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Viscosity of Reconstituted Milk Protein Concentrate Solutions as a Function of Shear Temperature and Concentration.

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Dev.Chem. Eng. Mineral Process., 7{1/2),pp.131-139,1999.
Viscosity of Reconstituted Milk Protein
Concentrate Solutions as a Function of
Shear, Temperature and Concentration
S. O’Donnell and F. Butler*
Dept. of Agricultural and Food Engineering, University College
Dublin, Earlsfort Terrace, Dublin 2, Ireland
The viscosity of reconstituted milk protein concentrate solutions was determined at
various shear rates, (50- 1000 s-’ ), temperatures, (20-60°C) and concentrations, (200260 g/kg). For a given temperature and concentration, the solutions were shear
thinning and the effect of shear was adequately described by the Ostwald power law
model. Viscosity increased with concentration and decreased with temperature. The
effect of temperature on the consistency index followed an Arrhenius type
relationship. The effect of concentration on the consistency index was modelled with
both a power and an exponential relationship. The flow behaviour index was
independent of temperature and concentration. The combined effects of shear rate,
temperature and concentration on viscosity were modelled using an extended power
law model.
Introduction
Milk protein concentrate (MPC) is a relatively new product, based on ultrafiltration
and drying of skimmed milk, with a typical protein content from 50-85% of total
solids. Producing MPC is generally based on protein concentration by ultrafiltration
of skim milk using a membrane with a typical molecular weight cut-off of 1OkDa [I].
* Authorf o r correspondence.
131
S.O'Donnell and F.Butler
The product is then pasteurised, followed by final water removal by evaporation and
drying. Depending on the selection of the process parameters, the original properties
of the proteins can be preserved or functional features suitable for specific utilisation
purposes can be formed [2].
A major problem associated with MPC processing is its high viscosity at
concentrations above 2OOgkg of total solution, as the practical limits of its solubility
are approached. As it is a relatively new product, very little has been published on the
viscosity of MPC, particularly at high concentrations. The objectives of this study
were to measure the combined effects of shear rate, temperature and concentration on
the viscosity of MPC at high concentrations and to apply a rheological model which
would adequately predict their combined effects on the viscosity of MPC solutions.
Theory
The Ostwald power law model is commonly used to describe the effect of shear on
the fmal viscosity of a non-Newtonian time independent liquid:
,
n-I
77, = K Y
To adequately model temperature and concentration effects, the consistency
index, K , and the flow behaviour index, n, are not constant, but vary with temperature
and concentration. Several workers [3], [4], have described the temperature
dependency of the consistency index with an Arrhenius type relationship:
K = K, exp(E, / RT)
The effect of concentration on KO can be handled by either a power or an
exponential relationship, [ 5 ] :
132
Viscosity of reconstituted milk protein concentrate solutions
KO = K,C"
(3)
K O = K2e(bc)
(4)
The flow behaviour index is a measure of the shear-thinning property of a
substance. Several workers [4], [ 5 ] , have described the temperature and concentration
dependency of the flow behaviour index with a linear type relationship:
n(T,C) = n + n , C + n T T
To model temperature and concentration effects, equations (l), (2), (3), (4) can be
combined to give two possible extended power law models [ 5 ] :
Experimental
A single batch of commercially available MPC powder was used in all
experiments. Reconstituted MPC powder was used in this study. Sampling and
immediate viscosity measurement of the product during manufacture at a range of
concentrations and temperatures was not technically feasible. The protein content [6],
non-casein nitrogen content [7], lactose content [8], fat content [9] and moisture
content [ 101 of the milk protein concentrate were determined. Each compositional test
was repeated three times.
1 kg MPC solutions were prepared by reconstituting MPC powder with distilled
water to the desired concentration using a Silverson L2R mixer (Silverson Machines
Ltd. Chesham, UK) at a constant temperature of 40°C. Three concentrations were
used, (200, 240, 260 g k g ) . At concentrations above 260 g/kg the mixtures became
133
S. O'Donnell and F. Butler
paste like. The solutions were mixed for 1 1.1 to ensure even dispersion. The solution
was poured into separate 150 mm sample bottles that were then gently shaken in a
water bath at 25°C for 30 min to minimise the amount of air in the solution and then
allowed to equilibrate for a minimum of 30 min undisturbed in the water bath before
viscosity measurement.
A Physica Rheolab MC 100 Rheometer (Physica MeStechnik, Stuttgart, Germany)
was used for all viscosity measurements. A 2 2 cup and bob geometry to D M 53019.1
[ 111 was used, consisting of a 45 mm diameter rotating bob and a 48.8 mm diameter
faed cup. For each test the MPC solution was carefully loaded into the cup so as to
minimise damage to its structure, and the bob was lowered. The sample was allowed
to rest for 15 min before testing. Constant shear rate tests (50, 100,300,500, 1000 s-')
were carried out at various temperatures (20,30,40, 50, 60°C) to examine the effect
of time on the viscosity of the samples. One sample from each 150 mm sample bottle
was used for each combination of shear rate, temperature and concentration. Samples
were sheared for 15 min with viscosity readings recorded every 18 sec. All viscosity
measurements were repeated four times.
Results and Discussion
The MPC powder contained 856 g/kg protein, 28 gikg non casein nitrogen, 47 g/kg
lactose, 16 g/kg fat and 42 g k g moisture. This was typical of commercially produced
h4PC powders [ 1J and was similar to the declared composition by the manufacturer.
The influence of time of shear on viscosity was relatively small, with a maximum
difference of 5.1% between the initial and final viscosity values at 900 s. To eliminate
the effect of time in the rheological modelling, final viscosity values at 900 s were
used in the subsequent analysis.
Figure 1 shows a logarithmic plot of the effect of shear on the final viscosity at
20°C and 60°C.The viscosity of the MPC solutions decreased significantly with
increasing shear. At a given shear rate, viscosity increased with concentration and
decreased with temperature The Ostwald power law model, equation (l), was used to
characterise the variation of viscosity with shear rate at the various temperatures and
134
Viscosiry of reconstituted milk protein concentrate solutions
concentrations. Linear regression of the average results for log of viscosity and the
log of shear rate was used to calculate K and n for each concentration and
temperature. The coefficient of determination for the regressions, R2,varied from
0.9-0.99. In all cases the significance of the regressions was high (P<0.001).
Y
a"
1
..
0.1
..
-
v
.-h
.-gM
>
0.01
10
100
1000
Shear rate (5.')
Figure 1. A comparison of experimental data (points) with the power law modeI
(Equation I ) (lines) for the effect of shear rate on the final viscosity of milk protein
concentrate for concentrations of (g/kg) :0,200; 0, 240; A, 260. -2OOC.
-- -- 60OC.(Data at intermediate temperatures omitted for clarity)
Figure 2 shows the variation of the consistency index with temperature and
concentration. The temperature dependency of the consistency index increased
considerably with concentration. Similar increases in the consistency index values at
high concentrations have been reported for sodium caseinate solutions (>140 gkg)
[ 121, [131, and for whey protein solutions (>500 gkg) [ 141.
Multiple regression was used to determine the Arrhenius parameters (equation
(2)) and the constants for both the power and exponential relationship for the effect of
concentration on KO (equations (3) and (4)). In both cases the multiple regressions
were highly significant (P< 0.001).
Figure 3 shows the variation in the flow behaviour index, n, with temperature and
concentration. No correlation was found between n and concentration or temperature.
135
S, O’Donnell and F. Butler
As a consequence a mean value of n was used in the rheological model, even though
n varied from 0.25-0.71. The variation in n was unexpected but it was subsequently
found that other workers have experienced similar variation [ 121, [ 151.
20
3E:
30
50
40
Temperature
60
e C)
Figure 2. Consistency index as a function of temperaturefor milk protein concentrate
(g/kgl: 0,200; e, 240; A, 260.
-0
-5 0.8
8
2
2
0.6
0.4
.
I
i5
0.2
0
.
30
5
40
50
,
60
Temperature f C)
Figure 3. Behaviour Index as a function of temperaturefor milk protein concentrate
(g/kg): 0,200; e, 240; A, 260.
I34
Viscosity of reconstituted milk protein concentrate solutions
The effects of shear rate, temperature and concentration were modelled using
equations (6), and (7) except that the flow behaviour index value used was a mean
value. The method of calculating the sum of the residual squares (R.S.S.) [4]
determined which model provided the best fit to the experimental results. Equation
(6) (R.S.S.= 97), where the effect of concentration on
was modelled by a power
relationship, provided a better fit to the data than equation (7) (R.S.S.= 490). The
resulting parameters using the power law relationship was:
(y)
(0.451)-1
77,= 7.6 10".c~.~'.e
*Y
lo
T
A
10
100
1000
S h e a r rate, 11s
Figure 4. A comparison of experimental results (points) with predicted extended
power law model (Equation 8) (solid lines) for a concentration of 260 (g/kg)over a
temperature range PC) : 0 , 20; a,30; U,40; I.,50; A, 60.
Figure 4 compares experimental final viscosity values with predicted results
obtained using equation (8). The model tended to underestimate the viscosity values
at the lowest concentration of 2OOgkg and overestimate the viscosity values at the
higher concentrations of 240g/kg and 260gkg. In general the model's predictive
I37
S. O'Donnell and F. Butler
ability improved with increasing temperature. The worst error was 180%' which
occurred at a concentration of 260 g k g and a temperature of 20°C. At these
conditions the measured viscosity was at its highest. This illustrates the lhitations in
using a mean value for n in the model and in applying such a viscosity model where
the liquid is close to becoming paste like. At other concentrations and temperatures
the error was much lower (30 - 40%). The model was effectively built up step-wise,
allowing for shear rate, temperature and concentration. Consequently errors
introduced at each step were cumulated. This should be taken into account when
judging the model's predictive ability.
Conclusion
The viscosity of MPC solutions varied significantly with shear, temperature and
concentration. A modified power law equation fitted the viscosity data but caution
has to be exercised in its use at high concentrations and ambient temperatures when
the error between predicted and actual viscosity was as high as 180%. Generally the
-
error was lower (30 40%). The viscosity of MPC solutions increased dramatically
above concentrations of 200gikg. From a processing/flow perspective, a
concentration of 240 - 260 g/kg is suggested as a practicaI limit. The use of elevated
temperatures (50 - 60°C)would help to reduce viscosity significantly.
Acknowledgement
This work was financed by E.U. structural funds money.
Nomenclature
a
Power index in equation (3).
b
Exponential index in equation (4).
c
Concentration
(kgfl<g)
Ea
Activation energy
(Jkg mole)
K
Consistency index
(Pa s")
138
Viscosity of reconstituted milk protein concentrate solutions
KO
Constant of proportionality in equation (2)
(Pa s")
K,
Constant of proportionality in equation (3)
(Pa s")
K2
Constant of proportionality in equation (4)
(Pa s")
n
Flow behaviour index
nc
Constant of proportionality for concentration in equation (5).
nT
Constant of proportionality for temperature in equation ( 5 ) .
(TI)
R
Gas constant
(Jkg mole K)
T
Temperature
(K)
11,
Final viscosity
(Pa s)
Y
Shear rate
(s-')
References
1. Zwijgers, A. 1992. Outline of milk protein concentrate. De Mekindustrie Veghel
technical bulletin.
2. Novak, A. 1993. New applications of membrane processes: Milk protein
concentrates. Bulletin of IDF No. 920 1,5 1-65.
3. Cervone, N.W., and Harper, J. M. 1978. Viscosity of an intermediate moisture
dough. J. Food Process Eng., 2,83-95.
4. Verges, B., and Villemaire, J.P. 1987. Rheological behaviour of low moisture
molten maize starch. Rheologica Acta, 26, 570-576.
5 . Harrod, M. 1989. Modelling of flow properties of starch pastes prepared by
different procedures. J. Food Process Eng., 11,257 - 275.
6. IS0 5549. 1978. Method for the determination of the protein content in casein.
7. IDF 29. 1964. Method for the determination of non-casein nitrogen in casein.
8. IS0 5548. 1980. Method for the determination of the lactose content of casein.
9. IDF 1A. 1969. Method for the determination of the fat content in casein.
10.I S 0 5550. 1978. Method for the determination of the water content in casein.
11. DIN 53019.1. 1980. Viscometry; Determination of viscosities and flow curves
using standard design rotary viscometers with a standard geometry measuring
system.
12. Hermansson, A.M. 1975. Functional properties of proteins for foods: flow
properties. 3. Texture Studies, 5,425-439.
13.Fichtali, J. 1993. A rheological model for sodium caseinate. J. Food Eng., 19,
203-2 1 1.
14.Alizadehfard, M. R. & Wiley, D. E. 1996. Non-Newtonian behaviour of whey
protein solutions. J. Dairy Research, 63,3 15-320.
15. Hernandez, E. 1995. Viscosity changes in orange juice after ultrafiltration and
evaporation. J. Food Eng., 25, 387-396.
139
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