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Mass transfer properties of osmotic
solutions. I. Water activity and osmotic
pressure
a
b
c
Vassilis Gekas , Chelo Gonzalez , Alberto Sereno , Amparo
b
Chiralt & Pedro Fito
a
b
Food Engineering, Lund University, Lund, Sweden
b
Universidad Politecnica de Valencia, Valencia, Spain
c
Escola Superior de Biotecnologia, Oporto, Portugal
Available online: 02 Sep 2009
To cite this article: Vassilis Gekas, Chelo Gonzalez, Alberto Sereno, Amparo Chiralt & Pedro Fito
(1998): Mass transfer properties of osmotic solutions. I. Water activity and osmotic pressure,
International Journal of Food Properties, 1:2, 95-112
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INTERNATIONAL JOURNAL OF FOOD PROPERTIES, 1(2), 95-112 (1998)
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MASS TRANSFER PROPERTIES OF OSMOTIC SOLUTIONS. I. WATER
ACTIVITY AND OSMOTIC PRESSURE
Vassilis Gekas1'*, Chelo Gonzalez2, Alberto Sereno3, Amparo Chiralt2, and Pedro
Fito2
1
2
3
Food Engineering, Lund University, Lund, Sweden
Universidad Politecnica de Valencia, Valencia, Spain
Escola Superior de Biotecnologia, Oporto, Portugal. *Corresponding author
ABSTRACT
In this review paper data on water activity, solute activity and osmotic pressure of"
binary and multi-component osmotic solutions are provided. The Characteristics of the
osmotic solutions are needed for the optimization of mass transfer during osmotic
process, and for the improvement of final product quality. The vant Hoff equation and
Gibbs Duhem theorem are commonly used to estimate osmotic pressure and solute
activity. Water activities can be easily estimated through experimental determination of
the freezing point depression. The possibilities of the group contribution models such
as the Analytical Solution of Groups (ASOG) approach are also explored. The future
needs especially in the case of multicomponent solutions consisting of electrolyte and
non-electrolyte mixtures are pointed out.
INTRODUCTION
A number of food processing unit operations imply immersion of the food in a high
osmotic pressure medium containing sugars, such as sucrose, glucose, fructose, syrups
and salts, such as sodium chloride or their mixtures. Foods that are treated this way are
fruits and vegetables or also meat and fish (Fito et al., 1994; Lazarides, 1994; Lenart
and Flink 1984a, 1984b; Lenart, 1994; Lerici et al., 1985). The aims of the osmotic
process are: partial dehydration before the final treatment such as drying or freezing,
impregnation of solute to improve quality (i.e., cryoprotectant), osmo-freezing or
thawing directly in an osmotic medium, and direct formulation of food products.
95
Copyright © 1998 by Marcel Dekker, Inc.
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96
GEKAS ET AL.
Research on the above topics so far has shown that the performance of the
osmotic unit operations depends on the properties of the osmotic solutions used. From
the mass transfer point of view the most important osmotic solution parameter is its
water activity lowering capacity in terms of water activity or osmotic pressure- this is
an important property for the purpose of dehydration. Due to the simultaneous mass
transfer, i.e. water transport from the food to the osmotic medium and solute transport
from the osmotic medium to the food, additional information on the solute size and
solute activities are also important.
A literature review has shown that so far the properties of the osmotic solution
considered in order to interprete the unit operations results were solute concentration
and only in a few cases there has been reported solution water activity data and to the
authors' knowledge there is absent of osmotic pressure data or solute activity data. It is
also known that concentrated solutions used in osmosis are real solutions which might
deviate strongly from the ideal situations, thus activities in addition to concentrations
should provide a more sound theoretical basis for the characterization of the osmotic
solutions and better interpretation of the osmotic process.
Commonly used osmotic solutions, based on FSTA database 1969-1996 are
presented in Table 1. As it is shown, a common osmotic medium used especially for
fruits is the sucrose solution or syrup of a concentration range of 40-70 Brix and most
frequently used one is 60 Brix. Other sugars such as glucose, fructose, lactose have also
been used. Various Dextrose Equivalent (DE) corn syrups have been used for fruits and
vegetables whereas for potato, fish and meat, salt solutions (NaCl 15% are being the
most common among them) were the preferred media. In a few cases a combination
between a sugar(s) and a salt was used.
The objective of this paper is to review data of water activity and their
prediction models for binary and multi-component osmotic solutions commonly used
for osmotic dehydration of fruits.
A. PUBLISED EXPERIMENTAL DATA ON WATER ACTIVITIES.
In Table 2 there are shown values of freezing point depression for various osmotic
solutions obtained at our laboratory of Lund University. For comparison litterature
values are also presented. In Table 3 the values of water activity of the same solutions
as in Table 2 are presented along with the litterature values for comparison. Table 4
shows water activity values of glycerol solutions along with refractive index values of
this solutions (Rizvi, 1995). Table 5 contains water activity values of NaCl from
Chirife and Resnik (1984). Tables 6 and 7 provide literature data of osmosities and
water activity of sugar and electrolyte solutions.
B. METHODS OF MEASUREMENT
Freezing Point Depression
Different methods of water activity measurement are reviewed by Labuza (1984), Rizvi
(1995), and Rahman (1995). It is common and simple to measure water activity (or
osmotic pressure) of two-component and three-component osmotic solution using
OSMOTIC SOLUTIONS. I
97
Table 1. Osmotic solutions commonly used in osmosis
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Solution Type Concentration & temperature Types of foods
BINARY
Sucrose
40-70B, 30-70°C
Apple, pineapple, carrot, kiwi, grapes,
mushroom, papaya, coconut.
Glucose
40-60 B, 25-40°C
Strawberries, plum, pineapple, apple, pear,
cherry, apricot, carrot
Glyserole
10/25%, 5°C
Strawberries
NaCl
8-25% , 8-40°C
Potato, okra, pepper, carrot, aubergine,
green beans, meat, fish
MULTICOMPONENT
Sucrose + NaCl
45 % - 15%
or 50%-10%
20-40°C
Sucrose +Xylitol
30% + 70%
Corn syrup solids
34-70%,
DE10-40
35-55°C
Corn Syrup / Sucrose/Water 5/3/1, 70B
Potato, apple, pineapple
Vegetables
Papaya, apple, some vegetables
Cherries
Table 2. Freezing point depression of sugars (Gonzalez et al., 1995)
Solution type
Fructose 30%
Sucrose 50%
Sucrose 52%
Sucrose 60%
Sucrose 60% + NaCl 10%
Measured values
in the authors's laboratory
Mean
-4.84
-4.79
-4.75
-7.24
-7.64
-7.54
-7.64
-8.97
-8.87
-8.92
-12.30
-12.90
-12.70
-12.90
-28.54
-28.14
-28.34
Litterature values
-4.70
-7.61
-8.40
-12.45
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GEKAS ET AL.
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Table 3. Water activity measured in the authors' laboratory and the litterature
values
Solution
Fructose 30%
From measured values
0.955
Sucrose 50%
0.930
Sucrose 52%
0.918
Sucrose 60%
0.882
Sucrose 60% + NaCl 10%
0.757
(a) From Ferro-Fontan-Chirife Equation
(b) Measured by electric hygrometer
(c) From Caurie model
From litterature values
0.954 (a)
0.961 (b)
0.929 (a)
0.922 (a)
0.874 (a)
0.751 (c)
Table 4. Water activity of glycerol solutions (Rizvi, 1995)
Concentration
(kg/L)
0.2315
0.3789
0.4973
0.5923
0.6751
0.7474
0.8139
0.9285
0.9760
Refractive Index
1.3463
1.3560
1.3602
1.3773
1.3905
1.4015
1.4109
1.4191
1.4264
1.4387
1.4440
1.4529
Water Activity
0.98
0.96
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.55
0.50
0.40
OSMOTIC SOLUTIONS. I
99
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Table 5. Water activity of NaCl solutions1"2
Concentration
(%, w/w)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
9.0
1
2
a
Water Activity
0.997
0.994
0.991
0.989
0.986
0.983
0.980
0.977
0.973
0.970
0.967
0.964
0.960
0.957
0.954
0.950
0.943
Concentration
(%, w/w)
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Water Activity
0.935
0.927
0.919
0.911
0.902
0.892
0.883
0.873
0.862
0.851
0.839
0.827
0.815
0.802
0.788
0.774
0.759"
In the temperature range 15-5O°C
Data source Chirife and Resnik (1984)
Saturation point
freezing point depression method. The solutions were immersed in an ethanol
thermostatized bath, kept at a temperature of approximately -46 °C (Lerici et al.,
1983). The solutions were vigorously agitated in order to avoid external resistances in
heat transfer. Agitation was found very important and also the ethanol temperature to
be kept at least 30 degrees below the freezing point (FP) of the solution. To" obtain
water activities from freezing point depression values three alternative equations were
used i.e. one for ideal solutions, secondly one for real ones, and lastly a numerical
approximation of the equation for real solutions suggested by Ferro-Fontan and Chirife.
The differences between the second and third case were minimal. The equation for the
real solutions is:
- l n a w = L m AT/(RTT o )
(7)
The equation of Ferro-Fontan and Chirife (1981):
- In a w = 9.9693 E-3 (To - T) + 4.761 E-6 (To - T) 2
(8)
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GEKAS ET AL.
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Table 6. Osmosities1 and water activities of other sugar solutions (Wolf et al.,
1974)
Concentration
(%, w/w)
6
8
10
12
14
16
18
20
22
24
26
28
30
Glucose
Fructose
Lactose
0.194
0.266
0.361
0.422
0.506
0.594
0.687
0.785
0.892
1.007
1.124
1.244
1.369
0.192
0.263
0.338
0.417
0.500
0.587
0.677
0.769
0.887
0.993
1.100
1.205
0.103 0.996
0.143 0.995
0.993
0.991
0.988
0.987
0.984
0.981
0.978
0.973
0.969
0.965
0.962
0.957
0.953
0.933
0.991
0.989
0.987
0.984
0.982
0.981
0.979
0.970
0.966
0.962
0.960
1
Osmolality or Osmosity is the molar concentration of the isoosmotic NaCl solution,
i.e. the solution of equal water activity or osmotic pressure or freezing point as the ones
of the given solution
Table 7. Solute activities of salts (Vanysek, 1994)
Molality
0.001
0.005
0.01
0.05
0.1
0.2
0.5
1
2
5
10
NaCl1
0.965
0.928
0.903
0.822
0.779
0.734
0.681
0.657
0.668
0.874
KC1
0.965
0.927
0.901
0.816
0.768
0.717
0.649
0.604
0.573
0.593
CaCl2
0.888
0.787
0.727
0.577
0.517
0.469
0.444
0.495
0.784
0.591
0.431
K 2 SO 4
0.885
0.772
0.704
0.511
0.424
0.343
0.251
Na2S04
0.886
0.777
0.712
0.529
0.446
0.366
0.268
0.204
0.155
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OSMOTIC SOLUTIONS. I
101
where a w is water activity, L m the molar latent heat of freezing of the pure water and
AT =To - T the freezing depression value of the solution.
A good agreement with water activities (effective concentrations) measured
using the freezing point depression method and with textbook values for both sucrose
and NaCl solutions was also found recently by Chen et al. (1996). Other measuring
methods are: standardized solutions (Dora and Favetto, 1988), vapor pressure
measurement, hygrometric instruments (especially the electrical hygrometer), isopiestic
transfer measurement, and suction potential.
Details of the various methods are discussed by Rizvi (1995), Rahman (1995),
Trailer (1983), Uedaira and Uedaira (1969). There is no single method to be a good
choice for all applications. The freezing point depression method has chosen for
osmotic solutions based on its preference by the researchers working in the field
(Marcotte and Le Maguer, 1991; Lerici et al., 1983 ).
C. AVAILABLE MODELS FOR WATER ACTTVITIES
Water Activity
Models for water activity of solutions in general were recently reviewed by Rahman
(1995) and Gonzalez et al (1996). A number of the models used for the prediction of
water activities are shown in Table 8. Some of the models make use of the concept of
the activity coefficient, such as the Norrish, the Margules and the Crapiste ones.
Others, such as Chen and Schwarzberg provide a direct correction of Raoult's law
which is valid for ideal solutions. The nonideality of the solutions are due to: solute
size, intermolecular forces, solvation effects, solute-solute interaction, solute-solvent
interaction, dissociation effects of ionic solutes, order of mixing (Rahman, 1995).
Flory and Huggins (1941), as cited by Rahman (1995), were the first to express
non-ideality due to size differences between solute and solvent. Lilley and Sutton
(1991) combined the effects of size, solvation and solute-solute interaction in one
equation. In the absence of heterotactic interactions their model reduce to the well
known multicomponent Ross equation (Rahman, 1995). The order of mixing was
found to play a negligible role as mentioned by Bonne and Shannon (1991).
Osmotic Pressure
For osmotic pressure the non simplified vant Hoff equation can be used. Thus osmotic
pressure is another way of expressing water activity of a solution. Plant physiologists
are users of the components of the "water potential" in units of pressure. The
relationship between water activity and osmotic pressure is shown in Figure 2. The
non simplified Van't Hoff equation is as follows:
lna w
where Vm is the partial molar volume of water.
(3)
GEKAS ET AL.
102
Table 8. List of water activity models
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Equation
Mathematical expression
=
xw exp (-kx^ )
Use
1. Norrish
aw
2. Caurie
a w = 1- (w/k) (1+ Aw + Bw2)
a w binary
3. Crapiste
aw / x w = exp{-A(l-xw ) ^ }
aw binary
4. Margules
aw /xwr exp(-Ax s )
aw binary
5. Favetto-Chirife
aw = 1- km
aw binary
6. Ross Modified
aw = ns(aw>s)ms/m
multi component
aw binary
7. Caurie
multicomponent
a w = (a w )i (a w ) 2 - 2 WjWj/kjkj
In the above equations, a« is activity, A is constant of non-ideality, A and B constants
in the Caurie model, k is a constant defined differently in each model, x is molar
feaction, m is molality. w grams per kg of water and y is activity coefficient.
Superscript, q ia an exponent equal to 2 for sugars and to 1 for salts
Subscripts denote, w water, s solute, i =1,2 etc denote components and T denotes total.
<X> in Equation 1 is osmotic coefficient defined as -55.51n a w /ms
Solute Activities
For solute activities in binary systems, Gibbs-Duhem theorem can be used and be
solved by numerical integration.
(4)
where
m = -55.5 In aw
In the above equation y is the activity coefficient of the solute, m is the molality of the
solute and § is known as the osmotic coefficient defined in terms of water activity and
solute molality.
Temperature and pressure dependence of activities
The Clausius-Clapeyron equation is used to predict the temperature effect on water
activity as:
OSMOTIC SOLUTIONS. I
103
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Table 9. Comparison of various activity prediction models. Modelled activities
Solution
Water activity (%)
Solute activity
2
4
6
7
8
1
3
5
Cone. (%)
95.44
95.46
95.33
2.730
95.46
Fructose 30
89.22
89.42 89.33 89.22
50
8.534
92.89
4.556
Glucose 40
92.96 92.94 92.74
86.74
9.574
55
87.03 86.90 86.71
60
83.65
84.00 83.87 83.69
12.448
2.898
Sucrose 40 95.88 95.93 95.88 95.89 95.18
50
93.47 93.47 93.49 93.51 92.75
5.180
60
89.46 89.48 89.42 89.54 89.13
10.037
86.45 86.54 86.41 86.57 86.55
14.786
65
82.41 82.71 82.38 82.58 83.11
70
22.976
75
76.65 77.93 76.78 76.89 78.27
38.834
Sucrose 50
+ NaCl 10
70.97 75.12
Sucrose 45
+NaCl 15
58.65 65.67
Note. The numbers refer to following models: 1. Norrish, 2. binary Caurie, 3. Crapiste,
4. Margules, 5. Chirife, 6. Modified Ross, 7. Caurie, and 8. Gibbs-Duhem (Equation 4)
ln(a 2 /a 1 ) =
- 1/T2)
(5)
The effect of pressure is usually small. The Okos relationship accounts for this effect
(Rahman, 1995) as:
(6)
In the above equations, the subscripts 1 and 2 refer water activity values at two
different temperatures or pressures, Q is heat of sorption, R gas constant, and A^, and
p w heat and density of water respectively.
In Table 9 there is a comparison of water activity values obtained through the
use of some of the models compiled in Table 8. The concentrations in % are meant by
weight (g of solute per 100 g of solution). There may be some possible variations in
litterature data from different sources, such as the degree of purity, since impurities
may alter the water activityof the solutions, and the degree of hydrated solutes (Reiser
et al., 1995). In order to apply these models compiled in Table 8, the concentrations are
also required as molalities (number of moles per kg of water) or as molar fractions
(moles of solute/ total number of moles). In Table 10, the concentrations of sucrose
solutions in terms of concentration (% w/w), molality and mole fraction are given
along with water activity values based on the Norish model. Tables 11 and 12 provide
104
GEKAS ET AL.
Table 10. Concentration and water activity of sucrose solutions (Reiser et al.,
1995)
Molality
(mol/kg of water)
2.921
3.165
3.429
3.571
3.873
4.204
4.325
4.382
4.767
5.194
5.425
5.931
6.503
6.817
7.512
7.810
143.150
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(%)w/w
50.0
52.0
54.0
55.0
57.0
59.0
59.6
60.0
62.0
64.0
65.0
67.0
69.0
70.0
72.0
72.8
97.8
Molar fraction
Water activity
0.050
0.054
0.058
0.060
0.065
0.070
0.073
0.073
0.079
0.085
0.089
0.096
0.105
0.109
0.119
0.124
0.700
0.936
0.929
0.923
0.919
0.911
0.902
0.900
0.898
0.887
0.875
0.869
0.854
0.838
0.829
0.810
0.800
0.016
Table 11. Water activity of aqueous electrolyte and non-electrolyte mixtures
(Rahman, 1995)
Concentrations
Water Activity
Norrish
Experimental
A.
20%w/wNaCl
20% w/w sucrose
0.769
0.744
Caurie
0.827
Experimental
0.822
B.
sucrose
NaCl
KC1
PEG
molality
2.72
0.75
0.40
3.68
OSMOTIC SOLUTIONS. I
105
Table 12. Water activity of starch mixtures (Rahman, 1995)
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Concentration
Water Starch Sucrose Salts
22%
44%
70.2% 7.8%
5.5% 5.5%
45%
Ross
0.979
0.933
Water Activity
Experimental
0.900
0.900
additional comparison of water activity of various osmotic solutions using the Norrish,
Ross and Caurie models.
There are only marginal differences among the results of the various models for
the osmotic solutions water activities. Then for both binary and multicomponent sugar
solutions the Norrish model could be selected as a good for engineering purposes
model. The model used by Crapiste is also a good for engineering purposes model and
besides, it covers the case of both electrolytes and non electrolytes.
For the non electrolyte, it can be shown that the Norrish, Crapiste and Margules
models, with a slight different formulation, they are based on the same idea, i.e. that
the logarithm of the water activity cofficient is proportional to the square of the molar
fraction of the solute. Crapiste extends the applicability to electrolytes with the
difference that the logarithm of the water activity coefficient is proportional to the
molar fraction of the salt. The involved k or A constants in these three models are
measuring the non-ideality of the solution, the higher the constants the more non-ideal
becoming the system. The Norrish equation is possible to be used for other types of
solutions (more "practical") as for example corn syrups, in that case the constants k for
the solutes were taken as follows glucose 0.7, maltose 2.6, triose and above 2.48
(Lazarides et al., 1997; Palou et al., 1994; Palou et al, 1993).
For multicomponent systems including both sugars and salts there was a worse
agreement between the two models used, the modified Ross equation and the Caurie
model. The latter model has been found by us as well as by others to give controversial
results, it works well in some cases and not in others. In our case it gave good results in
the case of sucrose solutions (but not in the case of glucose and fructose) and also in
the multicomponent case with sucrose and NaCl it gave a good agreement with the
experimental value. Lilley and Sutton (1991) also reported better agreement of their
model than the Ross models, for the systems glucose/sucrose and glucose/glycerol up
to molalities of 3 mol/kg (25°C).
The agreement between modeled values and experimental values using the
freezing point depression method was satisfactory. Then the aim is to obtain data for
difficult multicomponent systems (such as mixtures electrolytes-non electrolytes) for
which no satisfactory modeling up to now exist, through this experimantal method or
try to obtain more adequate models using experimental data of this type.
106
GEKAS ET AL.
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Water and solute activities from the group contribution models
Le Maguer (1992) pointed out few limitations of semi-empirical correlation models for
water activity. A different approach is suggested, based on the application of fluid
phase thermodynamics and excess Gibbs energy, G^, models. Attempts to use this
approach have been described with encouraging results and have been reviewed by Le
Maguer (1992). A further step in the use of G^ models to predict water activities in
aqueous solutions consists of the use of group contribution methods.
In many cases, equilibrium data involving the desired components are not
available for parameter regression. In such cases, it is possible to use group
contribution methods. These methods are based on the assumption that molecular
interactions can be represented by the combination of interactions among the functional
groups constituting them. This concept was developed for non-electrolyte solutions
leading to Analytical Solution of Groups (ASOG) based on Wilson equation (Derr and
Deal, 1969; Kojima and Tochigi, 1979) and UNIFAC (UNIQUAC Functional Group
Activity Coefficients) based on UNIQUAC equation (Fredenslund et al., 1975).
Sorrentino et al. (1986) used both ASOG and UNIFAC to predict infinite
dilution activity coefficients of aroma compounds in water-carbohydrate and waterpolyethylene glycol solutions and Choudhury and Le Maguer (1986) used UNIFAC to
predict a w in glucose solutions.
UNIFAC method has been used both by Gabas and Laguerie (1992) and Abed
et al. (1992) used to predict solid-liquid equilibrium of water-sugar systems. Achard et
al. (1992) on the other hand, described the use of UNIFAC-LARSEN model (Larsen et
al., 1987) to estimate activity coefficients in aqueous systems containing saccharides,
using the standard UNIFAC groups. The authors reported moderate, relative-deviations
between experimental and predicted a w values for such systems, particularly with
ternary systems.
Although the ASOG group contribution method has not been so widely tested
for prediction of a w , Correa and Correa (1992) and Correa et al. (1993) used the
method to predict water activities in aqueous solutions of sugars and urea with polyols.
Kawaguchi et al. (1981) and Correa (1997) used the same method to predict the water
activity of binary and ternary aqueous electrolyte solutions. The methodology used by
the latter is based on the former, but it includes simplifications with respect to anion
contribution.
It was realised that the electrical field created around most anions is
significantly weaker than the one corresponding to cations due to their larger ionic
radius. Only fluoride ion, the smallest but less frequent in these systems, has an ionic
radius similar to potassium. In addition, steric hindrance between water molecules and
hydration water may limit new hydration opportunities. These two aspects led to the
assumption that anions remain essentially in a non-hydrated state. According to the
model mentioned above, an aqueous electrolyte solution was then considered formed
by water (W), hydrated cations (CH) and anions (A) leading to the following binary
group interactions: water-hydrated water, water-anion, hydrated water-anion.
Correa et al. (1994) used the ASOG method in order to estimate water activities
of solutions of food engineering interest. Water activities in aqueous solutions of urea
OSMOTIC SOLUTIONS. I
107
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with sugars (glucose and fructose) and polyols (glycerol, sorbitol and mannitol) at 25°C
were measured with an electric hygrometer. Concentration ranges considered in this
study reached solubility limits for each solute. Correlation and prediction of water
activities using ASOG group contribution method required the use of a set of new
specific groups. The interaction parameters for such new groups were calculated from
new and previously published experimental data. Average percent deviations of 0.4 %
between experimental and predicted a w values were obtained.
A set of new ionic type functional groups for the prediction water activities (a w ) in
aqueous solutions of electrolyte solutes using ASOG group contribution method is
proposed. Previously published experimental data on water activities, osmotic
coefficients and freezing temperatures for binary solutions of electrolyte salts and water
at different temperatures were used to calculate interaction parameters. With such
parameters values of a w for binary (14), ternary (28) and quaternary (3) systems, at
different temperatures, were predicted and compared with experimental data. This data
included both published and new data, measured with an electric hygrometer, for
sodium nitrate (at 20°C) and potassium nitrate (at 20°C and 30° C). Calculated average
relative deviations of a w predictions using the ASOG method were 0.21%, 0.28% and
0.20% respectively.
On the basis of the results obtained for the prediction of water activities in
aqueous solutions of urea with either sugars or polyols and of other sugar/sugar and
sugar/polyol solutes, it can be concluded that ASOG group contribution method as
described by Kojima and Tochigi (1979) complemented by a set of five new interaction
groups proposed here, was able to produce results with an average relative deviation of
0.4 %, which can be considered very acceptable and suggests the possibility of its
extension to other similar systems.
Concerning electrolyte solutions and to check the applicability of the proposed
model, water activities predicted by this method were compared with the predictions
obtained by Teng and Seow (1981) using the Ross, and modified Ross methods.
Results obtained are clearly better than the ones obtained with Ross's method and a
little worse than modified Ross methods. It should be stressed, however, that ASOG
predictions were based on general group contributions obtained from data obtained for
completely different systems. The other mentioned methods represent essentially
interpolating models requiring experimental binary data for all pairs of the system
being studied, at the desired temperature; in principle, any extrapolation to other
conditions or system is not possible.
Interaction parameters presented were calculated from different types of
experimental data obtained at several temperatures. This single set parameters was able
to make a w predictions for other binary, ternary and quaternary systems at different
temperatures with acceptable deviations from experimental data.
D. CURRENT LIMITATIONS AND FUTURE DIRECTION
Water activity data is possible to find in the litterature. Those data are still good for
engineering purposes and to develop simplified semitheoretical models. To the author's
opinion approaches such as the Lilley Sutton (1991), and use of the Gibbs Duhem
GEKAS ET AL.
108
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Sucrose solutions 40%- 75%
1.0
0,8
0,9
water activity
Figure 1. Dependency of solute concentration and water activity of a sucrose
solution.
4,00e+6
•fa
3,00e+6
Q.
0,00e+0
40
50
60
Concentration (%)
70
80
Figure 2. Relationship between osmotic pressure and concentration for sucrose
solution.
theorem for solute activities are most promising. Application of group contribution
models are also at their infancy as far as application to the osmotic solutions is
concerned.
Future Needs
1. Although water activity data exist in many cases of osmotic solutions, the
expression of the osmotic capacity of the media in other equivalent terms such as
OSMOTIC SOLUTIONS. I
109
osmotic pressure or osmosity could be helpful since water activity is not sensitive in
the region 0.9-1.0. (small differences in a«, give high differences in "Ina«,"). This
remark should also to be considered in the case of sorption isotherms in the high
range of water activity.
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2. More fundamental effords are needed to estimate water and solutes' activities of
mixtures and solutes interations.
3. In general, solute activity data are very scarse and there is a future need to obtain
such data for the various osmotic solutions. Our results show that solute activity
data for concentrated sugar solutions are promising (Figure 1). The application of
the water activity in order to estimate osmotic pressure of concentrated solutions
give high pressure values in the order of 100 MPa (Figure 2). Solute activity
growing smoothly up to more or less 50% sugar concentration shows an
exponential trend as the concentration approaches the sugar solubility limit. This
fact could explain certain observations from studies of osmotic dehydration
reported in the literature, for example the levelling off water loss and solid uptake
attained at high concentration values. It could also reveal other kinds of non
idealities, probable inflecion points etc. In conclusion, both activity coefficient
models and group contribution models could be considered to fill the gap.
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