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Mass transfer properties of osmoticsolutions. I. Water activity and osmoticpressureVassilis Gekas a , Chelo Gonzalez b , Alberto Sereno c , AmparoChiralt b & Pedro Fito ba Food Engineering, Lund University, Lund, Swedenb Universidad Politecnica de Valencia, Valencia, Spainc Escola Superior de Biotecnologia, Oporto, Portugal

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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)

MASS TRANSFER PROPERTIES OF OSMOTIC SOLUTIONS. I. WATERACTIVITY AND OSMOTIC PRESSURE

Vassilis Gekas1'*, Chelo Gonzalez2, Alberto Sereno3, Amparo Chiralt2, and PedroFito2

1Food Engineering, Lund University, Lund, Sweden

2Universidad Politecnica de Valencia, Valencia, Spain

3Escola 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 theosmotic solutions are needed for the optimization of mass transfer during osmoticprocess, and for the improvement of final product quality. The vant Hoff equation andGibbs Duhem theorem are commonly used to estimate osmotic pressure and soluteactivity. Water activities can be easily estimated through experimental determination ofthe freezing point depression. The possibilities of the group contribution models suchas the Analytical Solution of Groups (ASOG) approach are also explored. The futureneeds especially in the case of multicomponent solutions consisting of electrolyte andnon-electrolyte mixtures are pointed out.

INTRODUCTION

A number of food processing unit operations imply immersion of the food in a highosmotic pressure medium containing sugars, such as sucrose, glucose, fructose, syrupsand salts, such as sodium chloride or their mixtures. Foods that are treated this way arefruits and vegetables or also meat and fish (Fito et al., 1994; Lazarides, 1994; Lenartand Flink 1984a, 1984b; Lenart, 1994; Lerici et al., 1985). The aims of the osmoticprocess are: partial dehydration before the final treatment such as drying or freezing,impregnation of solute to improve quality (i.e., cryoprotectant), osmo-freezing orthawing 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 theosmotic unit operations depends on the properties of the osmotic solutions used. Fromthe mass transfer point of view the most important osmotic solution parameter is itswater activity lowering capacity in terms of water activity or osmotic pressure- this isan important property for the purpose of dehydration. Due to the simultaneous masstransfer, i.e. water transport from the food to the osmotic medium and solute transportfrom the osmotic medium to the food, additional information on the solute size andsolute activities are also important.

A literature review has shown that so far the properties of the osmotic solutionconsidered in order to interprete the unit operations results were solute concentrationand only in a few cases there has been reported solution water activity data and to theauthors' knowledge there is absent of osmotic pressure data or solute activity data. It isalso known that concentrated solutions used in osmosis are real solutions which mightdeviate strongly from the ideal situations, thus activities in addition to concentrationsshould provide a more sound theoretical basis for the characterization of the osmoticsolutions and better interpretation of the osmotic process.

Commonly used osmotic solutions, based on FSTA database 1969-1996 arepresented in Table 1. As it is shown, a common osmotic medium used especially forfruits is the sucrose solution or syrup of a concentration range of 40-70 Brix and mostfrequently used one is 60 Brix. Other sugars such as glucose, fructose, lactose have alsobeen used. Various Dextrose Equivalent (DE) corn syrups have been used for fruits andvegetables whereas for potato, fish and meat, salt solutions (NaCl 15% are being themost common among them) were the preferred media. In a few cases a combinationbetween a sugar(s) and a salt was used.

The objective of this paper is to review data of water activity and theirprediction models for binary and multi-component osmotic solutions commonly usedfor osmotic dehydration of fruits.

A. PUBLISED EXPERIMENTAL DATA ON WATER ACTIVITIES.

In Table 2 there are shown values of freezing point depression for various osmoticsolutions obtained at our laboratory of Lund University. For comparison litteraturevalues are also presented. In Table 3 the values of water activity of the same solutionsas in Table 2 are presented along with the litterature values for comparison. Table 4shows water activity values of glycerol solutions along with refractive index values ofthis solutions (Rizvi, 1995). Table 5 contains water activity values of NaCl fromChirife and Resnik (1984). Tables 6 and 7 provide literature data of osmosities andwater 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 (orosmotic pressure) of two-component and three-component osmotic solution using

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OSMOTIC SOLUTIONS. I 97

Table 1. Osmotic solutions commonly used in osmosis

Solution Type Concentration & temperature Types of foodsBINARYSucrose 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% Potato, apple, pineappleor 50%-10%20-40°C

Sucrose +Xylitol 30% + 70% VegetablesCorn syrup solids 34-70%, Papaya, apple, some vegetablesDE10-40 35-55°CCorn Syrup / Sucrose/Water 5/3/1, 70B Cherries

Table 2. Freezing point depression of sugars (Gonzalez et al., 1995)

Solution type Measured values Litterature valuesin the authors's laboratory

Mean

-4.79 -4.70

-7.54 -7.61

-8.92 -8.40

-12.70 -12.45

-28.34

Fructose 30%

Sucrose 50%

Sucrose 52%

Sucrose 60%

Sucrose 60% + NaCl 10%

-4.84-4.75-7.24-7.64-7.64-8.97-8.87

-12.30-12.90-12.90-28.54-28.14

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98 GEKAS ET AL.

Table 3. Water activity measured in the authors' laboratory and the litteraturevalues

SolutionFructose 30%

Sucrose 50%Sucrose 52%Sucrose 60%Sucrose 60% + NaCl 10%

From measured values0.955

0.9300.9180.8820.757

From litterature values0.954 (a)0.961 (b)0.929 (a)0.922 (a)0.874 (a)0.751 (c)

(a) From Ferro-Fontan-Chirife Equation(b) Measured by electric hygrometer(c) From Caurie model

Table 4. Water activity of glycerol solutions (Rizvi, 1995)

Concentration Refractive Index Water Activity(kg/L)

0.23150.37890.49730.59230.67510.74740.81390.92850.9760

1.34631.35601.36021.37731.39051.40151.41091.41911.42641.43871.44401.4529

0.980.960.950.900.850.800.750.700.650.550.500.40

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OSMOTIC SOLUTIONS. I 99

Table 5. Water activity of NaCl solutions1"2

Concentration Water Activity Concentration Water Activity(%, w/w) (%, w/w)

0.51.01.52.02.53.03.54.04.55.05.56.06.57.07.58.09.0

0.9970.9940.9910.9890.9860.9830.9800.9770.9730.9700.9670.9640.9600.9570.9540.9500.943

1011121314151617181920212223242526

0.9350.9270.9190.9110.9020.8920.8830.8730.8620.8510.8390.8270.8150.8020.7880.7740.759"

1 In the temperature range 15-5O°C2 Data source Chirife and Resnik (1984)a Saturation point

freezing point depression method. The solutions were immersed in an ethanolthermostatized bath, kept at a temperature of approximately -46 °C (Lerici et al.,1983). The solutions were vigorously agitated in order to avoid external resistances inheat transfer. Agitation was found very important and also the ethanol temperature tobe kept at least 30 degrees below the freezing point (FP) of the solution. To" obtainwater activities from freezing point depression values three alternative equations wereused i.e. one for ideal solutions, secondly one for real ones, and lastly a numericalapproximation 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 thereal solutions is:

- l n a w = LmAT/(RTTo) (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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100 GEKAS ET AL.

Table 6. Osmosities1 and water activities of other sugar solutions (Wolf et al.,1974)

Concentration(%, w/w)

68

1012141618202224262830

Glucose

0.1940.2660.3610.4220.5060.5940.6870.7850.8921.0071.1241.2441.369

0.9930.9910.9880.9870.9840.9810.9780.9730.9690.9650.9620.9570.953

Fructose

0.1920.2630.3380.4170.5000.5870.6770.7690.8870.9931.1001.205

0.9330.9910.9890.9870.9840.9820.9810.9790.9700.9660.9620.960

Lactose

0.103 0.9960.143 0.995

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 onesof the given solution

Table 7. Solute activities of salts (Vanysek, 1994)

Molality0.0010.0050.010.050.10.20.512510

NaCl1

0.9650.9280.9030.8220.7790.7340.6810.6570.6680.874

KC10.9650.9270.9010.8160.7680.7170.6490.6040.5730.593

CaCl20.8880.7870.7270.5770.5170.4690.4440.4950.7840.5910.431

K2SO40.8850.7720.7040.5110.4240.3430.251

Na2S040.8860.7770.7120.5290.4460.3660.2680.2040.155

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OSMOTIC SOLUTIONS. I 101

where a w is water activity, Lm the molar latent heat of freezing of the pure water andAT =To - T the freezing depression value of the solution.

A good agreement with water activities (effective concentrations) measuredusing the freezing point depression method and with textbook values for both sucroseand NaCl solutions was also found recently by Chen et al. (1996). Other measuringmethods are: standardized solutions (Dora and Favetto, 1988), vapor pressuremeasurement, hygrometric instruments (especially the electrical hygrometer), isopiestictransfer 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 goodchoice for all applications. The freezing point depression method has chosen forosmotic 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 ofwater activities are shown in Table 8. Some of the models make use of the concept ofthe 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 lawwhich is valid for ideal solutions. The nonideality of the solutions are due to: solutesize, intermolecular forces, solvation effects, solute-solute interaction, solute-solventinteraction, dissociation effects of ionic solutes, order of mixing (Rahman, 1995).

Flory and Huggins (1941), as cited by Rahman (1995), were the first to expressnon-ideality due to size differences between solute and solvent. Lilley and Sutton(1991) combined the effects of size, solvation and solute-solute interaction in oneequation. In the absence of heterotactic interactions their model reduce to the wellknown multicomponent Ross equation (Rahman, 1995). The order of mixing wasfound 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 osmoticpressure is another way of expressing water activity of a solution. Plant physiologistsare users of the components of the "water potential" in units of pressure. Therelationship between water activity and osmotic pressure is shown in Figure 2. Thenon simplified Van't Hoff equation is as follows:

lnaw (3)

where Vm is the partial molar volume of water.

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102 GEKAS ET AL.

Table 8. List of water activity models

Equation

1. Norrish

2. Caurie

3. Crapiste

4. Margules

5. Favetto-Chirife

6. Ross Modified

7. Caurie

Mathematical expression

a w = xw exp (-kx^ )

a w = 1- (w/k) (1+ Aw + Bw2)

aw /x w = exp{-A(l-xw ) ^ }

aw /xwr exp(-Axs)

aw = 1- km

a w = n s ( a w > s )ms /m

aw = (aw)i (aw)2 - 2 WjWj/kjkj

Use

aw binary

a w binary

aw binary

aw binary

aw binary

multi component

multicomponent

In the above equations, a« is activity, A is constant of non-ideality, A and B constantsin the Caurie model, k is a constant defined differently in each model, x is molarfeaction, 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 saltsSubscripts denote, w water, s solute, i =1,2 etc denote components and T denotes total. in Equation 1 is osmotic coefficient defined as -55.51n aw/ms

Solute Activities

For solute activities in binary systems, Gibbs-Duhem theorem can be used and besolved by numerical integration.

wherem = -55.5 In aw

(4)

In the above equation y is the activity coefficient of the solute, m is the molality of thesolute and § is known as the osmotic coefficient defined in terms of water activity andsolute molality.

Temperature and pressure dependence of activities

The Clausius-Clapeyron equation is used to predict the temperature effect on wateractivity as:

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OSMOTIC SOLUTIONS. I 103

Table 9. Comparison of various activity prediction models. Modelled activities

SolutionCone. (%)Fructose 30

50Glucose 40

5560

Sucrose 405060657075

Sucrose 50+ NaCl 10Sucrose 45+NaCl 15

195.4489.2292.8986.7483.6595.8893.4789.4686.4582.4176.65

Water2

95.9393.4789.4886.5482.7177.93

activity395.4689.4292.9687.0384.0095.8893.4989.4286.4182.3876.78

(%)495.4689.3392.9486.9083.8795.8993.5189.5486.5782.5876.89

595.3389.2292.7486.7183.6995.1892.7589.1386.5583.1178.27

Solute activity6 7 8

2.7308.5344.5569.57412.448

2.8985.18010.03714.78622.97638.834

70.97 75.12

58.65 65.67Note. 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(a2/a1) = - 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 twodifferent temperatures or pressures, Q is heat of sorption, R gas constant, and  , andpw heat and density of water respectively.

In Table 9 there is a comparison of water activity values obtained through theuse of some of the models compiled in Table 8. The concentrations in % are meant byweight (g of solute per 100 g of solution). There may be some possible variations inlitterature data from different sources, such as the degree of purity, since impuritiesmay alter the water activityof the solutions, and the degree of hydrated solutes (Reiseret al., 1995). In order to apply these models compiled in Table 8, the concentrations arealso 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 sucrosesolutions in terms of concentration (% w/w), molality and mole fraction are givenalong with water activity values based on the Norish model. Tables 11 and 12 provide

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104 GEKAS ET AL.

Table 10. Concentration and water activity of sucrose solutions (Reiser et al.,1995)

(%)w/w

50.052.054.055.057.059.059.660.062.064.065.067.069.070.072.072.897.8

Molality(mol/kg of water)

2.9213.1653.4293.5713.8734.2044.3254.3824.7675.1945.4255.9316.5036.8177.5127.810

143.150

Molar fraction

0.0500.0540.0580.0600.0650.0700.0730.0730.0790.0850.0890.0960.1050.1090.1190.1240.700

Water activity

0.9360.9290.9230.9190.9110.9020.9000.8980.8870.8750.8690.8540.8380.8290.8100.8000.016

Table 11. Water activity of aqueous electrolyte and non-electrolyte mixtures(Rahman, 1995)

Concentrations Water ActivityNorrish Experimental

A.20%w/wNaCl20% w/w sucrose

B.

sucroseNaClKC1PEG

molality2.720.750.403.68

0.769

Caurie0.827

0.744

Experimental0.822

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OSMOTIC SOLUTIONS. I 105

Table 12. Water activity of starch mixtures (Rahman, 1995)

Concentration Water ActivityWater Starch Sucrose Salts Ross Experimental

22%44%

70.2%45%

7.8%5.5% 5.5%

0.9790.933

0.9000.900

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 forthe osmotic solutions water activities. Then for both binary and multicomponent sugarsolutions the Norrish model could be selected as a good for engineering purposesmodel. The model used by Crapiste is also a good for engineering purposes model andbesides, it covers the case of both electrolytes and non electrolytes.

For the non electrolyte, it can be shown that the Norrish, Crapiste and Margulesmodels, with a slight different formulation, they are based on the same idea, i.e. thatthe logarithm of the water activity cofficient is proportional to the square of the molarfraction of the solute. Crapiste extends the applicability to electrolytes with thedifference that the logarithm of the water activity coefficient is proportional to themolar fraction of the salt. The involved k or A constants in these three models aremeasuring the non-ideality of the solution, the higher the constants the more non-idealbecoming the system. The Norrish equation is possible to be used for other types ofsolutions (more "practical") as for example corn syrups, in that case the constants k forthe 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 worseagreement between the two models used, the modified Ross equation and the Cauriemodel. The latter model has been found by us as well as by others to give controversialresults, it works well in some cases and not in others. In our case it gave good results inthe case of sucrose solutions (but not in the case of glucose and fructose) and also inthe multicomponent case with sucrose and NaCl it gave a good agreement with theexperimental value. Lilley and Sutton (1991) also reported better agreement of theirmodel than the Ross models, for the systems glucose/sucrose and glucose/glycerol upto molalities of 3 mol/kg (25°C).

The agreement between modeled values and experimental values using thefreezing point depression method was satisfactory. Then the aim is to obtain data fordifficult multicomponent systems (such as mixtures electrolytes-non electrolytes) forwhich no satisfactory modeling up to now exist, through this experimantal method ortry to obtain more adequate models using experimental data of this type.

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106 GEKAS ET AL.

Water and solute activities from the group contribution models

Le Maguer (1992) pointed out few limitations of semi-empirical correlation models forwater activity. A different approach is suggested, based on the application of fluidphase thermodynamics and excess Gibbs energy, G^, models. Attempts to use thisapproach have been described with encouraging results and have been reviewed by LeMaguer (1992). A further step in the use of G^ models to predict water activities inaqueous solutions consists of the use of group contribution methods.

In many cases, equilibrium data involving the desired components are notavailable for parameter regression. In such cases, it is possible to use groupcontribution methods. These methods are based on the assumption that molecularinteractions can be represented by the combination of interactions among the functionalgroups constituting them. This concept was developed for non-electrolyte solutionsleading to Analytical Solution of Groups (ASOG) based on Wilson equation (Derr andDeal, 1969; Kojima and Tochigi, 1979) and UNIFAC (UNIQUAC Functional GroupActivity Coefficients) based on UNIQUAC equation (Fredenslund et al., 1975).

Sorrentino et al. (1986) used both ASOG and UNIFAC to predict infinitedilution activity coefficients of aroma compounds in water-carbohydrate and water-polyethylene glycol solutions and Choudhury and Le Maguer (1986) used UNIFAC topredict a w in glucose solutions.

UNIFAC method has been used both by Gabas and Laguerie (1992) and Abedet al. (1992) used to predict solid-liquid equilibrium of water-sugar systems. Achard etal. (1992) on the other hand, described the use of UNIFAC-LARSEN model (Larsen etal., 1987) to estimate activity coefficients in aqueous systems containing saccharides,using the standard UNIFAC groups. The authors reported moderate, relative-deviationsbetween 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 aw, 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 wateractivity of binary and ternary aqueous electrolyte solutions. The methodology used bythe latter is based on the former, but it includes simplifications with respect to anioncontribution.

It was realised that the electrical field created around most anions issignificantly weaker than the one corresponding to cations due to their larger ionicradius. Only fluoride ion, the smallest but less frequent in these systems, has an ionicradius similar to potassium. In addition, steric hindrance between water molecules andhydration water may limit new hydration opportunities. These two aspects led to theassumption that anions remain essentially in a non-hydrated state. According to themodel mentioned above, an aqueous electrolyte solution was then considered formedby water (W), hydrated cations (CH) and anions (A) leading to the following binarygroup interactions: water-hydrated water, water-anion, hydrated water-anion.

Correa et al. (1994) used the ASOG method in order to estimate water activitiesof solutions of food engineering interest. Water activities in aqueous solutions of urea

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OSMOTIC SOLUTIONS. I 107

with sugars (glucose and fructose) and polyols (glycerol, sorbitol and mannitol) at 25°Cwere measured with an electric hygrometer. Concentration ranges considered in thisstudy reached solubility limits for each solute. Correlation and prediction of wateractivities using ASOG group contribution method required the use of a set of newspecific groups. The interaction parameters for such new groups were calculated fromnew 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 (aw) inaqueous solutions of electrolyte solutes using ASOG group contribution method isproposed. Previously published experimental data on water activities, osmoticcoefficients and freezing temperatures for binary solutions of electrolyte salts and waterat different temperatures were used to calculate interaction parameters. With suchparameters values of a w for binary (14), ternary (28) and quaternary (3) systems, atdifferent temperatures, were predicted and compared with experimental data. This dataincluded both published and new data, measured with an electric hygrometer, forsodium nitrate (at 20°C) and potassium nitrate (at 20°C and 30° C). Calculated averagerelative deviations of a w predictions using the ASOG method were 0.21%, 0.28% and0.20% respectively.

On the basis of the results obtained for the prediction of water activities inaqueous solutions of urea with either sugars or polyols and of other sugar/sugar andsugar/polyol solutes, it can be concluded that ASOG group contribution method asdescribed by Kojima and Tochigi (1979) complemented by a set of five new interactiongroups proposed here, was able to produce results with an average relative deviation of0.4 %, which can be considered very acceptable and suggests the possibility of itsextension to other similar systems.

Concerning electrolyte solutions and to check the applicability of the proposedmodel, water activities predicted by this method were compared with the predictionsobtained 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 alittle worse than modified Ross methods. It should be stressed, however, that ASOGpredictions were based on general group contributions obtained from data obtained forcompletely different systems. The other mentioned methods represent essentiallyinterpolating models requiring experimental binary data for all pairs of the systembeing studied, at the desired temperature; in principle, any extrapolation to otherconditions or system is not possible.

Interaction parameters presented were calculated from different types ofexperimental data obtained at several temperatures. This single set parameters was ableto make a w predictions for other binary, ternary and quaternary systems at differenttemperatures 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 forengineering purposes and to develop simplified semitheoretical models. To the author'sopinion approaches such as the Lilley Sutton (1991), and use of the Gibbs Duhem

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108 GEKAS ET AL.

Sucrose solutions 40%- 75%

0,8 0,9water activity

1.0

Figure 1. Dependency of solute concentration and water activity of a sucrosesolution.

4,00e+6

•fa 3,00e+6Q.

0,00e+040 50 60

Concentration (%)70 80

Figure 2. Relationship between osmotic pressure and concentration for sucrosesolution.

theorem for solute activities are most promising. Application of group contributionmodels are also at their infancy as far as application to the osmotic solutions isconcerned.

Future Needs

1. Although water activity data exist in many cases of osmotic solutions, theexpression of the osmotic capacity of the media in other equivalent terms such as

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OSMOTIC SOLUTIONS. I 109

osmotic pressure or osmosity could be helpful since water activity is not sensitive inthe region 0.9-1.0. (small differences in a«, give high differences in "Ina«,"). Thisremark should also to be considered in the case of sorption isotherms in the highrange of water activity.

2. More fundamental effords are needed to estimate water and solutes' activities ofmixtures and solutes interations.

3. In general, solute activity data are very scarse and there is a future need to obtainsuch data for the various osmotic solutions. Our results show that solute activitydata for concentrated sugar solutions are promising (Figure 1). The application ofthe water activity in order to estimate osmotic pressure of concentrated solutionsgive high pressure values in the order of 100 MPa (Figure 2). Solute activitygrowing smoothly up to more or less 50% sugar concentration shows anexponential trend as the concentration approaches the sugar solubility limit. Thisfact could explain certain observations from studies of osmotic dehydrationreported in the literature, for example the levelling off water loss and solid uptakeattained at high concentration values. It could also reveal other kinds of nonidealities, probable inflecion points etc. In conclusion, both activity coefficientmodels and group contribution models could be considered to fill the gap.

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