6
=
0.5
S
0.4
■3
0.3
0.2
0.1
0.0
0
[0
20
30
40
50
Rehydration time (min)
Freeze drying
Tray drying! air=70“O
MWSB drying (atr=70JC)
SB drying (with EO & NaOH dipping: air=70°O
MWSB drying (with EO&NaOH dipping and sucrose osmosis)
Figure 3. Comparison of Rehydration Capacity of Elliott Blueberries Dried with Different
Methods
213
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 2. BLUEBERRY COLOR MEASUREMENT RESULTS
L*
a*
b*
AE
thawed
31.07 ± I3 a
1.62 ±0.3
-0.74 ±0.1
0
freeze drying
38.52 ±0.8
0.62 ±0.3
-0.83 ±0.1
752
tray drying
3555 ± 0 3
0.51 ±0.2
-0.06 ±0.1
4.67
MWSB drying
34.28 ± 0.4
3.11 ±0.3
0.47 ± 0.1
3.74
SB drying
34.95 ±0.4
0.48 ±0.1
-0.03 ±0.02
4.11
MWSB + dipping +
osmosis drying
35.47 ±0.3
0.21 ±0.01
-0.13 ±0.03
4.66
Treatment
the intact surface wax layer and altered surface reflection to the incident light of the color
meter. A higher AE value for freeze dried blueberries was also reported by Nsonzi and
Ramaswamy (1998).
Bulk density
Bulk densities of blueberries dried with selected methods are compared in Figure 4.
Compared to thawed blueberries, the bulk density of freeze dried and MWSB dried blueberries
is significantly lower, only 49% and 57% of the density of thawed blueberries. The low bulk
density of freeze dried product was attributed to the well protected porous structure and
minimized shrinkage when freeze-dried (Yang and Atallah. 1985). The puffing effect of
microwave drying may be responsible for the low bulk density due to MWSB drying. A similar
puffing effect was reported by Torringa et aL (1996) and Feng and Tang (1998a) in studies
regarding the drying of fruits and vegetables. Hot air drying methods (tray and SB drying) were
characterized by a high bulk density close to that of the thawed blueberries. In contrast to
MWSB drying, the MWSB + dipping + osmotic treatment had the highest bulk density. This is
very likely related to the sugar infusion. The introduction of additional sugar may have changed
the Theological properties and glass transition temperature of the berry. This may result in a
complex internal contracting hygrostress state during drying that may exceed internal pressure
214
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produced by the dielectric heating. Our results agree with those of Ertekin and Cakaloz (1996)
reported higher bulk density due to sucrose infusion of dried peas.
Flavor volatile analysis
Elliott' blueberries that were dried by selected drying methods was analyzed by GC/FID with
purge and trap injection. The compounds detected are listed in Table 3. A typical chromatogram
for microwave dried blueberries is illustrated in Figure 5. The major findings from Table 3
include: I) heating caused some aroma compounds, such as acetyaldehyde and ethyl 3-methyl
butyrate found in thawed juice, to vanish or to decrease until they were undetectable: 2) several
aroma volatiles disappeared from freeze-dried samples as a result of prolonged drying: 3) heat
treatment altered aroma by creating ten new flavor notes (2-methyl propanal. butanal. 2butanone. 2-methyl butanal. 3-methyl butanal. 2-pentanone. 2-ethenyltetrahvdro 2.6.2h-pyran.
l-limonene. l.8-cineole. and 2-furancarboxaIdehyde). Among the compounds newly detected
after heating, limonene and l.8-cineole have been identified as blueberry aroma in previous
studies (Parliment and Koloe. 1975; Lugemwa et al., 1989; Simon et al.. 1996). It is likely that
the heating increased the intensity of these compounds; 4) microwave heating generated some
unique flavor compounds (2-Butanone. 2-methyl butanal, and 3-methyl butanal). The
mechanisms under which the flavor volatiles are generated during drying are unknown for both
the ordinary heating and the microwave heating. Luning et al. (1995). in a study regarding the
effect of hot-air drying on the flavor compounds of bell peppers, found that the hot-air drying
can release new odor compounds which can be related to the autoxidation of unsaturated fatty
acids. Microwave-hot air drying of mushrooms positively affected retention of characteristic
aroma compounds (Riva et al.. 1991). Further study is required to understand the interaction
between heat treatment and flavor compound retention/degradation/generation.
CONCLUSION
MWSB drying of frozen blueberries was characterized by a substantial reduction in drying
time and an improved product quality as indicated by a low bulk density, a high short-time
rehydration ratio, and a more reddish and less blue color compared to samples freeze dried, tray
dried, and SB dried. Pretreatment using 2.5% Ethyl Oleate & 02% NaOH dipping followed by
215
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sucrose osmotic dehydration can prevent blueberries from bursting when microwaved but
resulted in a high bulk density and low rehydration ratio. Freeze drying of frozen blueberries
did not yield a high-quality dried product with regard to rehydration ratio and color change.
Characteristics of the flavor volatile compounds of 'Elliott' blueberries were changed by
both hot air and microwave heating. Microwave heating produces new volatile compounds not
found when blueberries are dried by other methods. Several flavor compounds disappeared
from freeze-dried blueberries.
1400
)
WdZfA
6SSSSSJ
sm sm
t
l
tj.ti.tiiI
L
Fresh
Freeze drying
Tray drying (air =70°C)
MWSB drying (air=70“C)
SB drying (with EO & NaOH dipping; air=70°C)
MWSB drying (with EO&NaOH dipping and sucrose osmosis)
Figure 4. Bulk Density of Elliott Blueberries under Different Processing and Pretreatment
Methods
216
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ACKNOWLEDGEMENTS
The authors acknowledge support from the Washington State Agricultural Research Center.
Washington State University IMPACT Center and Northwest Center for Small Fruits Research.
REFERENCES
ANONYMOUS. Cultivated Blueberries. The North American Blueberry Council.
AOAC. 1990. Official Methods of Analysis. 15th ed. Association of Official Analytical
Chemists. Washington. DC.
BADINGS, H.T.: DE JONG, C.; DOOPER. R.P.M. 1985. Rapid analysis of volatile
compounds in food products by purge-and-cold-trapping/capillary gas chromatography. J. High
Res. Chrom. and Chrom. Commun. 8 . 755-763.
DUXBURG. D.E. 1992. Dried blueberries fill functional gap. Food Processing. Dec. 30-32.
ERTEKIN. F.K. and CAKALOZ. T. 1996. Osmotic dehydration of peas. IL Influence of
osmosis on drying behavior and product quality. J. Food Processing and Preservation. 20. 105119.
FENG. H. and TANG. J. 1998a. Microwave finish drying of diced apples in a spouted bed. J.
Food Sci.. 63. 679-683.
FENG. H. and TANG. J. 1998b. Quality changes during drying and quality change history of
biomaterials, unpublished work.
BOM. M.H. and TOLEDO, R.T. 1987. Effect of osmotic dehydration and high temperature
fluidized bed drying on properties of dehydrated Rabbiteye blueberries. J. Food Sci.. 52. 980984.989.
L1M. L.T.. TANG, J. and HE. J. 1995. Moisture sorption characteristics of freeze dried
blueberries. J. Food Sci.. 60, 810-814.
LOZANO, J.E., ROTSTEIN, E. and URBICAIN, M.J. 1980. Total porosity and open-pore
porosity in the drying of fruits. J. Food Sci., 45,1403-1407.
217
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LUGEMWA. F.N., LWANDE. W.. BENTLEY, MX)., MENDEL. M.J. and ALFORD. A.R.
1989. Volatiles of wild blueberry, vaccinium angustifolinm: possible attractants for the
blueberry maggot fruit fly, rhagoletis mendax. J. Agric. Food Chem.. 37. 232-233.
LUNING, P.A.. EBBENHORST, T. and DE RUL. T. 1995. Effect of hot-air drying on flavor
compounds of bell peppers (Capsicum anuum). J. Sci. Food Agric.. 68,355-365.
MATTEIS. J.P.. FELLMAN, J.K., CHEN, P.M. and PATTERSON. M.E. 1991. Rapid analysis
of volatile
compounds
in
food
products
by
purge-and-cold-trapping/capiltary
gas
chromatography. J. Agric. Food Chem. 3 9 . 1902-1906.
NSONZI. F. and RAMASWAMY. H.S. 1997. Kinetics of moisture loss and solid gain during
osmotic dehydration of blueberries. In Afew Frontiers in Food Engineering. Proceedings of the
5th Conference of Food Engineering (CoFE '97), (Barbosa-Canovas. G.V. et al.. eds.) pp. 309314. American Institute of Chemical Engineers.
NSONZI. F. and RAMASWAMY. H.S. 1998. Quality evaluation of osmo-cor.vective dried
blueberries. Drying Technol.. 16 (3-5). 705-723.
PARLIMENT. T.H. and KOLOE. M.G. 1975. Identification of the major volatiles of blueberry.
J. Food Sci.. 40, 762-763.
PRABHANJAN, D.G.. RAMASWAMY. H.S. and RAGHAVAN. G.S.V. 1995. Microwaveassisted convective air drying of thin layer carrots. J. Food Eng.. 25.283-293.
RAMASWAMY. H.S. and NSONZI. F. 1998. Convective-air drying kinetics of osmotically
pre-treated blueberries. Drying Technol.. 16.743-759.
RIVA. M.. SCHIRALDI. A. and DI CESARE. L.F. 1991. Drying of agaricus bisporus
mushrooms by microwave-hot air combination. Lebensm.-Wiss. U.-Technol.. 24 .479-483.
SAPERS. G.M. and PHILLIPS. J.G. 1985. Leakage of anthocyanins from skin of raw and
cooked highbush blueberries (Vaccinium corymbosum L.). J. Food Sci.. 50. 437-439,443.
SIMON. J.E.. HETZRONL A., BORDELON. B.. MILES. G.E. and CHARLES. DJ. 1996.
Electric sensing of aromatic volatiles for quality sorting of blueberries. J. Food Sci.. 61. 967969.972.
STRUMILO. C.. ZBICINSBQ. I. and LUI, XT). 1996. Effect of particle structure on quality
retention of bio-products during thermal drying. Drying Technol.. 14 (9), 1921-1946.
218
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T A B L E I, C O M P O U N D LIST O P B L U E B E R R Y SA M P L E S D E T E C T E D BY P U R G E - A N D T R A P INJECTIO N W ITH GAS
C H R O M A T O G R A P H Y /F ID U N D E R D IFFE R IN G P R E T R E A T M E N T S
Compound
Acelynldchyde
2-Methyl Propnnul
Propanol
jo
so
Acetone
M ethyl A cetate
Butanal
Ethyl A cetate
2-B ulanonc
2-M ethyl Butanal
3-M ethyl Butanal
Ethanol
2-Penlnnonc
2,3-Butudionc
2-M ethyl Propyl A cetate
4-M ethyl-2-Pentanone
Ethyl 3-M ethyl Bulyrate
Hexanul
2-B thenyltetrahydro 2,ft, 2H -Pyrnn
|-Lim onene
1,8-Cineole
Trnns-2-Hcxnnnl
Octunnl
Nonunal
2-Eurancarhoxaldohydc
Decanal
Benzaldehydc
Microwave
Juice
Hot Air
Juice
Freeze Dry
Juice
Control
Juice
+
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+
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Abundance
TIC;
0101001.D
31 92
3500000
6.78
3000000
2500000
2000000
12.36
7.83
1 6 . 45
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Figure I, ChroimU ogram .showing the purgeuble flavor volatiles detected by purging ou r sam ple with lie onto lennx and then
perform ing purge-and-trap gas chrom atography with mass spectrom etry
SULLIVAN. J.F.. CRAIG JR.. J.C.. DEKAZOS. E.D.. LE1BY. S.M. and KONSTANCE. R.P.
1982. Dehydrated blueberries by the continuous explosion-puffing process. J. Food Sci.. 47.445448.
TORRINGA. E. M.. VAN DUK, E. J. and BARTELS. P. S. 1996. Microwave puffing of
vegetables: modeling and measurements. In Proceedings of 31st Microwave Power Symposium.
pp. 16-19. Int. Microwave Power Inst.. Boston. MA.
VENKATACHALAPATHY. K. and RAGHAVAN, G. S. V. 1997. Osmotic and microwave
drying of blueberries. In Proceedings o f 32nd Microwave Power Symposium. pp. 136-139. Int.
Microwave Power Inst., Ottawa. Ontario.
YANG. C. S. T. and ATALLAH. W. A. 1985. Effect of four drying methods on the quality of
intermediate moisture lowbush blueberries. J. Food Sci.. 50. 1233-1237.
YANG. A. P. P.. WILLS. C. and YANG. T. C. S. 1987. Use of combination process of osmotic
dehydration and freeze drying to produce a raisin-type lowbush blueberry product. J. Food Sci..
52. 1651-1653. 1664.
ZOG2AS. N. P.. MAROUUS. Z. B. and MARINOS-BCOURIS. D. 1994. Densities, shrinkage
and porosity of some vegetables during air drying. Drying Technol.. 12 (7). 1653-1666.
221
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CONCLUSIONS
This work addresses the development and theoretical/numerical/experimental studies of
a new combined microwave drying technique. The study is divided into three phases. In Phase
One. we proposed to combine microwave heating with spouted bed drying to utilize strengths
of both techniques and to overcome drawbacks of each other. The purpose is to improve
microwave heating uniformity and to improve product quality. This idea was experimental l\
verified in Phase Two by conducting experiments with diced apples and blueberries. In Phase
Three, after proving the technical feasibility in Phase Two. studies are focused on theoretical
study of mechanisms involved in the drying. A comprehensive heat and mass transfer model is
developed to describe complex transports phenomena. The model is composed of three coupled
nonlinear partial differential equations and has an ability to predict temperature, moisture, and
pressure fields for hygroscopic and nonhygroscopic materials. A 2450 MHz microwave and
spouted bed drying system was developed, which has a capacity to continuously adjust power
output and to measure both incident and reflected power. In order to bridge theoretical
endeavor with practice, an effort is made to use transport and other necessary parameters for
the very material we used in model validation. Experimental studies on transport properties
such as effective diffusivity. permeabilities, and dielectric properties are conducted to
determine both their values and temperature and moisture dependencies.
Experimental studies with diced apples demonstrated that microwave and spouted bed
(MWSB) combined method provides uniform heating within the microwave cavity as indicated
by uniform temperature distribution during the drying and even color in final products. Drying
time needed to reduce moisture from evaporated apples to the moisture dehydrated apples
(=5%) was shortened by > 80%. MWSB dried products exhibited least discoloration compared
with spouted bed or commercially dried products. MWSB dried products had better
reconstitution characteristics. An improvement in density was also achieved for Red Delicious
and Granny Smith cultivars by MWSB drying.
Drying of diced apples in a microwave and spouted bed dryer can be expedited by
increasing either spouted-bed air temperature or microwave power level. Temperature leveling
effect is achieved in MWSB drying in tested temperature ranges. Product temperature is 12°C
to 15°C above hot air temperature when microwave power was set at 6.4 W/g. Thus, selecting
222
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
proper spouted-faed air temperature and microwave power level can control final product
temperature.
Experiments in MWSB drying of frozen blueberries were characterized by a substantial
reduction in drying time and an improved product quality as indicated by a low bulk density, a
high short-time rehydration ratio, and a more reddish and less blue color compared to samples
freeze dried, tray dried, and SB dried. Pretreatment using 2.5% ethyl oleate & 0.2% NaOH
dipping followed by sucrose osmotic dehydration can prevent blueberries from bursting when
microwaved but resulted in a high bulk density and low rehydration ratio. Freeze drying of
frozen blueberries does not yield a high-quality dried product with regard to rehvdration ratio
and color change. Characteristics of flavor volatile compounds of 'Elliott’ blueberries are
changed by both hot air and microwave heating. Microwave heating produces new volatile
compounds not found when blueberries are dried by other methods.
Experimental studies with diced apples and blueberries demonstrate that MWSB drying 1 1)
can provide uniform heating in microwave drying as evidenced by a bright and uniform color
and a small temperature variation among apple dices: (2) can improve product quality as
demonstrated by good color, better rehydration capacity, low density, and improved flavor. (3)
can significantly reduce drying time: and (4) can provide an temperature leveling effect to
maintain fixed dying temperatures during drying, which is unique and very important for
microwave drying of heat sensitive biological products.
A comprehensive heat and mass transfer model was developed for MWSB drying in this
study. A total gas equation is introduced to highlight the influence of internal vapor generation,
which characterizes the MWSB drying, on the drying behavior. Model prediction compares
favorably with experiments for average moisture content and temperature. Pressure readings
from fiber optical probe measurement compared adequately with model predictions.
The simulation demonstrated that for low and medium moisture diced apples, a surface
moisture accumulation phenomenon can occur at the beginning of the drying, which is similar
to that often observed in high moisture microwave drying. This surface moisture increase has
also accompanied by a less noticeable temperature increase at the surface. A temperature
leveling effect is predicted and is in agreement with experiments. The internal pressure built up
in MWSB drying relied on both the moisture content and the temperature.
223
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Moisture diffusivity coefficients of Red Delicious apple tissues at 60. 80, 100 and I20°C
are obtained using a thermogravimetric analysis technique. The slope method is used to analyze
the drying data. Under the experimental conditions, the criterion for applying the slope method
is when dimensionless moisture ratio X* < 0.3. Temperature dependence of moisture
diffusivity can be described by an Arrhenius-type equation. The diffusivity obtained compares
well with the literature.
Dielectric properties of apple tissues are measured with the open-ended coaxial line
technique at 22°C over moisture content of 4 to 87.5 % (wb). and 60°C over a moisture content
of 4 to 68.7 % (wb). Dielectric relaxation spectra is analyzed to explain moisture and
temperature effects over a frequency range from 45 MHz to 3 GHz. Water and the ionic
conductivity have different effects on loss mechanism at different moisture and temperature
levels. When moisture is relatively high (-70%, wb). both free water dispersion and ionic
conduction are important in determining the dielectric behavior. At intermediate moisture
(-23%. wb). the ionic conduction determines the frequency response of dialectic properties. At
low moisture content (-4%. wb). the bound water is the main dispersion mechanism. Moisture
reduction results in a decrease in dielectric properties. An increase in temperature at low
moisture contents results in increased dielectric properties. At high moisture content, the
temperature response is determined by contributions of free water, ionic conduction, and bound
water and was difficult to predict. Penetration depth increased as moisture was removed from
the sample. Data are correlated with a polynomial equation to predict both moisture and
temperature effects.
224
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
RECOMMENDATIONS FOR FUTURE STUDIES
Microwave and spouted bed combined drying (MWSB) technique developed in this study has
been proven to be a promising technique for the drying of particulate foods and agricultural
products. Theoretical model developed has been experimentally validated and used to predict
MWSB drying behavior. There is vast opportunity for further studies relating to both practical
and theoretical aspects of this drying technique. Future studies could be directed to following
topics:
1). Scale-up MWSB drying from laboratory protocol to pilot scale and then to industrial scale.
The ultimate goal of an engineering study is to pave the road for practical applications. The
translation of MWSB drying technique to industrial application requires studies to upscale to
larger operations. This could include scale-up of the spouted bed itself as well as scale-up of
the microwave drying. The spouted bed scale-up could follow the classic geometric, kinetics,
and dynamic criteria used in other unit operations. However, the scale-up of microwave drying
could be the key for successful upscale of MWSB technique. An equivalent field distribution
could be important but difficult to achieve. A power density equivalent may be applicable.
2) A combined electromagnetic field and heat-mass transfer analysis is needed. This is the only
way to accurately calculate heat distribution inside products during MWSB drying. For small
particulate materials, an assumption of uniform distribution is acceptable. For slightly large
objects, however, this assumption will cause considerable error. Some commercial software,
which has a limited ability for coupled electromagnetic field and thermal analysis, is now
available. There is no software that can incorporate mass transfer calculations into a microwave
heating analysis.
3) Shrinkage of biological materials during a drying process is important. A drying model that
can simultaneously consider the effect of shrinkage is desirable. Such an analysis needs
knowledge of moisture and temperature dependent mechanical properties, such as Young's
modulus and Poisson ratio. Determination of these parameters will be a challenge.
225
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4) A drying model that can predict product quality degradation is needed for industrial
applications. Such an analysis needs to have an understanding of the kinetics for selected
quality attribute that degrades during a drying process.
226
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APPENDIX A
THEORETICAL AND NUMERICAL ANALYSIS OF HEAT AND MASS TRANSFER
IN MICROWAVE AND SPOUTED BED COMBINED DRYING OF POROUS MEDIA
I. Phenomenological Relations
I. I ) The generalized Darcy’s law is given by:
u
(1*1)
u
(
1- 2 )
1.2) Gas phase diffusion is estimated by:
f
\
(1-3)
1.3) Fourier’s law writes:
(1-4)
2. Equilibrium Relations
2.1) Capillary pressure is the difference between gas pressure and fluid pressure:
Pf - P r =Pc( T . X w)
(2 - 1)
2.2) Thermodynamic equilibrium
227
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Under the local thermal equilibrium assumption, the intrinsic average temperatures of three
phases are at the same value. The local vapor pressure reaches its equilibrium value and is
given by the sorption isotherm.
P=P°<p(T,Xw)
(2-2)
2.3) State Law
Gas is considered as a mixture of air and vapor. The ideal gas law applies, hence:
PM
P, = -pjT
^
P< =2*P>
v’
P*uv = 2 - A«,
i = a.v
(2-3)
3. Mass Balance
Freewaten
< l-£ )p ,
dX,
+ V h. = - m
dt
(3-1)
Bond water
dX
(I —e)p, — -+■ VR. = - m h
dt
(3-2)
Vapor
dX
(I- e ) p t — ±-+VRv =m + mh
dt
(3-3)
A ir
dX
a - £ ) p , — *- + V iiu =0
at
(3-4)
Denote Xw = Xf + Xb +■Xv = Xt + Xv ■=X{. where X/ = Xf + Xb- The solid density (p.) instead of
the apparent solid density of the material is used because it is a measurable parameter and is a
constant for a specific material.
4. Heat Balance
Total energy equation for a representative elementary volume writes
228
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(a)
(b)
(c)
(d )
Dr
(e) (/)
(4-1)
In Eq (4-1)
heat storage term
convection term due to temperature gradient
conduction term
viscous dissipation term
work done by pressure
internal heat source term
The viscous dissipation and pressure work are assumed negligible. Hence Eq (4-1) reduces to
enthalpy balance equation:
^-{ph) + V (puh) = -(Vq) + <t>
(4-2)
p h - p,h, + p X + P A + ( p , +Ph K
(4-3)
puh = pv«A + p„uA + (p t “ r + PA )Ai
(4-4)
where
The heat of sorption is ignored in (4-3) and (4-4) since for most materials in a wide moisture
range its value is negligible compared to the liquid enthalpy (Keev. 1972)
5. Fluxes
t ■V(Pe - P c)
Free water
Bound water nb = pbub - -Db(I - e')(
eVP
s
S
Pv
M*
-VT)
(5-1)
(5-2)
229
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The formulation in Eq (5-2) is from Stanish et al. (1986). Substituting Eqs ( l-l). (1-2). (1-3).
and (2-3) into expressions for the fluxes in Eqs (5-1) -(5-4). and ignoring the gravity effect
yields
Kkr
nr - - p ,
=~Pr
-V( P. - P )
Pr
Kkr
Kk.
u.
-vps + p ,
Kkm
=P r
dP.
VX +[*P
ar
*XW
Pr
VT
(5-6)
IX,
Kk„ rdPc '
KKr
VXw+p r ^ V T-p,
-VP,
dT .
P,
P,
eVP
P,
n, =
S
Mv
(5-7)
„ eR T fapv ]
vy w + '*P ' VT
ar x.
T
=- D b( l - £ )
PM,
=-D„( l - £ r)
eR'T ’ ap, '
\
VX„+Dh(\-£')
H JrT
Sv
m v
Dh{ \ - £ ) - ^ - V T
M,
£R'T rap
ar
p m .
VT
Kk
n
’VP, - p f D ^ V ( — )
P*
P<
n, = - p t —
P M ,
R'T p t
PM..
PM a+W v-M jP v
_ D
R'T
(5-8)
230
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pm ,
R'T p e
_n
r
M, p * w - P M y p . t
a R'T P,Ma + (M,. -M U)P,
M.
PM..
P. M . Kkr,
VP.
+ D.,
R'T P..MUr(M , - M J P ,
R'T p,
Mv
PM a
vp
R'T P M U-HM,. —Ma)Pv 1
-D
P M ,
K kn
R'T p ,
+D
M,
P M .,
R 'T P M a
VP
- M a )P x
PM.,
M
( ap.
R'T P M U-mM, —Ma)Px 3 * -
.
M,
PMa
R T P M « + ('W, - M
-D.
M
R ’T
+ <M,
- M u
dT
VT
A t.
VX*
v3** yr
ap
[ ar
(
)P
(ap
Ar
I L
U )P V
P M a
P M a
vx +
VT
P M , Kkr..
M
P M a
+ D„
VP.
R'T p .
R'T PMu +M , - M J P ,
- p . — VP, + p , D M ( — )
p.
p«
P M ,+ (M , - M jP ,
PM a **„
VP,
R'T
R'T p„
PM,
PM ,+(M.-MJP,
\
>
PM . Kkr,„„ . „ M, PM .V P - PM , VP.
VP, + D,
RT p c
RT P M , + \M X-M,)P,
P M a K k r*
PT
p;
1 n'*r
R'T P M a
P M ..
PM .
- M a)Pr
VP.
(5-9)
ap
ap '
v* +
“ R'T P M a +(MV-M J P , V3* - AT
dT
VT
A t.
231
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= D.
(dP,. )
Mv
PMg
V*
R'T Pt M a +(M l -/V/JP,
+ A.
PMa
' dPv '
vr
R'T P.MU+ (MV- M U)PVy. dT jxY
R'T
II t
PM a
VP.
R'T PeMu -i-(Mt - Ma)PV
6. Moisture Transport Equation
By adding mass balance equations (3-1). (3-2). and (3-3) yields
— (ATr + AT„ -r X v) - - - — —— V (nr +nh +nv
dt
a-e)pt
( 6- 1)
Substituting flux expressions (5-6). (5-7) and (5-8) into (6-1) and taking XK = X, + Xb + AT, =Xt
results in the total mass transport equation:
3y
at
= V ■(d x v x , + Dt VT + DPVP. )
( 6- 2 )
where
Dj —Dx +D* +D^
Dt = D-f +- Dj +■DP
(6-3)
DP=Dj, +DP +DP
The coefficients in Eq (6-3) are given by:
232
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l - e p,
Dhx
Pr
( a n
\
[dxKn
Kkn ( a n ]
l - e p. P r \ ar x .
I
(6-4)
P r K kn
I S P, Pr
I - e Dh eR'T I L
- r* *■v** v K™. ft
I —
C
A
P M
l - e ' Dh S,
l - e p,
Dt
Dp
Kkn
Pr
I
Di
D'p
Pr
I
DJX
e/?T r a n "
ar
(6-5)
=o
D*
A « n _________ m , a/ v
(l-£ )p , ^ T (P > /, + (A/t.
fa n '
D'r
n
m „m v
ra n A
(I-e)p , R'T{Pt Mu +(Afv - A f j n ) [ 3 r
I
n/V/y ^ r c _______Dm.MuM vPv
R r { P eM a + { M v - M
(l-e )P , R 'T H ,
6 6)
( -
j P v)
7. Thermal Transport Equation
Substituting Eqs (1-4), (4-3). and (4-4) into the enthalpy balance equation (4-2), we get
Trip A + P A + P A + (pr + P*K I
at
(7-1)
+ v [p A A + P A * ,+ ( P fw, + P A A ]=v UeffV7')+(I>
We have
a, t v
a/i,
3p,
ar , ap,
ar
ar(p5 , ) _ p , i r + ,_ a r _ p ' ^ aT+ 1 T ~ P,C'” aT
233
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_„
}
|* ( P A ) + V ' (Pu«A ) = Pu
dt
dt
dt
Pa“a ’VA„ +/laV ’ ipaU. )
ar
-P S /u i-^- + PaCn«“u VT + hu
dr
ar
(7-3)
—(p /t )-t-V - Ip it h )= p d l'■—h ^P' j~ n f7i -V/^ —h V-<p^ »J^ )
dr
dr
'd r
97*
= P , c , - , p , c ^ . . v r +^ ^ V '( P A )
(7-4)
97*
* P>C„ — + p,C pA v r + hv(m + mh)
^[(p,- + P h K ]+ V [(pf« r + p A K ]
=( p ,+ p j c * l 1 + * , ! ^ - + * , ^ .
(7-5)
+ c p/ (p f«r + p A ) v r + /»,v •(p rCi,)+ a, v ■(phi7„)
97*
= (p, +Ph)Cl„— JrCl>l{pt u, ~ pht7h)-VT-h,{m +mh)
Substituting Eqs (7-2) - (7-5) into Eq (7-t). we obtain
.
97*
lP<C/» +P*Cpa + PvCpv (pr +Ph)Cpt K —+ (^v -h,){m + nth)
dt
+ \p*“aCpa + P A
+ (p « f + PA ) Cp, ]V7 = V (yl^ VT)+ <t>
C
,,v
,
(7-6)
-
By introducing (pCp)eff = psCp<+ puCpu + pvCpv + (p, + pb)Cpl., Ahv = hv - ht, and ignoring the
convection terms. Eq (7-6) can be simplified to:
(p C p
^ + A / ; v(m + m J = 7 - (Ar/rV r ) + <t>
(7-7)
In Eq (7-7)
234
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AA, {rrt-t-mh ) = A A V
H -s)p .^+ V -n f
dt
(7-8)
=M v( l - e ) p , ^ - & h J l - £ ) p lV ( D ‘x VX! +D;VT + DlPV p J
dt
in Eq (7-8)
P M ,
9r
dt
dt
P M, (I
/?T
) P,
p r + p„
p m , {,
-v
*T
P r
l-g
p,
g
P, +P»
dX, t A/tg
p,
i- t-g
dt r '
g p , + p fc
■X,
3r \
p, a*,
+P„
dt
Mr
I- g
p.
lR'
g P, + P>
= ~ r | - (l ~ g ) —
*
R'T
l-
d{pv/ r ) d T
dT dt
- t + e J l z ! k L Xl
?APr + P J
M
R'
P; +Po
i a(/>jax,
T d X , dt
(7-9)
i a p ,} ax,
T dX, dr
d{PJT)dT
dr dt
In deriving Eq (7-9). the following equation is used to relate the liquid saturation to the
moisture content (dry basis):
I —g p
S, = — — ^ ---- X,
g P r + Pb
(7-10)
Substituting Eqs (7-8) into Eq (7-7) yields:
ax.
(7-11)
=AAl.(l-g )p IV -(^V X -,+D ^V r + Z5;VpJ+7-(Aqr7 r ) + 0
235
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Plugging Eq (7-9) into (7-11) and rearranging it results in the total thermal energy equation:
ar
c „ ^ 4 - ctt^ : = v .(d7Xv x ) +D7Tv r + z)TPvp><i>
(7-12)
where
r
-j1■' R■ ( p , +p„ r ' [
C TT = ( P C P )cn + A /lr
d -g )p . v 1 1 «*.]
p, + p » ' ' J r a x ,J
M e J l z £ K Xi a(p, i t )
ar
P r + Pb
(7-13)
Djx —4AV(i —£)p,Z}£
(7-14)
£>tt = K r r +AAv( l - e ) p , D f
DTp = 4/zv(l —£ )p,DP
8. Total Pressure Equation
The total pressure equation can be obtained using air balance equation (3-4). Substitutin
expression for the air flux Eq (5-9) into Eq (3-4) results in:
(l- £ ) p , y = - 7 - « ' a
M,
= -V -
P<Ma
f ap
R T P M U -M M , - M „ ) P
-V -
v-«
v
]
Va x lt.
“ r
v x HH
( 8- 1)
dP^)
vr
ar x.
Dm
(Pt - p v)Ml t Kkn_ ^ D
R 'T
Pt
PM ..
R ’T P . M . '
- M a )Py
J
VP.
'’ j
The left-hand side of Eq (8-1) can be expressed by:
236
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a ’eMa{Pt -P , ](l-5,)
R'T
ar
d x u _ a 'eMuPuSa'
R'T
dt
dt
it
e
M u
1
a
p ' dt
_ em u
, ~0
i
V1
[l l - g
1 g P
V
r
P ,-P v
I - g
P.
g
P r+ P />
R'
a x , + eMd
dr
R'
P.,
1 - - — —— ^ —
g
X,
dt
P t + Ph
_ eMa P. - P. (_ l - e
p,
)dX,
R'
T [ e p, + pb J dr
_ ( 8- 2 )
e
I —e
M
1--5—
R'
g
p
— - —
P r
eM.
R'
g
P '
P '
T dt
I —£
P'
g
t-—
gM„
X,
+ Ph
i-C
P r
+ P/ >
f a(pt / r ) ar i apt ax,
[ dT d t ^ T ax, dt
P
I_J—1 — — x
g P r Jr P h
+P/,
I dp
TdX,
ax
ar
P, d(PJT)) ar
dt
T1
dT
(
— - — X,
Pr
^ ar
T2 dt
1
A
I —e p
I - — — - — X,
T dt
g P r + P*
Substituting Eq (8-2) into Eq (8-1). we obtain the total pressure equation:
3X
^p
2T
C K - £ - + C „ — + C „ - £ - = V - \ p ‘t V X , + D f V T + D ; V P ' )
(8-3)
where
e M.,
Cpx
—
P.. - P
e M„
=
p.
g
P,+Ph
R'
^PT —
r
I- e
R'
I —£
I
giW,
I
p'
P
-----
^
I —£
g
= - ( i - e)p tDi
X,
Pr
+ P/ >
P
^
I —£ p
I-— —g Pr +
X,
P*
3 ( P , / P )1
r2
ar
i ar
rax,
(8-4)
X,
Pr + P *
(Vf
ra p , '
R'T Pt Mu +(Afv -M J P , ax„ ,r
237
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(8-5)
Finally, the microwave drying problem can be described by three coupled partial differential
equations with variables X|. T. and Pg as:
dy
- r — = v - {d xv x , + Dr V r + DpVP.)
( 6- 2 )
(7-12)
(8-3)
where Q s. (i = T. P: j = X. T and P) are capacity coefficients and given in Eqs(7-15) and (8-4):
D* s and D* s (i = T. P; j = X. T and P: k = a) are kinetic coefficients and given in Eqs (6-4) (6-6). (7-13). (7-14) and (8-5).
9. Initial and Boundary Conditions
9.1) Initial Conditions
(9-1)
9.2) Boundam Conditions'.
9.2.1) Moisture:
238
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Moisture transported to the surface from the interior of the material can leave the surface as
either liquid or vapor, depending upon the intensity of the drying. The moisture flux from the
material side can be expressed as:
+ n b ^ n x. ) n = - ( i - e ) p , { D x V X l + D T V T + D P V p j R
( 9 - 2 )
Assume that the moisture reached the surface from material side evaporates immediately and is
carried away by the hot air stream. The moisture flux leaving the interface due to convection
can be expressed as
| _ = E(pvs - pv« )hm. The boundary condition for mass transfer is then
given by:
- ( l- e ) p , (Dx VX, +DrV r + D,V/>J.n=e(pv, - p xJ h m
(9-3)
9.2.2) Temperature:
An energy balance over the interface requires, at the normal direction of the interface, the heat
flux from the interior of the material equal to the heat removal at the interface, that is Fhct I - =
Fh«t I where
Fw | - = q - n + h an a h + hx.nv -n + h ,[n r + nh )-n
F . J . =h{T_ - T j + h un u ■n + h, at, -n + fiv {n,
(9-4)
thus
(9-5)
q n = h { T „ - T , ) + ± h v (n t + n h )-n
Introducing Eqs (1-4), (5-6). and (5-7) into (9-5) yields temperature boundary condition:
- r t )-AAr (l-e)p,[(£>{ +Dbx yrx, + (/>' + D ^ r + D'VP.].n
(9-6)
9.2.3) Pressure
239
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p\| i =p‘ atm
(9 -7 )
‘
10. Complementary Conditions
10.
t ) Solid density ps (Krokida and Maroulis. 1999)
The solid density (ps) is the weight per unit volume of the solid material and excludes any
interior pores which are filled with air. The gas pycnometer is usually used to determine the
solid density of a material. The solid densities of apple and potato are given by:
ps= 1650 kg/m' (apple)
&
p,= 1610 kg/m’ (potato)
10.2) Porosity £
Porosity, when dealing with fluid flow in unsaturated porous media, is defined as
(10-t)
while the porosity used in the drying of fruits and vegetables often refers to
t
£ =
( 10- 2)
where pb and pp are the bulk density and particle density, and are defined by:
m, -i-m,
Pb
Pp
=
(10-3)
---------- :----------- —
V+V,
(10-4)
I/ p t + X ,/p .
240
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The bulk density pb can be determined using the water displacement method. The panicle
density can be calculated from the solid density ps and the liquid water density pi when
moisture is known. From the definition of porosity e. and £’. we have
( 10-5)
£ Pi
or
e = e'-pp.X,—
' Ip,
JLl
l + p tX ,/p ,
(
10- 6 )
In Eq (10-5). we used the expression for liquid saturation in Eq (7-12). The porosity e‘ of
apples can be manipulated from data given by Krokida and Maroulis (1999):
Plugging (10-7) and data for apples given by Krokida and Maroulis into Eq (10-6). we have:
, , 0- 8,
+
(l + l.65X,)(l.899 + X,)
10.3) Intrinsic and relative permeability (K, krg. and krL)
Both the intrinsic and the relative permeability data for fruits and vegetables are not available.
Any effort in either the measurement or the estimation of these parameters is of archival value.
Two experiments are designed to measure the intrinsic permeability and gas relative
permeability (see Appendix A)
10.4) Saturated Vapor pressure Pva (Turner. 1991)
=aO + al*T+ a2*Tz +a3*T:'
(10-9)
241
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where ao = -4002803.2427: ai = 40943.1692: a2 = - 139.945I; a3 = 0 .16. with Rz = 0.9998.
10.5) Vapor pressure Pv
Vapor pressure is given by the sorption isotherms.
P;=P>(X,.r)
(10-10)
The sorption isotherm <p(Xi, T) for apples is given by Feng el al. (1999) by fitting data reported
by Roman et a i (1982):
X , =------------------------
(water activity aw =
' (l-aj[ I + ( C - l) a J
( 10- I I )
PQ
where the parameters Xmand C are given by:
I IQ| ->
ln(Xm) = —7.036 +• ———
& ln(C) = —9.385 +
I
(10-12)
10.6) Bound water diffusivity Db
Bound water diffusivity for fruits and vegetables do not exist in the literature. A collection of
the bound water diffusivity for other biomaterials is presented in Table I to illustrate its
magnitude.
Table I. Bound water diffusivity data from literature
Material
Db (nr/s)
Reference
Wood
4.2 x t0'12- l_55 x 10'“
Turner era/.. 1998
Com kernel
1.86 x 10'“
Chen and Pei. 1989
Wool
4.57 x 10'“
Chen and Pei. 1989
10.7) Molar entropy Sv (Stanish et ai.. 1986).
242
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S, =187 + 35.1* In
298.15
—8.314* In '
K
I0I325
(10-13)
10.8) Capillary pressure Pc
Kelvin’s relation
0 =P° - [
{PiRJ )
(10-14)
10.9) Air-vapor binary diffusivity Dav
The air-vapor binary diffusivity is function of both gas pressure and temperature and is given
bv (Stanish et al.. 1986):
D„ = 2 .2 0 x 10
vl 75
_s 101325
(10-15)
273.15
10.10) Viscosity of gas and free water p*. (if (Turner. 1991)
ftr{T) =f i raexp(a-bT + cTz + d T '-eT * )
(10-16)
where a = 29.619: b = 0.152: c = 0.648 x I0“l:d = 0.815 x 10 °: e = 0.120 x 10‘8
Pro = I x I0a [kg m’1s'1]
PeCn = U,0tr l,1H a + b /T -c /T 1 + d /T :'))
(10-17)
where a = 0.672: b = 85.229: c = 2111.475: d = 106417.0: Ugo = I x IO'6 [kg rn 1 s ‘l. The
temperature range for Eqs (10-16) and (10-17) is 273.15 to 373.15 K.
10.11) Latent heat Ahv
243
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The latent heat of water as a function of temperature is given by fitting data presented in steam
table (Incropera and DeWitt. 1996):
(10-18)
Ah, = 3167.2 - 2.432 T
10.12) Effective thermal conductivity A*fr (Donsi et al.. 1996)
Thermal conductivities of apple and potato as a function of moisture are given by Donsi et al.
(1996):
Apples:
K,f = 0 .12631 + 0.0595 X,
Potato:
^ = 0.1445 + 0.1161 Xt
(10-19)
10.13) Specific heat (Cp«fr)
Specific heats of both apple and potato are given by (Niesteruk. 1996):
Cm =1415+
27.21 X,
I + X,
( 10- 20 )
10.14) Surface heat transfer coefficient h
The N'usselt number is defined as:
Nu =
hD.
( 10- 2 1 )
In the spouted bed drying. Markowski (1992) proposed a correlation for Nusselt number
-O S 5 2 f r r
V 1-*7 f p
\0 .W
Nu =0.0045Ar0225 Re0664( tan-^
2.301
S'.
10.15) Surface convective mass transfer coefficient h„
244
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( 10- 22 )
The mass transfer coefficient is defined by:
hd
(10-23)
Sh = - i - E D.„
In spouted bed drying, the Sherwood number Sh can be determined using the Lewis analogy:
x-O S S I
Sh = 0.0045A r 0 Z26 Re06^ |
tan-^
0
2.*01
(10-24)
d„
11. Heat Source Term Estimation
11.1 Constant power distribution
Power absorption by the sample in the microwave cavity is given by:
(U -l)
4Pabsorb = 4Pincident - Preflect - 4P/<m
The incident and the reflected power can be monitored with power meters. The loss at the wall
of the cavity is usually ignored. Suppose the dry solid mass of the sample is Ws, then the source
term d> is given by:
d>=
absorb
( 11- 2 )
w
Application of Eq (11-2) requires a uniform and constant power distribution through the
sample. For small particles at low moisture range, the penetration depth of the microwave in
the particle is much larger compared to the particle size. Hence this simplification is acceptable.
Using diced apples as an example, the apple dice has an equivalent diameter of 5mm. for 25%
moisture content (w.b.), the penetration depth is 26mm while for 4% moisture content, the
penetration depth is 360mm. It is reasonable if we apply constant power distribution
assumption for apple dice at low moisture range (to the 4% end).
245
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
One important point when considering the heat source term in microwave drying is the
reflection of the microwave waves when it reaches the particle-air boundary. Therefore, a
superposition of the traveling waves is needed for an accurate estimation. This approach needs
to consider the decay of the wave when traveling in the material.
11.2) Exponential decay model
For one-dimensional sample. Ni (1997) proposed a volumetric source term expression:
/
‘ J
)
-f— '
J8
In Eq ( 11-3) 4>o is the sample surface flux of microwave. 8 is the penetration depth and is given
bv:
a\0
d
=
05
,0.5
5
-
£
-I
(11-4)
where Ao is the wave length in free space.
12. Simplification of Drying Equations
12.1 Nondimensionalization o f the drying equations
Scaling technique is used in this section to simplify the drying equations. If we take the diced
apple particles as spheres, only radial transport is needs to be considered. Under this condition,
the governing equations (6-2), (7-12) and (8-3) can be written:
dX, =
dt
I
d
n
D x r
~ r z dr
r
^
“
dt
id X ,
,d T
_
,d P e
—
+ D Tr - — + D Pr - — ±
ar
dr
dr
2
ill—L 3
17 d t
r z dr
^
dX ,
( 12- 1)
,d T
5r
ar
+ 4>
( 12-2 )
246
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Following scaling groups are used (Plumb et al.. 1986):
T —T
*0
ft
.
„
‘
*o
O' p„
^
T0
T'nsu
V* _
.
r, ’
w_
‘
*0
P — Patm
Pam
Pmai
Ro
«t
Pa—Rq
K ^P ^-P ^)
^na» ~ Pgm
(12-4)
<£• _ ^
#0
$0
Substituting (12-4) into (12-1) - (12-3). we obtain:
Moisture equation:
dx;
d t’
. dx;
Dy
R ^ X 0r ’1 d r ’
3 r"
ar*
. ap;. \
------^ Ds ----
r dr’
P dr’
(12-5)
Thermal equation:
X0 d X ’
'~rx ~
T^-TodT
rT _ "h(-7T--------
3r-
ar‘
ar
dx;
R0zr ’z d r ’
dr’
TT
dr’
, dp;
TP T~
r
dr
(
+ O 0 O‘
Pressure equation:
247
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12- 6 )
(12-7)
In Eqs (12-5)-(12-7)
(
12- 8 )
(12-9)
(
12- 10)
Simplification of the nondimensionalized partial differential equations is facilitated by
estimating the magnitude of the modified capacity and kinetics coefficients in Eqs (12-5 ). (126) and (12-7). For microwave and spouted bed drying, we take Pmu = 2atm. Tmax = 100°C. T0 =
22°CandX0 = 7.
12.2 Moisture equation (12-5)
Constants and parameters in the capacity and kinetic coefficients are estimated by three
approaches: 1) calculated from equations listed in Section 10 by inserting the maximum and
minimum moisture values: 2) from references: 3) calculated from equations listed in Section 10
by assuming an average drying temperature of 70°C (343K).
e = 0.687 - 0.93 (take e = 0.5: er = 0.5):
ps = 1650 kg/m3
pf = 1000 kg/m31
pf = 5.0 x I0"1N s/m2
pg = 2.0 x 10° N s/m“:
K = I0‘lj m2 (for wood K = IO'15)
kef = krg = 0.5:
Db = 5 x 10'11 m2/s
Dav = 2.5 x IO*5 m2/s
Mv = 18
T = 343 K
Pv (T=343K. X=0.1 )= 31160 Pa
Pa (T=343K)= 101300 Pa
248
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12.2.1 Dx\ Dt , and D f
Since
I
Pr KK
.
l - e p, ix,
I
t
IO -l 5 x O J - l j 5 .: l 0 -,°
05 1.65 4.0xl0~*
we have
Dx( - 1-5 x 10
D t ~
Dp1-
ap
( 12 - 11 )
dx
,-io a p.
1.5 X 10
ar
to
1.5x10
( 12 - 12 )
(12-13)
Capillary Pressure vs Sample Moisture
70x10s
3x10' 4
60x10s
50x10s
X
ixlO ‘ •
40x10s
50
%
60
70
30
Moisture. % iwbi
U
30x10s
P = a* (surface tention)* (X +• b)A(-0.63)
a = 1.364* 10*5
b = I.2*I0/'(-4)
Surface tention = 0.1223 - 1.69* lO^M) * T
dP /dX = 5528*(X +- b)A(-l.63)
20x 10s
10x 10s
C
0
10
20
30
40
50
60
70
80
90
100
Moisture, % (wb)
Figure I. Change in capillary pressure with respect to moisture
249
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Capillary Pressure vs Sample Temperature
0.70
0.68
-
0.66
-
dP ./dT = 23. I *(X + b)A(-0.63)
0.64 0.62 0.60 0.58 0.56 0.54
260
280
300
320
340
360
380
Temperature K
Figure 2. Change in capillary pressure with respect to moisture
12.2.2 D\ and Dt
Since
\
Mv
M.
187 + 35.1* In
298.15 /
-8.314* In
(
rpv
V
, 101325 1
f 343 '
31160 ^
187+ 35. I* In
-8.314* In
18
298.15
101325
= J_
208.68
= 10
18
I - £ ' D„ E R 'T 5xlQ~" 03*8314 * 343
=8x10 - 1 4
l - e p, PtMv
1650
31160*18
l - e ' D b Sv
I - e p, Mv
5x10"“
-xIO = 3x10
1650
Thus
250
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Dx ~
8
Drb -
-3
x 10' 14
(12-14)
ax
AP
x 10 13 + 8 x 10 14 —
ar
(12-15)
12.2.3 Dx\ Dt . and Dp
btnce
MgM*
29x18___________
R'T[PjUa +(M v - M j P v\ 8314*343[t32485 * 29 - 11 * 31160] ~
5 -»xlO'“
DMPt _ 2.5xI0 "5 * 132485 _ 4xI0_; DmPr _. 23x10'* » 31160
(1 -£)p,
0.5*1650
(I-£)p,
0.5*1650
| ;g |Q.
31160*18*10 -I*
= 6 .0 x 10 '*'
1650 * 8314 * 343 * 2.0 x 10"
P.Kkrt
i l - e ) p t p,
Hence
Dx ~ 2 x
V13 d P
10
aa
(12-16 )
AP
Dxv- 2 x 10‘13^
ar
,12-17)
Dpv - 6.0 X 10' 13 - 5.0 X 10' 14 - 5.5 x 10' 13
(12-18)
A comparison of the coefficients in the dimensionless moisture equation ( 12-5) is tabulated in
Table I. In Table I. T ^ - T_ = 100 - 70 = 30°C
- Patm = 50000 Pa. The capillary
pressure and vapor pressure terms are evaluated from Figures 1-4 by assuming an average
ap
moisture content of 40% (wb) and an average temperature of 70°C. The values are: — - =
dX
AP
ap
Ap
7000. — =0.6.
= 150. and
= 1000.
ar
ax
ar
251
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2. Comparison of the magnitude of the coefficients in moisture equation
i
D
r
D '
n BP
1 5
x
1 0
—
2 .5
2 .5
b
3
8 x l O
v
I 0 ‘* ( X = 7 )
—
BX
O 'v
x
S e le c tio n
x
t O ’5 ( X = O . I )
x
1 0 ‘° ( X = 7 . 0 )
- M 2 * L
b x
V
1 .4
x
H r 1 2 ( X = 0 .I )
8 .0
x
I 0
3 .4
x
1 0 1 2 (X = 0 .1 >
l6 ( X = 7 . 0 )
2 x
BX
f
8
1 .2
x
I 0 ‘"
dT
D r‘
2
x
, 0
-
x
b
V
tO 'U
( X = 7 )
1i
1
\
x
x
I O '^ X s O r i )
I 0 - ‘- ( X = 7 )
o
X
00
8
5 .8
Dp
x
1 5
V
1 5
1
' ^
BT
f
1 0 “' ( X = 7 )
0 . 0 ( X = O . I )
b
2
x
—
x
I 0
'° ( X = 0 .I )
I 0 ' il
7 .6
x
10-°
t O ’ 1*
t . O x
1 0 “'
\
0
1 .0
x
252
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-6M500
t
300 r
=5 200
100
r
X
>
2___
35
45
50
Moisture Content. % (wb)
0
-t
0
10
20
30
40
50
60
70
SO
90
100
Moisture Content. % (wb)
Figure 3. The apple vapor pressure gradient over moisture content vs. moisture content
1200
1000
800 -
600 -
400 -
200
-
0
r
10
20
30
40
50
60
70
80
Temperature, °C
Figure 4. The apple vapor pressure gradient over temperature vs. temperature
253
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
From table L we can see that Dxv. Dtv and DPV are negligible in comparison with the
corresponding Df1 (i= X, T and P: j = f. b and v). In the comparison of D \J (i= X. T and P; j = f.
b and v). Drb and Drf can be ignored. Dxb is small compared to Dx'- However, at low moisture
range, the bound water term may be dominant. Hence, in the moisture equation, both free and
bound water terms are kept. The moisture equation (12-5) reduces to
dx; = r,
d r *if n
d t' RnXnr ’z dr'
v
dr'
' 3r
JJ
where
Dcrr =D>X +Dhx
(12-20)
Obviously, the effective diffusivity Deff lumps various transport mechanisms except the
filtration flow into a single parameter. Defr can be measured by a specially designed experiment
where the gas pressure build-up is eliminated. The vapor filtration diffusivity Dp can be
obtained by finding out the gas permeability Kkrg in a separated experiment.
12.3 Temperature equation (12-6)
Table 3. The magnitude of the pressure derivatives
Moisture (db)
dP
dX
dP.
dT
dP
dx
ap
dT
7.0
232
7
5.77 x tO"1
1.28
0.1
2.4 x 105
98.5
2.47
93.5
We know that
A^ff = 0.13—0.54 ;
Ahv = 2394 kJ/kg
Cp= 1416-1438 kJ/kg°C
254
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12.3.1 CjXr cind C jt
Since
MVPV (1 -£ )p , _
' R'T
p,
p,
^
■)T
18 * 9800 0.5* 1.65
= 179
8314*343
I
\
I
J343
= -7 x i0 ”
8314
Hence
Ctx = -179 + 7 x I0' 3 ^
C rr= I-1 x
106 + 8 .2
=-179
( 12 -2 1 )
^ L J U = u x I0 (
(
12- 22 )
12.3.2 Dj\, Drr- twd Dtp
Since
Ahv ( l-e) p, = 2394 *0.5 * 1650 = 2 x to 6
Thus
D
t x
= Ahv ( I-e) ps Dxv = -2 x 106 Dxv
= -2 x IO' 10 (X = 7.0)
, 12-23)
= - I x I0‘6 (X = 0.I)
Drr = A*ff + Ahv (l-e) ps Drv = ^ ff + 2 x I06 Dxv
= 0.54 (X = 7.0)
([ 2-24)
= 0.13 (X = OJ)
D tp = Ahv (I-e)
=
1.1
ps DPV= 2 x I06 DPV
XIO4
(12-25)
255
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4. A comparison of the magnitude of the coefficients in temperature equation
i
cr,
X
C Pi
( 7 )
T
1 7 9 0 0 0
( 7 8 )
1 .1
x
D r,
I 5 5 3 x
I 0 6 ( X = 7 )
8 .6
Di1
i
X
2
( 7 )
L .O x
x
1 0 "
( 7 8 )
0 .1 3
P
( X = 7 )
1 .4 x
7
( X = 7 )
V*
1 0 '
x
1 0 ° ( X = 7 )
10 '5 ( X = 0 . l )
4 2
( X = 0 .1 )
I . l x
x
V*
1 0 '
D ’/1
I 0 '5 ( X = 0 . I )
0 5 4
T
S e l e c ti o n
C ’ pi
( X = 7 )
\ *
I 0 ( X = 0 . I )
5 5 .7
1 0 ”
\ *
( 5 0 k )
—
When rearranging the thermal equation, it is desired to explicitly present the physical meaning
of the various terms. Some of the terms may be small compared to the others. However, the
summation of these terms yields the internal evaporation term. After rearrangement, the
thermal equation takes the following form:
(nC \
r'ctr
T
0w
d*r
‘ m^ax- T"O
*max
d t’
R z r ’z
d
/L<nr
dr'
dr \
+ A h M
+ 4 > 0 <£>‘
dr’
12.4 Pressure equation (12-7)
12A A Cpx. Chanel Cpp
Since
£ M a
O S
* 2 9
=
R'
1 . 7 x 1 0 ” ’
8 3 1 4
, I - e p,X,
, 0.5* 1650* X,
I
—I —■■ _ _ ■
^ —4v7 7 5 ( X
0 - 5 * 2 0 0 0
£ p , +Pb
Pg - P v l - e
p ,
1 0 1 3 0 * 0 . 5 * 1 6 5 0
p r + p b
3 4 3 * 0 . 5 * 2 0 0 0
=
T
£
=
7 )
&
0 . 1 7 5 ( X = 0 . 1 )
2 4 3
256
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(12-26)
P,___d_ P!_ P, +P,
I 3Pt 132460___ I 3Pt
r 7 a r l r )_ t 1
r a r ~ 343: 343 a r
dP
= 1.1 —3xl0~* —L = -I.l(X =7) & -I.t(X = 0.l)
ar
Hence
CPX= 1-7 x I0 ' (-285 + 4.4 x
10 °
( ^ + ) ) = -0.4
ax
(12-27)
Cpx = 1.7 x 10*5 (-4.775&0.175) (-1.5) = -1.2x IO’2 (X=7) & 3.3 xIO'2 (X=0.l) (12-28)
CPP= 1.7 x IO"3 (-4.775&0.175) / 343 = -2.3 x 10'5 (X=7)
8.6
x IO' 7
1 12-29)
12.4.2 Dx. Dt . and Dpu
Since
Dxa = -(1 - e) ps Dxv = -825 * ( t* t 0 ‘16 & -5*t0*13)
= -8.3x IO' 14 (X=7) & -4 x IO' 10 (X=0.1)
Dt3 = -(I - e) ps Dtv = -825 * ( I * I0‘t3 & -7.5* 10‘12)
(12-30)
-8.3x IO' 11 (X=7) & -6.2x I0‘9 (X=O.I)
p g_
^
R'T
Mv
pM a
m R'T PtMa + (Mv - Ma)PV
= 2.58x IO"8 +4.lx 10 " = 2.6 x 10‘9
A comparison of the magnitude of terms in (12-9) is given in Table 4.
Similarly. Cpx and Cpp are kept in the capacity coefficients. In the kinetic coefficients, only Dp3
is important and is kept. Further reduction can be made for Cpx and DPa.
257
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 5. A comparison of the magnitude of the coefficients in pressure equation
Cpt
i
CPi
C*Pi
Selection
X
0.4
2.8 (X=7)
\
0.04 (X=0.1)
T
P
8.9 x 10" (X=7)
0.69 (X=7)
3.0 x IO'5 (X=0.l)
2.34 x IO*2 (X=0.I)
2.3 x IO'5 (X=7)
1.2 (X=7)
8.6
D,J
D,a
D?
X
8.3 x IO*'*1(X=7)
5 x tO*,2 (X=7)
(7)
4x IO' 10 (X=0.I)
3 x I0'9 (X=0.I)
T
8.3 x 10*“ (X=7)
6.5 x I0*9 (X=T)
x lO^fX^.I)
4.8 x I0*T(X=0.l)
6.2
P
\
0.04 (X=0.I)
x IO'7 (X=0.t)
i
(78)
!1
i
2.6 x IO'8
I.3 x
10**
V
(50k)
Cpx = ( I -£)
(12-31)
Pr
R'T
.D
PVMU
nt '
R'T Pt Ma +(Mv - M a)P,
_ P u K k rv
<12-32)
P*
The total pressure equation is then reduced to:
(1
_ t
c ) PaP. *o M I . e£Ma
p T tc dt'
R'T
d_
R ^ r '1 d r '
- P „ BP;
rt
dt'
•Vo
o * Kk^dP;'
r ‘ ( ^ x ~Pam)Pu ---Pf
ar
where
258
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
r
=
l-—
£
(12-34)
- — —— X ,
P r + Pb
The simplified equations for microwave drying of non-saturated porous media are:
d X ] _ _______________
r.
d t'
R fiX o r '' d r '
(pC j
(I-e)
v a x ; , ( p^ - p^
[ e/r 0 dT"
i-£
r ^ - T o a r _ r nax- r 0 a '
at*
p„p( X0 ax*
p r rt. ar
i
a
t i r '1 dr
(^nax
eCA/u c
ar
ar-
p r ***
~p ^ ~ p ~17 jj
(12-19)
AhvM +
(12-26)
- P u(m 3/>;
KT
r.
Pom)Pa
**„ 3 p :
Me 3r*
d t'
(12-33)
where M is the internal evaporation due to both the free water and the bound water.
12.5 Boundary Conditions
12.5.1 Moisture boundary condition (9-3)
Boundary condition Eq (9-3) in spherical coordinate writes:
-(i-e )p .
= e(p v, - p _ > tm
(12-35)
The dimensionless form of Eq (12-35) is
_I_
*0
_
X dr'
T dr'
P dr'
gpt- bm
(l-o p ,
(12-36)
From the magnimde analysis in section 12.2, (12-36) can be written as
259
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
_1_
ud X (I
*0
dr'
^ P
1 max
~ P1 aim Pr
rr
~ T K k *T
l-£
g p t- K k - l )
<1 —O p,
.»
p, P, dr'
(12-37)
12.5.2 Temperature boundary condition (9-6)
Similarly, the dimensionless temperature boundary equation in the spherical coordinates writes
{r „ . —7T») d7*
.
.
.
— = h(T_ -T 0)-hT, ( T ^ - T 0)
Ru
dr
A/iv(l-e )p ,
dP;
dT‘
- T j ^ + D 'i P ^ - P ^ ^ r
~d7
a7
dX'
U>£ + D> )X0 — h H D /
Ro
(12-38)
From the scaling analysis in 12.3. (12-38) can be simplified to
<r «m -7*0) d rT = f>(T.-TQ) - h T ; ( T ^ - T Q)
9r
M ,(I-e )p ,
9A-; , ( P ^ - P ^ J Pr Mrr dp;
dr’
I-e
p, p , d r ’
( 12-39)
12.5.3 Pressure boundary condition (9-7)
The pressure boundary condition in dimensionless form is
P*s = 0
(12-40)
13. Finite Difference Solution
The microwave drying equations (12-9). (12-26) and (12-33) can be rewritten by introducing
coefficients £21 to £29 as follows:
d x ; _ £2i d f ^ 2 _ . , d x ; )
dr
r z dr
dr
%rM r *1
r ~dr
dr
(13-1)
260
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Q4
.\
d r _ os d
dr
£27
£26-r
~ r ’2 d r '
dr
dr
,d T _
dr'
(13-2)
- Ah.. M + 0
-A
.z
ap;
£29-r
r 'z dr'
(13-3)
w here
r
£21 =
—
P
r —
£ 2 2 =
R;X„
D _
X 0
£ 2 3 =
-
7
= a - e ) P
^
P,
^
C
£28 =
- P
—M l
R T
o
~ g - —
I-e
QJ = - i -
Q
^
K k ,
------------------
p. u.
Q 6=^
P —
(13-4)
£ 2 9
^ P ^ - P ^ P . —
r
/r
The Crank-Nicolson approach is used to discretize the partial differential equations. It has been
proved that the Crank-Nicolson method is second-order accurate in both time and space. Other
advantages of the Crank-Nicolson method include: I) it is unconditionally stable. 2) it has no
restriction on the size of the time step At for computation.
13.1 The moisture equation
The solution domain is divided into N layers with a thickness 5 = l/N. Thus N'+l nodes are
generated (i = 0 . 1.2.......N). The left side of the Eq (13-1) in the Crank-Nicolson scheme writes
dx;
dt'
yr • ft
~ A/r
(13-5)
A r
The terms on the right side of Eq (13-1) are discretized by taking the arithmetic average the
central difference equations of explicit and implicit schemes. The nonlinear coefficients in the
equation is linearized by the lagging method (Ozisik. 1994). Thus
261
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w h e re
«—I
a i ft-•'I
- 3*/‘£ 22 - / * —
W
3
i ' dr'
1Q2 i z —
£21 - •
(i+ i/ 2 ): Q 2 ;*‘ 2(A-*:;‘ - x ;;~l )- (/ -1 / 2 ): Q 2 ;;,'; (x
ai
^
" - '
-x ;::'
(13 -7 )
51
m »*' ( / + i / 2 )IQ2 ^ ,/ : x ;,:;1 - [ ( i> i/ 2 ): a 2 ;;t‘/ : + ( j - i / 2 ): a 2 n;t‘ : lx,7
'1
5The second term in Eq (13-6) is similar to the above expression except changing time step n+I
to n. The pressure term in Eq (13-1) can be discretized in a similar manner. The central
difference equation at time step n+I in the pressure term is written as:
£21
r
9 (
d r'
£23 r
- ap;
£23- r
£21
' £23-t ,3 P M
k
dr"
dr'
A -i/:
dr"
QI-* (/+ I/2)i £237*1,. f e * - P ; r l)-U -I/2)-£23^/2(Per I - P ^ )
Sz
(13-8)
Q i - ' ( £ + i / 2 ) 2£23;;1' ; /j; ; ; ‘ -lu+uircn:'1
,, + ( / - i / 2 ) I £23;:tl/ : Jp;;*1
s1
+
cir1rf .
f
1/ 2>- £23:*', z p;;*1
t
Finally the moisture equation can be written as:
262
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
'Jt+l
mr x;,*? + n i* p;,^1+ n 3; x ; r l + n 4"p ; r l +■n sr' x;,:T
+ n 6 r l p;,:r = r n ;
(13-9)
( / = i. 2.... iv - 1)
w h e re
Ql^l
Of*
ntr* = ^ - t ( ( - i / 2); Q2;;‘ ,
2r£*
ro :" 1= -
m r ‘ = - v - r 0 - i / 2 ) Ia3;:1,/,
2i*5*
[(/ -(-1 /2 )'0 2 " * ',, + (i - 1 / 2 )2Q 2 £ i‘, , ] - —
2i~8~
Ar
n 4 r*1 = - - ^ r f e + I / 2 ) : Q3r;,% +a-I/2)-£23r:t'/ ,]
2/~d'
Q./T-I
n s r 1= _ Ti _ ( t--M/2)2n2;;l'/,
2rS*
nr
Ar
-
a I"
2z2S 2
Qt*
2r d '
op **1
n e r 1= - 7 ^ a + i / 2 ) 2Q3r'i/:
2r5*
2 t"o *
i- i/ :
- 1/ 2 )2 Q2 n.t,,
x
(13-10)
Ar
Q!"
- —rfr(< -h / 2)2sb;., ,, p;;_t
2i~ o~
QI" r
t
QF"
- - r p - l ( r + I/2) 2Q3l uz + ( /- I/2 ) 2 Q3r.I/:Jp;; - - _ ^ u - l / 2 ) 2Q3r.1/ ; P;,:
2i~o~
2i~o~
13.2 Energy equation
The energy equation (13-2) is discretized in a similar way to the moisture equation.
ns:*1c r ‘ + n 9r ‘ 77“ +nio;*‘ 7 7 -1= n i i:___ (/=i.2__ /v - 1)
( 13- i n
where
263
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
OS"” 1
n
8
"
' 1
= t2 -r ~^o -~ ( ' - i/2 )Iq6": >‘
r\rn + l
-
r
■.
O J . 11* 1
rt9"~' = — ^ [ ( / + i / 2 ) : Q6;;1'/, +(r-i/2)-£26;*1,.,]—
2r~5~
'
~
—
At
O S "”1
niO ^ 1 = —^ -r(i + I/2)I£26,tl1/,
2 i~S~
Q4rt
m i; = a a " m ; -<t>; - - f - r r
At
(13-12)
OS'*
2 r S '
£25" f
1
£25"
- T ^ f c + i / 2 ) : £26,iI/: + (/—t / 2)2£26;_1/z ]7^‘"
lt'5 '
2r o ~
13.3 Pressure equation
The pressure equation (13-3) is discretized following the above procedure as follows
ni2"*‘ p;,--1+ m 3;*1x;;*1+ ni4 ;*' p;;*' +•ms;*' p;,^1 = ni6"
0 = 1. 2..... n
^
(13-13)
where
£2I""*1
ni2;*‘ = —
~ 1/ 2):£29^
2i~8~
nw;*' = -
2r
'
m 3 ;* 1 =
0 7 " ”*
At
+ 1/ 2)I£29;*'/: + ( t-l/2 ) 2Q 9^,/ J —
o ~
At
£21"*’
m s r ' = - ^ - t O + i / 2): £29;;i,/ ,
21~5~
( i3-t4>
~ x ; : - ^ (u i/D ^ r .^ p ;:, - ^ p ; :
At
2
tS~
At
q i;
13.4 Boundary conditions at node 0 and N
264
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
n
In order to be in consistent with the above finite difference equations, a second order
approximation, the three-point formula, is used to discretize the boundary conditions. The
boundary condition at r = R (12-37). (12-39), and (12-40) can be rewritten as:
d p:
02
_
dr'
e
Ra p ^ h „
0 6 <rIim- r _ ) a r
..
(13-15)
-0
m m
-
op
.
- H i ------------------ 0 2
dr’
p:=
(p»
(I-e)p,
dr’
ap; )
03-
(13-16)
dr’
(12-40)
i
13.4.1 Moisture boundary condition
At nodeO (r = 0)
d x:
dr’
=0
(13-17)
rsO
The three-point finite forward difference of (13-17) yields
dx;
dr'
r= 0
- 3x ; r +4 x ; r - x ; ;
28
=o
or
-3x;0"*' +4x;rl -x;r =o
(13-18)
At node N (r = R), we have, for example:
^ ♦ Y *ff*l t ^ y *B+t
02-
=£22"^
'
dr’
iV
,v~z
tx-1
28
(13-19)
265
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Finally, the moisture boundary condition at r = R writes:
+ni8r,/,eT!i +ni9^1x;;:1,+n2 o;*‘p;*:1,
r~'xT l
(13-20)
p ; r l =n23
where
Q2n~[
m i* " = - y
28
0 2 0 "*'
=-
0 3 "* '
n i 8"^1 =-
203"*'
n i9 ^ ‘ = -
v
28
. = i3 i0*711-1
2-.v
28
2H2nv
n 22"*1 =
v
28
(13-21)
ri23" = - g ^ o p„hm)
(I-g.v)P,
13.4.2 Temperature boundary condition
At node 0 (r = 0)
97"
dr
r=0
-37~(;'l~l +4rl",~l - r : ^ ‘
=o
25
or
- 3 T 0’n~l + 4T i
- 7;* =o
(13-22)
At node N (r = R)
rI24r‘x;;:l2+n25;~'7-;_;1+n 2 6 ;" p ;£2+n27;*' x;;:1,^n 2 8 r lr;; I
+n29r‘p;^', +n3o;*'x;;*1+n3ir'r.r' +n32;*‘p;7‘ =n33;
(13-23)
266
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w h e re
-n i 7 "
ri24 r =
n 26n"‘ = M v (I £,v )p' m s r 1
m s "*1 =
2 Q 6 "y‘t r
^ - r .)
6R0
„n-*>l .«
n30-« =
a, t
_nt*l
n32«-i _ M -v (l Cv )p- 022""'
Q 6 T (7 _ -7 L )
2 SR n
n 2 7 ^ 1=
n 29 ^«^ ^
=
,£ v ]p ~ n 2 r~‘
_
n25r =
n i-g rip ,
/?n
- n i9 n
n 2 o a .,
1i 3-24-1
n 3 r «, 3 0 6 7 ( 7 ^ - 7 1 )
25/?n
n 33" = - hn
v T„(r;; - 1)
13.4.3 Pressure boundary condition
At node 0 (r = 0). we have
9r‘
- 3 P x i + 4 p ;rl - p ; r ‘
= 0
25
or
- 3 p;;*‘ +4P;,""1 - p ; r ‘ =o
(13-25)
At node N (r = R). we have
p ;r =p;=!
(13-26)
13.5 The assembly o f the finite difference equations
267
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T h e
s e ts
o f
(13-26) a r e
e q u a tio n s
e x p r e s s e d
(13-9). (13-11). (13-13), (13-18). (13-20), (13-22), (13-23). (13-25)
in
m
a tr ix
f o r m
[D]“{ A r = { 5 } n
(13-27)
268
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a n d
( 1 3 - 2 8 )
M/viiMi/viii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A 10
*0
P'n~l
r sO
w•Itrl
- '• / I
T -~l
r i\
I
•
•
•
y
*n-»l
{*}"=■
I>
•
•
A !V
(13-29)
*V
*v
n ic
ni6"
•
•
r17 ;..,
m r v_,
ni6"v_,
rrn;
n33"
i
/ .v -i
n*"-l
•.*V -I
y *n*l
0
0
0
rn"
nnf
ni6"
•
•
•
n7" 1
(13-30)
’i.V -D xt
270
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(
B e g in
P a r a m
G r id
e t e r
G
I n p u t
e n e r a tio n
I n itia liz e
T im
C a lc u la te
)
e
{ A }
=
[ D
i *
] M
u tiliz in g
A t
&
{ B }
{ A } '* 1
S o lv e
f o r
{ A } ' -
{ A
{ A } '
N o
I f
} - 1 < £
Y e s
i =
i+
=
i *
I
N o
f f T i m
e
A t >
T L
Y e s
F ig u r e
5 .
H
o w
d i a g r a m
f o r th e
s im
u la tio n
271
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14. Convergence Study
T h e
c o n v e r g e n c e
s iz e s .
r e s u lts
In
t h e
a r e
t i m
o f
e
t h e
n u m
s te p
p r e s e n te d
in
e r ic a l
m
o d e l
c o n v e r g e n c e
F ig u r e
6
a n d
w a s
te s t ,
e x a m
t i m
7 . f o r m
e
in e d
s te p s
o i s t u r e
o f
a n d
b y
u s in g
2 .
I .
te m
d i f f e r e n t
a n d
0 .5
p e r a tu r e ,
tim
s e c o n d
e
a n d
s p a c e
s te p
w e r e
u s e d .
T h e
r e s p e c tiv e ly .
0.25
2
n u n
0.20
5
0.15
7
U
y
m in
0.10
0.05
T im e
s te p
=
2 s
T im e
s te p
=
Is
T im e
s te p
=
0 .5 s
0.00
0.0
1.0
L o c a tio n
F ig u r e
F r o m
7 . M
o is tu r e
F ig u r e s
7
c o n t e n t d is tr ib u tio n
a n d
n o n - d is c r e p a n c ib le
C r a n k - N ic o ls o n
d iv id in g
p r e s e n te d
a r e
th e
in
8 .
a n a ly tic a l
n o t s ig n if ic a n t. A
b e
d i f f e r e n c e
s c h e m
F ig u r e s
i t c a n
9
e
is
d o m
a n d
t s m
a l l
s e e n
in
o b t a i n e d
t h a t
th e
m
in s e n s ib le
to
a i n
in to
1 0 . F r o m
m
e s h
1 0 .
f o r
1 5 .
F ig u r e s
s iz e s ,
t h r e e
t h a t
e
(m m )
a t th r e e
o is tu r e
t i m
2.0
1.5
tim
e
tim
s te p s
c o n te n t
s te p
3 0 .
a n d
is .
3 0
4 0
1 0 . th e
a n d
4 0
s te p s .
a n d
a t
tw o
p r e d ic tio n s .
c h a n g e s .
a n d
9
e
T h is
F o u r - e le m
e le m
e n ts .
e le m
e n t
T h e
d if f e r e n c e s
d r y in g
tim
e s ,
th e r e
illu s tr a te s
th a t
s iz e s
s im
w e r e
u la tio n
b e tw e e n
r e s u lts
f o u r
e n ts , c o n v e r g e n c e
is
272
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
u s e d
m
e s h
is
a
th e
b y
a r e
s iz e s
o b v io u s .
360
U
3 5 5
7
m in
3 5 0
T im e
s te p
=
2 s
T im e
s te p
=
Is
T im e
s te p
=
0 .5 s
3 4 5
0.0
1.0
0 .5
L o c a tio n
F ig u r e
8 . T e m
p e r a t u r e
p r o f ile s
o b t a i n e d
a t
th r e e
2.0
1 .5
tim
1 5
( m m )
e
s te p s .
0 .3 0
0 .2 5
2
S
B
m in
0.20
u
I
0 .1 5
P
7
1
m in
0.10
E le m e n t
E le m e n t
0 .0 5
E le m e n t
E le m e n t
0.00
0 .0
O S
1 .0
I S
L o c a tio n
F ig u r e
9 . M
o i s tu r e
p r o f ile s
a t
f o u r
m
e s h
s i z e s
a n d
tw o
2 .0
2 .5
( m m )
d r y i n g
tim
e s .
2 7 3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
8 4
7
m in
8 2
2
m in
8 0
7 8
E le m e n t =
10
E le m e n t =
15
E le m e n t =
3 0
E le m e n t =
4 5
7 6
7 4
0.0
1.0
0 .5
2.0
L o c a tio n
F ig u r e
1 0 . T e m
p e r a t u r e
p r o f il e s
a t f o u r
m
e s h
s iz e s
2 .5
( m m )
a n d
tw o
d r y i n g
tim e s .
15. Notation
{ A }
s o lu tio n
IB }
c o e ffic ie n t v e c to r
C
p h e n o m e n o lo g ic a l c o e f f ic ie n t
c
P
s p e c if ic
v e c to r
h e a t . J - k g '1 B C 1
d P
p a r tic le d ia m e te r , m
D
p h e n o m e n o lo g ic a l c o e f f ic ie n t, s y s te m
D 1V
b in a ry
a i r - v a p o r d i f f u s i v i t y . m 2 - s '1
D b
b o u n d
w a t e r d i f f u s i v i t y . m 2 - s '1
D c
d ia m e te r o f th e
s p o u te d
b e d
m a trix
c o lu m n , m
274
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
f
re s is ta n c e
F
h e a t o r m a s s
g
g ra v ity
h
e n t h a l p y . J - k g ' 1: s u r f a c e
h 5h
h e a t o f s o rp tio n
h m
m a s s
A hv
l a t e n t h e a t . J - k g '1
H »
in itia l b e d
i
n o d e
j
d iffu s iv e
k r
re la tiv e
EC
in trin s ic
m
m a s s , k g
m
m o is tu re
M
m o l a r m a s s , k g - m o l '1
V/
te n s o r to
flu x
g a s e o u s
a t
m e d ia
'- s '1
h e a t t r a n s f e r c o e f f i c i e n t . W - m ’2 EC’ 1
t r a n s f e r c o e f f i c i e n t , m - s '1
h e ig h t, m
n u m b e r
m a s s
f l u x . k g - m '2 - s '‘
p e r m e a b ility
p e r m e a b ility , m 2
e v a p o ra tio n
to ta l m o is tu re
r a te , k g - n r - s '1
e v a p o ra tio n
P
p re s s u re . P a : m ic ro w a v e
q
h e a t flu x . J - m
R
s a m p le
R '
u n iv e rs a l g a s
S
s a tu ra tio n
S v
m o la r e n tro p y
t
tim e , s
T
in trin s ic
a v e ra g e
T L
ite ra tio n
lim it f o r tim e , s"1
u
s u p e rfic ia l a v e ra g e
I f
s p o u te d
X
m o is tu re c o n te n t (d ry
W
p o ro u s
i n t e n s i t y , m - s '^
m a s s
'
th r o u g h
b o u n d a r i e s . J - m '2- s '‘ o r k g - m
n
X
d iffu s io n
flu x , k g -m
’ s
v e c to r n o rm a l to
p o w e r.
1
th e
s u rfa c e
(o u tw a rd ly )
W
'- s '1
ra d iu s , m
b e d
" s ' 1: a
ra te , k g -m
'1
c o n s ta n t. J - m
o f 1 K '1
t e m p e r a t u r e . EC
v e l o c i t y , m - s '1
a ir s u p e r fic ia l
v e l o c i t y , m - s '1
b a s i s ). k g
m o is tu re c o n te n t (w e t b a s is ), k g
H :0 / k g
s o lid
H iO /k g
w e t m a te r ia l
m a s s , k g
G reek sym bols
275
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6
fin ite
e
p o ro s ity , to le ra n c e
e '
p o ro s ity : d ie le c tric c o n s ta n t.
£"
lo s s
7
a n g le
o f c o n ic a l b a s e
0
s h a p e
fa c to r =
d>
h e a t s o u rc e . W -(k g
A.
th e rm a l c o n d u c tiv ity .
R
d y n a m ic
nt-33
c o e f f ic ie n t in
p
d e n s ity , k g -m ”
p<
s o lid
F
£ 2 1 -9
d iffe re n c e e le m e n t th ic k n e s s , m
lim it o n
ite ra tio n
s c h e m e
fa c to r.
in
th e
s h e a r s tre s s
b e d . d e g
l/s p h e ric ity
s o lid )”
W
v is c o s ity , k g - m
d e n s ity
s p o u te d
- m
’- K " : w a v e
1- s '1
fin ite d if f e r e n c e
(s o lid
le n g th , m
e q u a tio n s
w e ig h t / s o lid
v o lu m e ), k g -m ”
t e n s o r . k g - m ':
c o e ffic ie n t
p a r a m e te r d e f in e d
in
E q
(1 2 - 3 4 )
S u b s c r ip ts a n d s u p e r s c r ip ts
0
a t s a tu ra te d
c o n d itio n
a
a ir
a tm
a tm o s p h e r ic
b
b o u n d
c
v e lo c ity
e f f
e f fe c tiv e
f
fr e e
g
g a s
1
s p a c e
s te p
I
liq u id
=
m a x
m a x im u m
n
tim e
p
p a r tic le
P
p re s s u re
s
s o lid , o r re la tin g
T
te m p e r a tu re
o r fr e e
s p a c e : in itia l m o is tu r e c o n te n t ( r e f e r s
to
fre s h
s a m p le )
p re s s u re
w a te r, b u lk d e n s ity
o r te m p e ra tu re
s c a le s
w a te r
=
a ir +
s te p
v a p o r
in
fr e e
fin ite d iffe re n c e
w a te r +
b o u n d
s c h e m e
w a te r
v a lu e s
in
fin ite d iffe re n c e
to
s c h e m e
s u rf a c e
276
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V
vapor
w
total m oisture = free w ater + bound w ater +■vapor
X
moisture
OQ
s u r r o u n d in g
Dimensionless groups
edio
Io -l — o
_)
Particle A rchim edes num ber
Particle R eynolds N um ber
16. References
Bird. R. B.. Stewart. W. E. and Lightfoot. E. N.. I960. Transport Phenomena. John Wilev &
Sons. New York.
Bories. S. A.. 1991. Fundamentals of drying of capillary-porous bodies, in Convective Heat and
Mass Transfer in Porous Media. S. Kakac et al. (eds.). Kluwer Academic Publishers.
Dordrecht.
Chen. P. and Pei. D. C. T.. 1989. A mathematical model of drying processes. Int. J. Heat and
Mass Transfer. 32(2). pp. 297-310.
Donsi. G.. Ferrari. G. and Nigro. R.. 1996. Experimental determination of thermal conductivity
of apple and potato at different moisture contents. /. Food Eng.. 30. pp. 263-268.
Feng. H.. Tang, J. and Cavalieri. R.. 1999. Combined microwave and spouted bed drying of
diced apples: effect of drying conditions on drying kinetics and product temperature. Drying
Technol.. 17(10).
Gong. L.. 1992. A Theoretical. Numerical and Experimental Study of Heat and Mass Transfer
in Wood during Drying, PhJD. Dissertation. Washington State university.
Incropera. F. P. and DeWitt. D. P.. Introduction to Heat Transfer. John Wiley & Sons. New
York.
Keey, R. B., 1972. Drying Principles and Practice, Pergamon Press, Oxford.
277
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Krokida. M. K. and Maroulis. Z. B.. 1999. Effect of microwave drying on some quality
properties of dehydrated products. Drying Technol.. 17(3), pp. 449-466.
Markowski. A.S.. 1992, Drying characteristics in a let-spouted bed dryer. The Canadian J.
Chem. Eng., 70. pp.938-944.
Mayne. C. and Perre. P.. 1991. Processes related to drying: Part I. Theoretical model. Drying
Technol.. 9(5). pp. 1135-1152.
Ni. H.. 1997. Multiphase Moisture Transport in Porous Media under Intensive Microwave
Heating, Ph. D. Dissertation. Cornell University.
Niesteruk. R.. 1996. Changes of thermal properties of fruits and vegetables during drying.
Drying Technol.. 14(2), pp4I5-422.
Ozisik. M. N.. 1985. Heat Transfer. A Basic Approach. McGraw-Hill Book Company. New
York.
Ozisik. M. N.. 1994, Finite Difference Methods in Heat Transfer. CRC Press. Ann Arbor. MN.
Patankar. S. V.. 1980. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing
Corporation. New York.
Pulmb. O. A.. Couey. L. M. and Shearer. D.. 1986. Contact drying of wood veneer. Drying
Technol.. 4(3). pp. 387-413.
Roman. G. N.. Urbicain. M. J. and Rotstein. E.. 1982. Moisture equilibrium in apples at several
temperatures: experimental data and theoretical considerations. /. Food Sci.. 47. pp. 14841489.
Turner. I. W.. 1991. The Modeling of Combined Microwave and Convective Drying of a Wet
Porous Material. Ph.D. Thesis. University of Queensland.
Turner. I. W.. Puiggali. J. R. and Jomaa. W.. 1998. A numerical investigation of combined
microwave and convective drying of a hygroscopic porous material: A study based on pine
wood. Trans IChemE.. 76, Part A. pp. 193-209.
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APPENDIX B
FINITE DIFFERENCE PROGRAM
B-I Main function
function [a.mynorm.d.b.omega.paral .kapaJcapanl=main( paraO.aO)
9 Contents of array paraO
9c I ...... Gas constant
1
.... K
3 ...... Pr
4
... ps
5
.... Ma
6 ..... ■PfO
9c 7
-PjO
8
.... Ro
9 ..... Xo
9
9c 10 ..-.T o
It ..... T™*.
t2 ....-T,nf
9 13
— Pnrn
14
15 ....—P V.inr
9 : 16
— Pvmr
17 ...... Ppb
18 ....
20 ......Ho
21 .... ..y (degree)
9c 19
Dc
9C *>'» ....U
9c 24
.......P«m
23
.... W s(or Ao)
9c 25 ...... Patoont at t=0 (or <t>0)
9 26
N'
27 ..... Nt
9c 29
norm
30 ...... It max (max number o f iterations)
9c 31
.... C l
9c 32 .. .... C2
28 ....... TL
( 0 for apple. I for potato )
( 0 for linear <t>. 1 for variable <t>)
9c 33 ...... Mv
9 Contents of array para I
9c I ...... porosity
T
9c 4
Aaf
5 .. ... Eqn 12-34
6 ..... Ahv
h*
8 .. ... h
9 . — Drff
II
.....^
12 ___ Pv
14
— (p Cp)rff
15
9
7 .
9c 10
.. krf
9c 13 .... -Pa
9
16
...
n,
3 . .... P?
_____£"
e”
N=para0(26):
para0(2l)=para0(2l)/l80*pi;
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% initialization o f a( I.:)
a< 1:3:3*(N+1 ).I )=a0( 1:3:3*(N+1 ).I):
Tc dimensionless XI at t=0
ai2:3:3*(N+l).t )=aO(2:3:3*(N+l ).l);
% dimensionless T at t=0
at 3:3:3 *( N-t-1). I )=a0( 3:3:3*( N+-1). I ):
% dimensionless Pg at t=0
for it=l:para0(27)
% main loop
it
unpa=a( :.it):
*5 max number of iterations
Jit
para I=get_paral( paraO.tmpa):
% update first level parameters
o mega=ge t_o megat paral.paraO.tmpa);
% update all the omegas
tf jit =
I
[b.phiti=get_b_Komega.paraO,paral.tmpa): % fixed elements in B array
end
kapa=get_kapa( omega.para0):
% update all the kapas
kapan=get_kapan(omega,para I .paraO):
% update all the kapas at node N
d=get_d( kapa.kapan.N):
% D array
tn=tmpa(3*N+2.I);
[b.phit|=get_b_2( omega.para I .paraO.tn.b.phit):
%update elements in B array
na=d\b:
% get AA*
mynormt it)=norm(tna-tmpa).2):
% find the norm of AA*-AAn
if mvnormtit) < para0(29)
break;
end
tmpa=na:
end
for j= 1:3:3*(N+t)
ifn a (j.l)< 0.00518
natj.11=0-00518;
end
ifn a (]+ l.I)< 0
na(j+Ul)=0:
end
if na(j+2.I) < 5e-5
na(j-t-2.1 )=5e-5:
end
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end
a( :.it+l )=na;
end
B-2 Subfunction 1 - get_paral
function para I=get_para I (paraO.a)
N'=paraOi 26i:
tmpl=a( l:3:3*N +l.l)‘paraO(9):
9c dimensional XI
tmp2=ai2:3:3*N+2.l)*(paraO( 11 )-paraO( lO)H-paraO( 10);
9c dimensional T
tmp3=a(2:3:3*N+3.l )*(paraO( I3)-para0( l4))+paraQ( 14):
9c dimensional Ps
paraK I:N+l.l)=( 1.282+1.65*(1.899+tmpI).“tm pI)./(l+l.65*tm pl)./( l.899+unpl):
para I (:.2)=para0( 6 )*exp( 29.619-0.152*tmp2+0.648e-4*tmp2.A2+0.815e-6*...
tmp2.A3-0.12e-8*tmp2.A4);
parat(;.3)=para0(7')*tmp2.A0.5./(0.672+85.229./tmp2-2l I I.475Jtmp2.A2+...
l064I7Jtmp2.A3);
if para0(3t) = 0
parali :.4)=0.1263 l+0.0595*tmpI;
9c apple
else
parall :.4)=0.1445+0.1161*tmp I
9c potato
end
paral (: J ) = I-para0(4)/2/para0(3)*tmp I .*( I -para I(:. I ) ) 7 p a r a l( 1);
para1(:.6 )=( 3 167.2-2.432* tmp2)* 1000;
Ar=9.81’(2*para0(8))A3*paraO( 18)*(paraO( I7)-para0( l8))/paraO(23)A2:
Re=paraO( 22) *2*para0( 8) *paraO( 18 )/paraO( 23);
Sh=0.0045” ArA0.226*ReA0.664*( tan(paraO( 21 )/2))A( -0.852)*( paraOl 20)/...
2/para0( 8) )A(- 1.47) *( para0( 19 )/2/para0( 8))A0.947;
Nu=Sh:
paral (:.7)=Sh/2/para0(8)*2.2e-5* 101325.7tmp3.*( tmp2/273.15 ) A1.75:
paral (:.S )=Nu/paraO( 19 ).*(0.0035+7.67e-5*tmp2);
para I (:3 )=6.273e-4*exp( -(5.843e3-2.038e2*tmp I )7tmp2)’ 0.5e2:
s=( l-paral(:.I))*I.65/2.*tmpl:
para I (:. 11 )= 1.01 *exp( -14.48 *s);
paral(:.lO)=L-paral(:.I t ) ;
para I(:. 12)=get_pv( tmp l.tmp2);
para I (:. 13 >=para0(5)/para0( I )*( tmp3-para I ( 12))7tmp2:
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paral(:.L4)=t.0*para0(l7)*( 1415+27.21*tmp 17( l+tmp I )):
% for variable Phi
if para0(32) = I
unp=tmp LVf L+tmp I )*100:
para I (:. 151=1.2159+0.3477*tmp+0.0074*tmp.A2-0.0001*tmp.A3:
paral t 16 (=-23.5999+0.L58233*tmp2-2.56978e-4*tmp2.A2- L.87998*tmp I...
+0.00768435*tmp I .”tmp2-5.6363e-6*tmp L,*tmp2.A2+...
0.0289568*tmp l.A2-7.66337e-5*tmp I .A2.*tmp2-4.09947e-5*tmp 1.A3;
B-3 Subfunction 2 —get_omega
function omega=get_omega(paral,para0.a)
N'=para0(26):
9c Pmx.-P.um
dp=paraO< I3)-para0( 14):
tc=para0(23 )*paraO( 8 )A2/paraO( 2)/dp:
tmp=a('2:3:3*N+2.1 HparaOL 11)-paraO( I0))+para0( 10):
% dimensional T
omegat l:N+l.I )=tc/paraO(8)A2/paraO(9):
omegat 1:N+1.5i=t paraCK 11 VparaQt L0))/para0( 8)A2:
9c constant <t>
if paraO( 3 2 )= 0
omegat I :N+1. 11)= I0*para0( 24)/paraO(25)*paraI<16):
end
omegat :.2)=para0(9)*paral(:.9):
omegai :.3 l=dp*paraO( 3 )/para0(4)*para0(2)*para I (:. 10)7para 11 2)./...
( L-paraI(:.l));
omegat :.4)=<para0( 11)-paraO( IO))/tc*paraI( 1 4 ) :
omega( :.6)=paral(:.4):
omega( :.7)=paraO(9)/tc*paraO(4)/2/paraO(3)*paraI(:. I3).*( I-paraI(:.I));
omegat :.8 )=dp*para0(5)/tc/para0( I )*paral(:. I ).*para I <:j)7 tm p :
omegat :.9 I=dp*para0( 2)/paraO(8)A2*paral t 1 3 ).*paral ( LI )7paral( :3):
omegat :.I0)=para0(9)*para0( I7)*paral(:.6)/tc/t I+para0t9)):
9c variable O
if paraQ(32)=l
omegat :.I l)=get_phi(paraI.paraO);
end
B-4 Subfunction 3 - get_b_I
function [b,phitI=get_b_l(amega,para0.paral.a)
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ic=paraO(23)*paraO(8)A2/paraO(2)/(paraO( l3)-para0( 14));
’Jc dimensionless dt
dt=para0(28)/para0f27)/tc;
N=para0(26):
deIta=t/N;
for i=l;N -l
% calculate omega2.3.6.9 at i-rl/2 and i= l/2
tmp2p( i)=( i+0.5)A2*( 2*omega( i+L.2) ‘ omegat i+2.2)/( omegat!+-1.2 H-omegat i-t-2.2)));
tmp2m( i )=( i-0 .5)A2*( 2‘ omegat i+1.2)*omegat i.2)/( omegat i-t-1.2 )+omega( t.2)));
tmp3pt i)=t i+0.5)A2*( 2 ‘ omega( i-t-1.3)‘ omegat i-r2J)/(omega( i+1.3 )+omegat i-t-2.3)));
unp3 mt i >=i i-0.5r'2*( 2*omegat i-t-i .3 )*omegai i,3)/'t omegat i-t- i .3 H-omegat i.3)) k
tmp6pt i)=( i+0.5)A2*(2*omegat i-t-1.6 )*omega( i-t-2.6)/( omegat i-t-1.6)+omega( i-t-2.6)));
tmp6mt i)=t i-0.5)A2*(2*omegat i+1.6)*omega( i.6)/(omegat i-t-1.6 )+omegat i.6)));
tmp9p( i)=( i+0.5) A2*( 2*omega( i-t-1.9)*omega( i-t-2.9)/(omega( i-t-1,9)+omega( i+2.9)));
tmp9m( i )=t i-0.5)A2*(2*omega( i-t- L.9 )*omega( i.9)/(omegat i-t-1.9 )+omega( i.9)));
end
a=a:
tor i=I:N-l;
j=3*i+l;
tmp l=2*iA2*de!taA2:
btj. I )=omegat i-t-1. 1)/unp t *(( tmp2pt i )+tmp2mt t))*a(j >-<tmp2pt t )‘ a(j+3 )+...
tmp2mt i)*alj-3) H-t tmp3pt i)+tmp3mt i) )*a<j-t-2)-< tmp3p( i)*atj+5 H-...
tmp3m(i)*a(j-I >))-a(j)/dt;
btj+1. 1)=t omegat i-t- LJVtm p I *((tmp6pt i )+tmp6mt i) )*atj-t-1 )-t tmp6pt i )*a<j+4)...
+tmp6mt i)*a(j-2)) )+omegat i-t-1. 10)*( b(j )+atj )/dt t-omegat i-t-1. I I ))...
/omegat i-t-1.4)-a(j-t-1 )/dt;
btj+2.1 )=t I/tmp I *( t tmp9p( i)+tmp9m( i))*a(j-t-2)-( tmp9pt i)*a(j-t-5)+...
tmp9m( t)*a(j-1)) )-omega( i-t-1.7) •( b(j)-i-a(j )/dt) (/omegat i+1.8 )-...
atj-t-2)/dt;
end
for t=l:3
b(i.I)=0;
end
b<3*N-t-Ll)=-paraI(N-t-LI)*paraO(8)*paraO( I6)*paraI(N-t-LT)/< I-paral (N+LI))...
/paraO(4)*(paraO( l2)‘ paraI(N+t.l2)/paraO( I5)/(a(3*N-t-l )*...
(paraO( 11 )-paraO( I0))+para0( 10))-1);
b(3*(N-t-l),l)=0:
b(3*N+2.I)=tpara0( I2)-para0( I0»/(para0( 11 )-paraO( 10));
phit=omega(:.I t)yomega(;.4)/2;
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B-5 Subfunction 4 —get_kapa
function kapa=get_kapatomega.paraO)
tc=paraO(23)*paraO(8)A2/paraO(2)/(paraO( l3)-para0( 14));
dt=para0(28)/para0(27)/tc:
% dimensionless dt
N=para0(26);
de!ta=I/N:
% calculate omega23.6.9 at i+I/2 and i=
for t= I:N-1
tmp2p( t )=t i+C.51A2 “(2'om egat i+ 1.2) "‘omegat i+2.2)/( omegat i+1,2)+omegat i+2.2)));
tmp2mt i )=t i-0.5)A2*(2*omegat i+L2)*omegat i.2)/( omegat i+ L.2)+omegat i.2))):
tmp3pt i )=( t+0.5)A2*( 2*omega( i+1,3)*omega( i+2.3)/(omegat i+1.3)+omegat i-t-2.3))):
tmp3 mt i )=<i-0.5) A2 '( 2'omega( i+ 1J )'omegat i.3)/( omegat i+1.3)+omegat i.3)));
tmp6pt i i=<i+0.5)A2*t 2*omega( i+1.6 )*omegat i+2.6)/< omegat i+1.6 )+omegat t+2.6))):
tmp6mt i )=t i-0.5 )A2*( 2'omegat i+1.6)'omegat i.6)/(omega( i+1.6 )+omegat i.6)));
tmp9p< i i=t i+0.5 )A2*( 2'omegat i+1.9 )*omegat i+2.9)/(omegat i+1.9 )+omegat i+2.9)));
tmp9mt i )=( i-0.5 )A2*( 2'om egat i+1.9)*omega( i.9)/( omegat i+l .9)+omegat i.9)));
tmpt i )=2*iA2*deltaA2:
end
kapat:. I )=omega( 2:N. I ). *tmp2m'./tmp’;
kapat :.2i=omega( 2:N. I ).*tmp3m'./tmp';
kapat:J i=-omegat 2:N. I ). *( tmp2p'+tmp2m')7tmp'- l/dt;
kapat :.4 )=-omega( 2:N. I ). *( tmp3p'+tmp3m')./tmp';
kapat :S )=omega( 2:N. I ).'tmp2p'./tmp';
kapat :.6)=omega(2:N. I ).*tmp3p'./tmp';
kapat :.7)=omega< 2:N. I0)./omega( 2:N.4).'kapat;. I );
kapat :.S)=omegat2:N.5)7omega(2:N.4).*tmp6m'7tmp':
kapat :.9 )=omega( 2:N. 10)7omegat 2:N.4).*kapa( ;.2);
kapat :.10)=omega(2;N. 10)7omega(2:N.4). *t kapat :.3)+ I/dt);
kapat :.I I )=-omega( 2:N3)7omega(2:N.4). *( tmp6p'+tmp6m')7tmp'- I/dt:
kapat ;.I2)=omega(224.10 )7omega( 2.N.4). *kapa( :.4);
kapat -13 )=omega( 2:N. 10)7omega(2:N.4).'kapat :25):
kapat :.I4)=omegat2;N3)7omega(2;N.4).*tmp6p'7tmp';
kapat :.I5)=omega(2:N. I0)7omega(2J4.4).'kapaf :.6);
kapat :.l6)=-omega(2:N.7)7omega(2:N.8).*kapa(:.t);
kapat :.l7)=(tmp9m'7tmp'-omega(2:N.7).*kapac.2))7omega(2:N.8);
k ap a t1 8 )=-omega( 2:N.7)7omega( 2:N.8 ).*f kapat :3>+I/dt);
kapat:. I9)=f-< tmp9p'+unp9m')7tmp’-omegaf 2:N.7).*kapa( :.4))...
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./omegat 2:N.8)-1/dt:
kapa( :.20)=-omegaf2:N.7)./amega(2:N.8)-*kapa(:.5):
kapat :.2l )=(tmp9p'./tmp’-omega(2:N.7).*kapa(:.6))7omega(2:N.8):
B-6 Subfunction 5 —get_kapan
function kapan=get_kapan(omega.para I .paraO)
N'=paruui26).
delta=l/N:
R0=para0(8):
kapant I )=omegat N+1.2 )/2/de!ta:
kapant 2)=omega( N+1.3 )/2/delta;
kapant 3 )=-2*omega( N+1,2)/deita;
kapan(4 )=-2*otnega(N+13)/deIta;
kapant 5 )=3 *omega( N+1.2)/2/deita:
kapant 6 )=3 "omegat N+ i 3 )/2/deIta:
tmp I =-para i (N+1.6) *( 1-para t (N+1. 1) )*paraOt 4)/R0/para I(N+1.8 )/...
tparaOt 11 )-paraO( 10));
tmp2=omega( N+1.6)/deita/R0/para I (N+1.8);
kapant 7)=tmp I *kapant I );
kapant 8 )=tmp2/2:
kapant 9 )=tmp I "kapant 2);
kapant I0)=tmp i "kapant 3);
kapant 11 )=-2*tmp2:
kapant I2)=unpl "kapant 4):
kapant 13)=tmp I *kapant5);
kapant I4)=3*tmp2/2-t-k
kapant I5)=tmp I *kapan(6):
tmp=para I(N+1. 1)*paraO( 8 )*paraO( 16 )*para I (N+1 J)/( I -para I (N+1. 1))/para0(4);
B-7 Subfunction 6 - getjd
function d=get_d(kapa,kapan.N)
% at node 0
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for i=l:3
d(i.i)=-3;
d(i.i-t-3)=4:
d(i.i+6)=-l:
end
9c for the internal nodes
for t=l:N*l
J *—- *‘ *
9c elements for X equation
J2=jl-3:
d(jl.j2)=kapa(i.l):
d(j l.j2+2)=kapa( i.2>:
dtj I .j2+3 )=kapa( i.3);
dtj I .j 2+5 )=kapat i.4):
dtj l.j 2 +6 )=kapa(0 ):
dtj l.j2+8)=kapat i.6);
jl= jl+ l;
9c elements for the T equation
for k= 1:9
dtj 1.j2+k-1)=kapa( t.6+k);
end
j l = jt + l;
9c elements for the P equation
d(jI.j2)=kapati.I6);
dtj I .j2+2)=kapa( i. 17);
dtj I .j2+3 )=kapat i. 18):
dtj I ,j2+5)=kapa( 1. 19);
dtj I .j2+6)=kapat i.20):
dtj I.j2+8)=kapa(i22I);
end
9c at node N
i=3*N+I;
j=3*(N-2)+I:
dti.j)=kapant I):
d(i.j+2)=kapanf2)
d(i.j+3)=fcapan(3)
d( i.j+5)=kapan(4)
d(i.j+6)=kapan(5)
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d( i.j+8 )=kapan( 6):
for k= 1:9
dt i+l.j+k-l i=kapan( 6+k):
end
d(3*(N+l).3*(N+I))=I:
B-8 Function 7 - get_b_2
function [b. phitl=get_b_2(omega.paral.para0.tn.b.phit)
N=para0(26):
bt 5:3:3 *N. t )=b( 5:3:3 *N. I )+phit( 2:N. I )-omega< 2:N. 11 )7omega( 2:N.4)/2:
%
phit=omega( :.l I )./omega( :.4V2:
update «t> term
B-9 Function 8 - get_phi
function phi=get_phi( para 1.paraO)
N=paraO( 26):
JeIta=0.5./( pi/paraO(24 )*( 2*para I (:. 15) ).A0 J . *(11-h para I(:. 16 i7para I(:. 15 )...
).A2) A0.5-t) A0.5):
dx=paraO( 8 )/paraO( 26 );
phi(N+I t=paraO( 25 )/deIta( N +1):
phi( N)=paraO( 25)/delta( N)*exp(-0.5*dx*( l/delta( N+-IH-1 /deltat N))):
fori=I:N-l
phiti)=paraQt25)/delta(0*exp(-Q3*dx*< l/delta( N-t-1 l-rl/delta{i))-...
dx*sumt I ./deltat i+1 :N))):
end
phi=phi’:
B-IO Subfunction 8 - get_pv
function pv=get_pv( xl.tetnp)
c=exp(-9385+3829.1Jternp);
b=c. *f -xI+exp(-7.036 + 1191.2./temp))+2*xI:
a=( -b+{b A2+4*xl.A2.*(c-1 )).A0_5)i(c-1 )JxI/2;
% a< I
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pv0=exp(-7511 J2item p+89.63121+0.02399897*temp-1. 1654551e-5*temp.A2.~.
-1.28l0336e-8*temp.A3+2.0998405e-I I *temp. A4-12 .15079*log( temp)):
pv=a.*pvO*IOOO:
288
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