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Use of Sorption Isotherms for the Estimation of Shelf Life of Two Zimbabwean Flours.

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Dev. Chem. Eng. Mineral Process. 13(1/2), pp. 79-90, 2005.
Use of Sorption Isotherms for the
Estimation of Shelf Life of Two
Zimbabwean Flours
D.I.O. Ikhu-Ornoregbe’* and X.D. Chen’
School of Chemical Engineering, University of KwaZulu-Natal,
Durban, 4041, South Africa
Department of Chemical and Materials Engineering,
University of Auckland, Private Bag 92019, Auckland, New Zealand
The water sorption characteristics of two Zimbabwean flours, i,e. maize-meal and
millet, were obtained using the gravimetric method at temperatures of 20, 30 and
4OoC. The GAB, BET and the modified BET models were found to describe the data
reasonably well. The heat of sorption, which varied from 1.915 kJ.mot’ at 20%
moisture content to 30.5 kJmot’ at I% moisture content dry-basis was calculated
for the maize meal. Similar values for the millet were found to vary from
1.87 kJ.mot’at 20% moisture content to 18.3 kJ.mot’ at 1% moisture content. The
shelf lives for both materials were estimated from the sorption data, and
recommendations on packaging and storage conditions are suggested.
Introduction
A moisture sorption isotherm equation is used to describe mathematically the
relationship between the activity (aw)and the equilibrium moisture content of a
food product. Moisture sorption isotherms are used for a number of purposes in
food research [ 11. These include calculations for drylng time, ingredient mixing and
packaging predictions, modeling moisture changes that occur during storage, and
prediction of shelf-life stability [2]. They also provide fimdamental information
about specific interactions between water and the product, since that directly relates
the thermodynamic potential (or Gibbs free energy) of water in the system to
its mass fraction. Related thermodynamic properties such as the heat of sorption, as
* Author for correspondence (ikhuomoregbe@ukzn.ac,za).
79
D.I. 0.Ikhu-Omoregbe and X.D. Chen
well as information on the structure of the product (e.g. specific surface area, pore
volume, and crystallinity in some cases), can also be derived [3].
A useful method of presenting food isotherms is through the use of isotherm
equations, where the constants of the equations can be tabulated for each food
isotherm. However, it is sometimes argued that the validity of a sorption model
cannot be proved by its ability to fit observed data; a physico-chemical basis is also
needed [4]. For most food products these water sorption isotherms have a sigmoid
shape and give an impression of how strongly the water is bound by the product.
For fresh, or very moist food substances, the water present exerts a vapour pressure
nearly equivalent to that of pure water, that is unity [ 11. This vapour pressure value
is maintained until the moisture content of the food decreases to approximately
22%, below whch the vapour pressure begins to decrease. The changes of vapour
pressure with atmospheric humidity results in the characteristic sigmoid and other
shapes of water sorption isotherms [ 5 , 6 ] .
The sorption of water molecules on polar groups of drying food-solid is also a
process of localised physical gas adsorption on an initially rigid adsorbent. The
formed hydrogen bonds are responsible for a major part of the interaction energy.
However, other interactions are also involved. Water is a platicizer for the structure
of food solids and upon increasing sorption, a food system gradually gains the
nature of a polymer solution in which available small molecules are dissolved. The
structure is plasticized at water contents above one water molecule per site, i.e. the
polymer chains become flexible by undergoing a rubber-glass transition. At
increasing water contents, i.e. three water molecules per site, the system becomes a
polymer solution. This is shown by the sigmoid shape of the sorption isotherm [7].
A number of empirical, semi-empiricaland theoretical models have been derived
for the correlation of water sorption in food substances. Among these, the threeparameter Guggenheim-Anderson-de Boer (GAB), Brunauer, Emmet and Teller
(BET) and modified-BET equations have been found to be more popular and
reliable [3, 8-10]. They are widely used in determining monolayer moisture values
and specific surface areas of sorbent materials. Whereas the GAB equation is found
applicable over a wide range of a, values, the BET is applicable at low a,
(aw < 0.43) and the modified-BET gives a good fit at a, less than 0.75.
This paper presents data for the sorption characteristics at three temperatures for
maize meal and millet flour obtained in Zimbabwe, and the results of the
application of the sorption models to the data. In most Southern African countries,
maize meal serves as the main staple food for the greater number of the local
population. Although millet is not used as a stapIe food in Zimbabwe, it finds
extensive use as an animal feed-supplement. Hence it is widely cultivated
throughout the country. The shelf-life of these substances will depend upon its
storage temperature, relative humidity (RH), and hence the water activity (aw).The
observed shelf-life is usually less than 10-12 weeks, after which time they start to
deteriorate. These being very important food materials, cheap and effective methods
of storage are essential. Therefore, it is beneficial to know how these materials will
store in different humidity conditions. This information, as well as theoretical shelflife values, can be deduced from the sorption isotherms. Furthermore, the binding
energy or excess heat of sorption can be calculated from these data.
80
Sorption Isotherms for the Estimation of ShelfLife of Two Zimbabwean Flours
Adsorption Models Tested
a
The GAB model
The GAB equation has been claimed to provide the best equation for the description
of food isotherms up to a, of 0.9 [ 111, and was also adopted by the EEC-COST 90
Group on water activity [12]. The transformed GAB may be written as:
a
X
x=
a a t + p a w+ y
where a = “[k-l];
p
1
xm
X is percentage water content on dry basis, X,,, is water content corresponding to
occupation of all primary adsorption sites by one water molecule ( X , is also called
the ‘monolayer’ moisture); C and K are GAB constants that are temperature
dependent and related to the energies of interaction between the first and further
molecules at the individual sorption sites; C is a constant, (also referred to as the
Guggenheim constant), and K is correction factor for the multilayer molecules. The
coefficients a, p and y of the GAB model were determined for each temperature
using non-linear regression as recommended by Schar and Ruegg [9], and the
values of the GAB constants (X,,,, C and K ) were also calculated.
b.
The BET model
The well-known BET sorption isotherm given below is applicable at low a, values,
and was also tested:
where C is a constant related to the net heat of sorption.
c.
ModifiedBET model
The BET equation can be modified to give another equation, which is found
applicable for a, up to 0.75, and can be written as:
The fitting confidence was judged by the relative root mean square error (% RMS),
defined [ 121 as:
D.I.O. Ikhu-Omoregbe and X.D. Chen
(
c x1;,xq2
%RMS
=
N
x 100
(4)
where N is the number of experimental points; X,is the experimental value of water
content; and Ni* is the calculated water content value.
Moisture-Binding Energy
The water activity of a food substance is known to be a function of temperature,
hence it is important to quantify the effect of temperature on its sorption isotherm.
Temperature affects the mobility of water molecules, and the equilibrium between
the vapour and adsorbed phases. An increase in temperature, at constant water
activity, results in a decrease in the amount of adsorbed water [13]. However,
certain sugars and low-molecular-weight food constituents, which undergo glasstransition and crystallization, dissolve in water, and become more hygroscopic at
higher temperatures, are exception to th~srule.
The level of moisture content at which the heat of sorption approaches the heat
of vapourisation of pure water is often taken as indicative of the amount of “bound”
water existing in the food [14]. Knowledge of the heat of sorption is important for
dqmg process equipment design. This is because heat of vapourisation of sorbed
water may increase to values above the heat of vapourisation of pure water as food
is dehydrated to their low moisture levels [ 151.
The binding energy is defined as the difference between the isosteric heat of
water sorption by the solid substrate and the condensation heat of water vapour at
the same temperature. The relationship between activity and temperature can be
described by the Clausius-Clapeyron equation:
where AI& is the binding energy or the excess heat of sorption.
Materials and Method
In Zimbabwe, maize meal is produced by milling dried corn grains, in most cases
without complete dehusking of the grains. Complete dehusking is only carried out
in large factories that produce fine and ultra-fine flours, which are always
comparatively very expensive. Thus the majority of the people obtain their maize
meal from small millers who do not normally dehusk the grains.
82
Sorption Isothermsfor the Estimation of Shelf Lge of Two Zimbabwean Flours
Maize meal milled in a local mill in Bulawayo was used for this study. Millet
grains were obtained from a local market and milled into powder in the laboratory,
and sieved to obtain a uniform size range for the study. A sieved-size range of
+700 pm to -1400 pm was collected for both materials used for the sorption
isotherm determination. The sorption isotherms of these materials were measured at
20, 30 and 40°C using a standard gravimetric method, as recommended by the
COST 90 project, with thermally stabilized desiccators (16). The temperature of the
desiccators was maintained by placing them in a thermostatically controlled water
bath set at the required temperature. The desiccators contained saturated salt
solutions that create a known relative humidity in the surrounding atmosphere [ 173.
The saturated salt solutions used in this study are LiC1, CH3COOK, MgC12, K2C03,
NaBr, CuClZ,NaCl, (NH4)2S04 and KN03 with corresponding water activities of
0.1 1,0.23, 0.33,0.43,0.57,0.67,0.75,0.80 and 0.93 respectively [18].
The materials were first dned over P205for a period of about 2 weeks to ensure
that they were very dry, and all at the same initial moisture content. About 2-gram
portions of the material (in triplicates) were placed on watch-glasses, and exposed
to the different humidities in the desiccators. In order to prevent mould growth at
high a, values, 0.25% of sodium azide was applied to the samples. The weights of
the samples were determined at 2-day intervals until stable constant weights were
obtained. The time interval for the removal, weighng and replacing in the
desiccators of a sample, was less than one minute each time in order to minimise
any effect of opening the desiccators on the results. Each experiment was run for
about two days. The moisture content of the equilibrated samples was determined
by drylng each sample in an oven at 1 10°C for between 16 and 24 hours. The
samples were then cooled over silica gel before the final weights were taken.
Results and Discussion
(0 Adsorption isotherms
The sigmoid characteristic curves of the isotherms were obtained for both materials
shown in Figures 1 and 2. Figure 3 compares the isotherms for the two materials
and indicates that both substances show a similar pattern. The estimated parameters
of GAB, BET and modified-BET equations, as obtained by nonlinear regression for
both the maize-meal and millet, are shown in Tables 1 and 2 respectively. The
results show that these equations describe the moisture sorption isotherms of both
materials reasonably well, as shown by the values of correlation coefficients and the
root mean square error (%RMS). The monolayer moisture content (A',,,) obtained
from the GAB analysis (see Tables 1 and 2) at the three temperatures of both
materials do not appear to be significantly different, and they are similar to values
obtained for starchy foods [19]. The monolayer value decreases with increasing
temperature, and is also a function of the particular model used for its estimation.
However, the equations correlate the maize meal better than the millet flour within
the water activity range in which the particular model is said to be valid. For the
maize meal, the monolayer values ranged from 5.45 to 6.27 g.HzO/lOO g solids for
the GAB model, 3.37 to 3.49 g.H20/100 g solids for the BET model and 7.76 to
7.94 g.HzO/lOO g solids for the modified-BET. The corresponding monolayer
83
D.I.O. Ikhu-Omoregbeand X.D. Chen
values for millet ranged from 4.52 to 4.74 g. H20/100g solids for the GAB model,
from 3.40 to 3.62 g. H20/100g solids for the BET model, and from 9.37 to 11.92
g. H20/100g solids for the modified-BET. These values are similar to those in the
literature [6, 19-23].
Comparison of these three models for both materials indicates that the modifiedBET model gave the highest monolayer moisture estimates, followed by the GAB
model, and then the BET equation. However, the BET gave a rather high relative
root mean square error (%RMS) suggesting a poorer fit in both cases, over the
water activity range for which it is applicable.
-
20c
30C
40C
I
I
0
0.2
0.4
0.6
0.8
1
Water activity (aw )
Figure 1. Adsorption isothermsfor maize meal at three temperatures.
P
'0
B.
ON
2 -
M "
~2
30
-
20 25
-2CC
-3oc
-4%
15-
c s
3
3
f
'
.-I
105 O T
Figure 2. Adsorption isothermsfor millet at three temperatures.
84
Sorption Isothermsfor the Estimation of SheIfLve of Two Zimbabwean Flours
0
--C
Maize meal
-m-
Millet
0.2
0.4
0.6
Water activity, a,
0.8
1
Figure 3. Comparison of the adsorption isotherms of the two materials at 30'C.
Table 1. Estimated parameters for the GAB, BET, and modi3ed-BET models for
maize meal.
~
Model
tested
Fitting
range
Monolayer
Moisture
(aw!
x
4
4
Constant
C
Correction
factor
K
Correlation
coefficient
0.77
0.85
0.87
0.990
0.979
0.969
0.843
1.300
1.830
YdMS
J
k H@/
I00 g soIid)
GAB
20°C
30°C
40°C
0 - 0.93
BET
20°C
30°C
40°C
0 - 0.43
ModGedBET
20°C
30°C
40°C
6.27
5.72
5.45
20.85
41.17
48.79
3.38
3.49
3.37
6.08
5.08
5.48
0.990
0.984
0.983
26.97
28.79
27.92
7.80
7.94
7.66
11.55
11.93
24.67
0.994
0.996
0.992
1.11
1.78
9.57
0 - 0.75
a
85
D.I.O. Ikhu-Omoregbe a n d X D . Chen
Table 2. Estimated parameters for the GAB. BET, and modified-BET models for
millet.
Model
tested
Fitting
range,
fad
Constant
C
Correction
jactor
K
Correlation
coefficient
6.44
6.52
7.09
6.34
9.10
7.75
0.70
0.66
0.64
0.995
0.997
0.997
11.532
8.692
6.743
3.82
3.74
3.63
4.82
5.13
4.44
0.983
0.978
0.987
3 1.02
28.81
30.32
10.30
10.74
10.43
6.99
5.13
5.78
0.993
0.978
0.998
3 1.02
28.81
24.42
Monolayer
Moisture
XM
Y6MS
J
(g H20/
I00 g solid)
GAB
20°C
30°C
40°C
0 - 0.93
BET
20°C
30°C
40°C
0 - 0.43
ModrfiedBET
20°C
30°C
40°C
0 - 0.75
Moisture-binding energy results
From Equation (5), plots of In(a,) vs (1/T) at different moisture contents can be
considered as straight lines, whose slopes yield AH& which can be calculated by
regression analysis [24]. Figures 4 and 5 are the plots of excess heat of sorption for
both materials obtained by such analysis. The values obtained varied from
1.91 kJ.gmo1-' at 20% moisture content to 30.5 ki.gmo1' at moisture content of 1%
(dry basis) for maize meal. The values obtained for millet varied from 1.87 kJ.mo1'
at 20% moisture content to 18.3 kJ.mol-' at 1% moisture content (dry basis). This
shows that the process of water sorption by both materials is endothermic. Chuzel
and Zakhia [25] observed that when the soluble fractions of gari starch undergoes
collapse and leaches out, the sorption phenomenon becomes endothermic rather
than the usual exothermic behaviour found in sorption theory. The monolayer
concept is also very relevant to physical and chemical deterioration of dehydrated
foods, such as lipids, enzyme activity, non-enzymic browning reactions, aroma
retention and textural characteristics [26, 271. Furthermore, Iglesias and Chirife [28]
explained that as more water is adsorbed there is a decrease in sorption energy due
to reduced activity at the sorption sites. The results also suggest that the maize meal
has a greater interaction energy at the sorption sites compared to the millet flour.
This is supported by the observation that the millet is more powdery (less
hygroscopic) compared to the maize meal.
86
Sorption Isotherms for the Estimation of ShelfLife of Two Zimbabwean Flours
-
35
'a,
0
5
10
I5
20
25
Moisture content (g H,0/100 g dry solids)
Figure 4. Excess heat of sorption of maize meal as a function of moisture content
i
5
35 'I
30
1
1
0
I
5
10
15
20
25
Moisture content (g H20/100g dry solids)
Figure 5. Excess heat of sorption of milletflour as a function of moisture content.
Application of a,,,to shelf-life estimation
The establishment of the sorption isotherm of a packaged food can aid in the
estimation of shelf-life for a given storage condition. The model of Heiss and
Eichner [29] can be used to estimate the potential storage time based on a critical a,
for a particular system under given storage conditions. This model is based on the
assumption that water sorption vapour is the determining factor, as well as the
presence of spoilage bacteria, oxygen and light, in limiting shelf-life. Also, it is
assumed that moisture diffuses through the package material from the surrounding
atmosphere to the material inside. The equation is given as:
87
D.I.O. Ikhu-Omoregbe and X D . Chen
where Ks is the permeability of the package to moisture vapour (kg.m-'.Pa.-'.day-' );
ts is potential shelf life of product (time in days for the packaged product to spoil
due to microbial and biochemical deterioration with loss of sensory quality); A is
surface area of package (m'); Wsis weight of the product (dry matter, kg); Po is the
vapour pressure at storage temperature; S is slope of the products isotherm
X , is equilibrium moisture content; X, is
(assumed linear over the range X, and Xc);
safe storage moisture content; Xi is initial moisture content of material when
packaged (kg.kg-' dry basis).
The shelf-life of packaged maize-meal in 5-kg polyethylene bags (A = 0.266 m-';
Ks = 2.28 x1Os6 kg H20.m-'.Pa*'.day-') was estimated at the three temperatures
(2OoC, 3OoC, 4OoC). In Zimbabwe, the average temperature is between 2OoC and
25OC and the relative humidity rarely exceeds 80%. The theoretical shelf-life
estimated for different initial moisture contents are shown in Tables 3 and 4. A safe
storage water activity of 0.7, which is generally used for most products [25], was
assumed. Thus at these conditions for low-cost storage of at least three months
shelf-life, an initial moisture content of 8% for maize meal and 5% for millet using
polyethylene materials is recommended. Polyethylene material was chosen because
of its lower cost compared to the more expensive polypropylene, which also has a
lower permeability to water vapour and oxygen. In this paper attention was directed
only to permeability of water vapour to polyethylene, however, it should be noted
that it is also permeable to oxygen and carbon dioxide, which can cause oxidation
and hence deterioration.
Table 3. Estimated shelf-life (days)for safe storage at a, of 0.7 at different initial
moisture content (dty basis)for the maize meal.
12
14
16
Table 4. Estimated shelf-life (days)for safe storage at a, of 0.7 at different initial
moisture content (dry basis)for the millet.
content, % d.b.)
88
(at 2OoC
(at 3OoC)
(at 4OoC
Sorption Isothermsfor the Estimation of Shelf Life of Two Zimbabwean Flours
Conclusions
The sorption isotherms of maize-meal and millet flour were measured at three
temperatures (2OoC, 3OoC and 4OoC) using the conventional gravimetric method.
The results show that the sigmoid characteristic curves of sorption isotherms were
obtained as expected. The data obtained were well described by the three models
tested. The monolayer water content value was found to decrease with increasing
temperature, and is also a function of the particular model used for its estimation.
The modified-BET equation gave the highest estimates for monolayer moisture,
followed by the GAB equation, and then the BET equation. The BET was found to
give a rather high %RMS, suggesting a poorer fit for both materials. Excess heat of
sorption values varied from 30.5 kJ.mo1' at 1% to 1.91 kl.mol-' at 20% moisture
(dry basis) for maize meal. For the millet, the values ranged from 18.3 kJ.mol-' at
1% moisture content to 1.87 kJ.mor' moisture content (dry basis). A theoretical
estimation of the shelf-life for both materials shows that low-cost storage of at least
three months can be obtained using 5-kg polyethylene bags, with the material
having a moisture content of 8% for the maize meal and 5% for millet flour.
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