aw dan osmotik effec

7/29/2019 aW Dan Osmotik Effec

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Prediction of water activity of osmotic solutions

A.M. Sereno a,*, M.D. Hubinger b, J.F. Comesa~na c, A. Correa c

a Department of Chemical Engineering, University of Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugalb Faculty of Food Engineering, University of Campinas, 13.083-970 Campinas, S. Paulo, Brazil

c Department of Chemical Engineering, University of Vigo, Apdo. 874, 36200 Vigo, Spain

Received 1 June 2000; accepted 1 December 2000

Abstract

Models to correlate and predict water activity in aqueous solutions of single and multiple solutes, including electrolytes, relevant

for osmotic processing of foods are reviewed. During the last decade a signicant number of theoretical thermodynamic models thatare applicable to these systems have been developed and published. Though their use is still limited, their performance is in general

very good, similar to the best traditional empirical equations. Their predictive character together with built-in capabilities to work at

dierent temperatures and in some cases pressure suggests that an increased eort to their wide use should take place. It was found

that predictions of water activity in aqueous solutions may easily be made with average relative deviations of less than 2%; this value

is of the same order or in some cases less than the typical error of current instrumentation available to measure water activity. 2001

Elsevier Science Ltd. All rights reserved.

Keywords: Osmotic dehydration; Vapourliquid equilibria; Water activity; Sugars; Electrolytes; Aqueous solutions; Predictive models

1. Introduction

Osmotic treatments involve the contact of a material,usual of vegetal or animal origin, with a concentrated

aqueous solution and include namely osmotic dehydra-

tion and solute impregnation processes. These constitute

simple food processing operations conducted at ambient

or near ambient temperature, which achieve a signicant

degree of dewatering without phase change and allowing

some degree of product formulation and even restruc-

turing.

A special mention should be made about the use of

osmotic treatments in the preparation of intermediate

moisture foods (IMF) and the so-called fourth genera-

tion or minimally processed foods. Such processes have

been also referred to as dewatering and impregnationsoaking (Raoult-Wack, Rios, Saurel, Giroux, & Guil-

bert, 1994) and are mainly being used as a pre-treatment

introduced in any conventional fruit and vegetable

processing, in order to improve quality, reduce energy

costs or even formulate nal products. Applications

have been reported for sh and certain meat products

(Collignan & Raoult-Wack, 1994; Bohuon, Collignan,

Rios, & Raoult-Wack, 1998; Sabadini, Carvalho, So-

bral, & Hubinger, 1998), as well as for fruit products,

when the correct choice of solutes and a controlled ratioof water removal and impregnation allow to enhance

their natural avour and colour retention (Raoult-Wack

et al., 1994; Guerrero, Alzamora, & Gerschenson, 1996;

Alzamora, 1997; Forni, Sormani, Scalise, & Torregiani,

1997; Spiess & Behsnilian, 1998).

As a preliminary step to convective air drying,

several studies are found in the recent literature as well

as its inuence on nal food properties (Lenart, 1996;

Del Valle, Cuadros, & Aguilera, 1998; Sa, Figueiredo,

& Sereno, 1999; Salvatori, Andres, Chiralt, & Fito,

1999; Lewicki & Lukaszuk, 2000; Krokida, Kiranou-

dis, Maroulis, & Marinos-Kouris, 2000). The combi-

nation of osmotic dehydration to some less commondrying steps, such as microwave drying (Venkatacha-

lapathy & Raghavan, 1999) and freeze-drying (Ka-

rathanos, Anglea, & Karel, 1996) has also been

described.

Osmotic pre-treatments may be used before vacuum

frying, by immersion in solutions of high osmotic pres-

sure (Spiess & Behsnilian, 1998), the eect on mass

transfer rates of high hydrostatic pressure (HPP) pro-

cessing, previous to osmotic treatment of vegetable tis-

sues was also investigated (Rastogi & Niranjan, 1998;

Rastogi, Angersbach, & Knorr, 2000).

Journal of Food Engineering 49 (2001) 103114

www.elsevier.com/locate/jfoodeng

* Corresponding author. Fax: +351-22-508-1440.

E-mail address: [email protected] (A.M. Sereno).

0260-8774/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 2 6 0 - 8 7 7 4 ( 0 0 ) 0 0 2 2 1 - 1


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The transfer of mass, water and solutes observed

during the contact of a solid material with an osmotic

solution is due to dierences in chemical potential inside

and outside the material, usually expressed in terms of

the corresponding activity coecients. As dehydration is

the main objective of osmotic treatments, the activity of

water in both the material and the solution and its

prediction is of major importance. This relevance is

particularly emphasised when mathematical models are

used to describe the process. For cellular materials, as is

the case of most foods, water transfer takes place in the

vicinity of the cell through the semi-permeable cell

membrane (Le Maguer, 1988); again dierence of water

activity in both sides governs its physical behaviour and

mass transport.

The thermodynamic description of these osmotic so-

lutions has been the object of intense research all along

the last century, particularly those involving sugars and/or salts. Excellent reviews of such eorts have been

written by Van den Berg and Bruin (1981) and Le Ma-

guer (1992) to mention only two papers. Most thermo-

dynamic models used to describe vapourliquid

equilibrium of osmotic solutions are based on relations

involving Gibbs free energy of the system. Of particular

interest is the excess Gibbs energy (GE) and for each of

the components the partial molar excess Gibbs energy

(gEi ), both allowing a convenient way to quantify the

deviations from ideal behaviour.

From GE, a large number of physical parameters may

be calculated such as water and solute activities, partialequilibrium properties (solubility, relative volatility,

etc.) and others (Le Maguer, 1989).

The activity of water in aqueous solutions is dened

as (Prausnitz, Lichtenthaler, & Azevedo, 1986):

aWT;P;x cWT;P;xxW fWT;P;x

f0WT;P0;x0

; 1

where aW is the water activity, xW is the mole fraction of

water, cW is the activity coecient for water, fW;fW are

the fugacities of water in the system and at reference

conditions, respectively.

It is usually assumed that under normal working

conditions of ambient temperature and atmospheric

pressure, gas phases behave ideally and so the ratio of

fugacities can be taken as the ratio of partial pressures

(Reid, Prausnitz, & Poling, 1987):

fW

f0W

pW

p0W; 2

where pW and p0W are the vapour pressures of water in

the system and of pure liquid water at the same tem-

perature, respectively. Under this assumption, from

Eq. (1):

aW pW

p0W

RH

100; 3

where RH is the percent relative humidity of the air

layer in equilibrium with the sample. The activity coef-

cient cW may be calculated directly from the partialmolar excess Gibbs energy of water, gEW (Prausnitz et al.,

1986):

gEW RT ln cW; 4

and for the total molar excess Gibbs energy, gE:

gE RTXi

xi ln ci 5

for an ideal solution all the activity coecients,

ciT;P;x, are equal to one, corresponding to an excessGibbs energy equal to zero.

Several approaches have been used to calculate or

estimate excess Gibbs energy in liquid solutions, in-cluding empirical models based on solution composi-

tion, the use of equations of state extended to the

description of condensed phases and probably more

often, dierent theories developed to describe solution

structure and interactions among the chemical species.

In Table 1 the major methodological groups used by

published contributions to the prediction of water ac-

tivity of solutions are indicated.

Most of the models included in Table 1 are general in

themselves and may be used with food and related sys-

tems (Prausnitz et al., 1986; Le Maguer, 1992). The

Nomenclature

a activity

ARD average relative deviation (%)

f fugacity

GE Gibbs free energy (J)

gE molar Gibbs free energy (J mol1)

h molar heat of mixing (J mol

1

)M molar mass kg mol1P pressure (Pa)

p partial pressure (Pa)

R gas constant

RH relative humidity (%)

RMS root mean square

T temperature (K)

x mole fraction

Greeks

c activity coecient

tFHi no. of non-hydrogen atoms in molecule i

tki no. of non-hydrogen atoms in group k of component i

Subscriptsi component i

W water

Superscripts

reference state

104 A.M. Sereno et al. / Journal of Food Engineering 49 (2001) 103114


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diculties usually arise from the fact that as most food

systems are not well characterised both from a chemical

and structural point of view, and consequently ther-

mophysical property data required to use (and t) the

models to such systems are not available. One way to

overcome these diculties in practical applications is to

look for correlations between these thermodynamic

properties and some easy method to measure physical

properties. This approach produced a series of empirical

and semi-empirical models which provide in many cases

excellent results and constitute relevant contributions of

widespread use in the food industry (Table 2).

All the models mentioned in Tables 1 and 2 refer to

solutions, more specically aqueous solutions. A parallel

eort has been dedicated to the correlation and predic-

tion of sorption isotherms in solid foods; a large number

of equations and models used to describe and predict

water activity and sorption isotherms of food systems

containing solid phases (Van den Berg & Bruin, 1981;

Iglesias & Chirife, 1982). Such models were not included

here, as only aqueous solutions constituted the scope ofthis work.

An alternative approach to the use of empirical and

semi-empirical equations consists in the application of

group contribution methods, namely ASOG (analytical

solutions of groups, Derr & Deal, 1969; Kojima &

Tochigi, 1979) and UNIFAC (UNIQUAC functional

group activity coecients, Fredenslund, Jones, &

Prausnitz, 1975; Larsen, Rasmussen, & Fredenslund,

1987). These two proposals probably constitute the only

general accessible predictive technique for water activity

of osmotic solutions. Their main advantage is to provide

a technique for aW prediction for complex systems

without requiring parameters for each specic com-

pound, but instead characteristic interaction parameters

for the chemical groups that constitute each molecule.

The eect in the solution of each of such chemical group

is assumed to be the same, irrespective of the molecule

where it is contained.

The ASOG method, based on the Wilson model

(Wilson, 1964), has been used for this purpose by Correa

et al. (1994), who obtained good aW predictions for

aqueous solutions of both sugar/polyol and sugar/urea.

Kawaguchi et al. (1981, 1982) have combined the

method with an hydration model of ionic species origi-

nated in aqueous solutions of electrolytes; later Correa

et al. (1997) have redened the groups in solution, ob-

taining improved predictions for several binary and

multicomponent salt solutions.

Attempts to predict water activity using UNIFAC

have also been extensively reported. Choudhury and Le

Maguer (1986) used this method to predict aW in glucose

solutions and Achard et al. (1992) described its use toestimate activity coecients in aqueous systems con-

taining sugars and polyols; Catte et al. (1995) used the

same group typology as suggested by Correa et al.

(1994) to characterise sugars, and successfully estimated

several thermodynamic properties. Christensen et al.

(1983) and Kikic et al. (1991) applied the same model to

predict equilibria in salt solutions. Very interesting ex-

tensions to cover organic acids (Velezmoro & Meirelles,

1998), polyethylene glycol and other polyols (Ninni et

al., 1999a, 2000), aminoacids (Ninni et al., 1999b) have

been developed by Meirelles and co-workers.

Table 1

Dierent approaches to calculate GE and activity coecients

Empirical equations based on solution composition

Simple equations, often including semi-theoretical basis, which often produce reasonable predictions of liquidvapour and liquidliquidequilibria; served in some cases as the basis for more complex models: Margules equation, the Wohl expansion, Van Laar equation, RedlichKister

equation, ScatchardHamer equation

Use of equations of state (EOS)

Hu, Liu, Soane, and Prausnitz (1991): use double lattice (Freed & Flory-Huggins) to calculate Helmholtz energy of mixing, used to describeequilibrium in non-polar or slightly polar non-ideal systems

Wu, Lin, Zhu, and Mei (1969): use modied version of Pitzer (1973) virial EOS with Fowler and Guggenheim (1939) instead of the morecommon DebyeHuckel contribution of long-range electrostatic forces

Simonin (1999): uses McMillanMayer theory, assuming molecules as hard bodies interacting through van der Waals short range forces; to allowfor the presence of polar molecules (alcohols) and weak electrolytes, and a volume exclusion contribution using CarnahanStarling hard sphere

EOS

Solution theories

Van der Waalsvan Laar theory: valid only for nearly ideal systems Regular solution theory (Hildebrand, 1929; Scatchard, Hamer, & Wood, 1938): systems without interactions among polar molecules (athermal),e.g. hydrocarbons

Debye and Huckel (1923) introduced a successful description of long-range polar and ionic forces contribution Lattice theory due mostly to Guggenheim (1935, 1952) and Eyring and Marchi (1963) Flory (1941, 1942) and Huggins (1942) extension of lattice theory to polymer solutions

Local-composition models, namely Wilson (1964); NRTL model of Renon and Prausnitz (1968); UNIQUAC model of Abrams and Prausnitz(1975)

A.M. Sereno et al. / Journal of Food Engineering 49 (2001) 103114 105


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These extensive and successful applications of the two

major group contribution methods to predict water ac-

tivity of osmotic solutions constitute an example, pos-

sibly one of the earliest, of the use of advanced

thermodynamic models to describe the behaviour of

food-related systems.

2. How group contribution methods work

The main principle underlying this technique is the

assumption that all chemical functional groups in solu-tion interact with other specic groups in a similar way,

independent of the types of groups in presence and of

the specic molecules where they are contained. To use

the method the rst step consists in `breaking' the

structure of the molecule in all its basic groups, for

which interaction and individual geometric parameters

are available. Since then, the method is applied as if the

solution was made of known groups instead of unknown

molecules.

Since their development the list of identied and

well-characterised groups is increasing. Unfortunately

some of the compounds found in food-related systems

are too complex and sometimes new groups have to be

identied and characterised. This happened with sug-

ars. Sugars in aqueous solutions, both monosaccha-

rides, like glucose and fructose, and disaccharides, like

sucrose, adopt a cyclic structure made of pyranose and

furanose unit rings (Fig. 1). To successfully describe

such compounds by the ASOG method, Correa et al.

(1994) dened three new groups named GR, FR and

CPOH standing for `glucose ring', `fructose ring' and

`cyclic-polyalcohol' (OH groups linked to consecutive

carbon atoms in a cyclic sugar structure). For polyhy-dric alcohols (e.g. glycerol, mannitol and sorbitol) a

new group POH referring to OH groups linked to

consecutive carbon atoms in a linear chain was also

adopted. A fth `group' dened was UREA for the

urea molecule, as it could not be adequately repre-

sented by a combination of available ASOG groups

(Table 3).

The method uses two specic individual group pa-

rameters tFHi and tki, and four interaction parameters for

each binary pair of groups. Table 4 lists the values of

these parameters for some relevant compounds.

Table 2

Models to calculate water activity in aqueous solutions relevant to food systems

1. Empirical equations

Simple early formulas applicable to the candy industry: Grover and Nicol (1940), Money and Born (1951) and Dunning, Evans, and Taylor(1951)

Zdanovskii (1936) and Stokes and Robinson (1966) proposed independently, equivalent models, valid, respectively, for electrolytes and non-electrolytes, whose merits were discussed in detail by Chen, Sangster, Teng, and Lenzi (1973)

Several authors attempted to correlate water activities with freezing point depression, with moderate success: Ferro-Fontan and Chirife (1981),

Lerici, Piva, and Rosa (1983) and Chen (1987)

Lin, Zhu, Mei, and Yang (1996) proposed a simplied formula with two parameters per solute and one additional per binary interaction;Comesa~na, Correa, and Sereno (2000) extended to sugars and salts

Roa and Tapia (1998) proposed a very simple yet reasonably successful formula with a single parameter per solute in mixed multicomponentsolutions

2. Semi-empirical equations

A rst group includes empirical approximation of deviations from Raoult's law, Caurie (1985) and the very successful model by Chen (1989,1990), which unfortunately involves three empirical parameters per solute

Based on the identity between equilibrium relative humidity and thermo-dynamic activity, Norrish (1966), developed one of the most successfulequations applicable to non-ionic solutes; extensions were made by Chuang and Toledo (1976) and Chirife, Ferro-Fontan, and Benmergui (1980)

calculated an improved set of parameters which has been generally adopted since then

Based on the GibbsDuhem equation for multicomponent aqueous solutions, Ross (1975) proposed a simple and successful mixing rule topredict water activity of multicomponent solutions; extensions made by Ferro-Fontan, Chirife, and Boquet (1981) and Ruegg and Blanc (1981)

3. Local composition models WILSON model has been used in some models combined with other contributions and is the basis of ASOG group contribution method topredict thermodynamic equilibria. Sorrentino, Voilley, and Richon (1986), used it to predict activity coecients of aroma compounds and

Kawaguchi, Kanai, Kajiwara, and Arai (1981, 1982), of electrolytes; Correa, Comesa~na, and Sereno (1994) applied to sugar/polyol/urea; later

Correa, Comesa~na, Correa, and Sereno (1997) applied to electrolyte solutions, introducing modications to Kawaguchi's approach

UNIQUAC model was used by Le Maguer (1981), Saravacos and Marino-Kouris (1990) and Sander, Fredenslund, and Rasmussen (1986),combined with DebyeHuckel contribution and applied to electrolyte systems. Le Maguer (1992) proposed a building block concept to calculate

individual molecular parameters. This model is the basis of the well-known UNIFAC group contribution method; Choudhury and Le Maguer

(1986) used it with glucose solutions; Gabas and Laguerie (1992) with sugar solutions; Achard, Gros, and Dussap (1992) with sugars and polyols;

Catte, Dussap, and Gros (1995) and Peres and Macedo (1997) introduced some improvements to describe sugars; Christensen, Sander,

Fredenslund, and Rasmussen (1983) and Kikic, Fermeglia, and Rasmussen (1991) applied to electrolytes. Velezmoro and Meirelles (1998) applied

the concept to systems of organic acids; Ninni, Camargo, and Meirelles (1999a, 2000), to polyethylene glycol and other systems with polyols;

Ninni, Camargo, and Meirelles (1999b), to aminoacids



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3. Solutions with electrolytes

Although some of the general models included inTables 1 and 2 have proved to be able to describe

aqueous electrolyte solutions, this group of systems has

deserved, from the early stages, a special separate at-

tention. Eective empirical and semi-empirical equa-

tions were derived, but their contribution to the

theoretical understanding of these systems has been

minimal. Several reviews have been published during the

last 20 years, focusing particular lines of research; a

special mention about the work of Zemaitis, Clark,

Rafal, and Scrivner (1986) where much of the published

previous information including data are collected and

that of Renon (1986). Loehe and Donohue (1997) give a

list of such reviews together with a general broad view of

recent advances.

Before 1985, most of the works have been conducted

along the principles introduced by Debye and Huckel

(1923) theories and their modication by Pitzer (1973),

Bromley (1973) and Sandler (1977). In terms of new

theoretical research on electrolyte systems, modern de-

velopments follow, according to Loehe and Donohue

(1997), four major lines: (i) extensions to DebyeHuckel

theories, which assume the system to be made of

charged ions in a continuous dielectric medium, and

employ dierent forms of the PoissonBoltzman equa-

tions to calculate potential energies in the system; (ii)perturbation theories that use a series expansion of the

Helmholtz free energy about a given reference state; (iii)

integral equation theories that include solutions of the

OrnsteinZernicke equation, namely using the spherical

approximation concept and (iv) uctuation solution or

Table 4

Values oftFHi and tki for some compounds considered

Compound tFHi Groups: tki

Glucose 12 GR:6 CPOH:4 CH2:1 OH:1

Fructose 12 FR:5 CPOH:3 CH2:2 OH:2

Sucrose 23 GR:6 FR:5 CPOH:5 CH2:3

Glycerol 6 POH:3 CH2:2.8 OH:3 O:1

Urea 4 UREA:4

Water 1 H2O:1.6

Partial list of ASOG group pair parameters, including the new groups

H2O GR FR O CPOH CH2 OH POH Urea

H2O )1.6667 )0.8312 )20.26 0.2826 0.5045 1.4318 )3.714 )0.0067 m

0.7717 1.5856 )1.2186 2.170 )2382. )280.2 )2.418 )2.186 n

GR 0.7435 0.8393 1.8119 2.014 0.3248 0.1652 )0.9060 1.0312 m

1.3432 )1.2930 )6.468 0.3987 3.473 1.5168 7.833 )4.198 n

FR )0.0377 )14.561 1.2042 0.6475 0.8477 0.7318 )1.6816 )2.126 m

)0.8764 )1.5918 0.2919 1.5562 1.6635 0.9593 2.309 )4.814 n

Fig. 1. Ring structures for sugars in aqueous solution.

Table 3

New ASOG interaction groups

POH Polyalcohol OH groups linked to consecutive carbon atoms in a linear chain

FR Fructose ring Furanose cyclic structure of fructose in water

GR Glucose ring Pyranose cyclic structure of glucose in waterCPOH Cyc lic polyalcohol OH groups linke d to conse cutive c arbon atoms in a c yclic sugar st ruc ture

UREA Urea Urea molecule



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KirkhoodBu theories, accounting for composition

uctuations in an open system.

From an applied engineering point of view recentresults on electrolyte systems may be divided into three

major groups (Loehe & Donohue, 1997): (i) local com-

position and hydration models, (ii) empirical and semi-

empirical equations of state for electrolyte systems and

(iii) equations for mixed electrolytes and mixed solvents.

These are summarised in Table 5.

4. Temperature eect on aW

Dependence of activity coecient on temperature

may be expressed in terms of the excess partial molar

enthalpy or the partial molar excess heat of mixing as

(Prausnitz et al., 1986):

d ln cidT

P

hEi

RT2: 6

After integration between two dierent temperatures, a

form of the well-known ClausiusClapeyron equation is

obtained:

lnaW T1aW T2

hEWR

1

T1

1

T2

; 7

when hEW is constant along the path T1 to T2.

In spite of this elegant way of expressing temperature

dependence, some empirical equations have been pro-

posed (e.g. Scott & Bernard, 1983; Kitic, Jardim, Fav-etto, Resnik, & Chirife, 1986), often involving a

considerable number system specic parameters.

Those models which involve local composition based

concepts (Wilson, NRTL, UNIQUAC) as well as

equations of state have explicit dependence on temper-

ature (and in some cases pressure), making this depen-

dence automatic.

5. Comparing model predictions with experimental data

As all the required information to apply the models

included in Tables 1, 2 and 5 is detailed in the originalpapers and some of the indicated reviews, they will not

be reproduced here; the reader is invited to look at those

papers for such information.

Several comparative studies have been presented in

the past, most of them involving only a small group of

models. It is apparent from these studies that for many

systems of growing interest for the food industry, there

is still a very important lack of reliable experimental

data on thermophysical properties. Experimental tech-

niques to measure them are delicate and very time

consuming.

Table 5

Equations for electrolyte solutions

1. Hydration models: ionsolvent interaction is modelled as producing solvated aggregates characterised through the use of solvating numbers and

solvating energy; this approach has been applied for many years

Zdanovskii (1936) and Stokes and Robinson (1966): based on a linear relation existing between the molalities of isopiestic systems of single ormixed solutes

Robinson and Bower (1965): use specic expressions to describe hydration and association of ions in solution

Pitzer (1973): is a virial development ofGE

in terms of molalities of the solutions; is very widely used Meissner and Tester (1972): use a relation of mean ionic activity coecient and ionic force of the solution through a single parameter per salt

Bromley (1973): improved previous model including extended DebyeHuckel equation Chirife et al. (1980): proposed a relation between solutions of mixed solutes and single solutes of same ttal ionic strength

Heyrovska (1989): considers the association degree and hydration number as parameters for direct correlation of equilibrium data Schoenert (1990a,b) and subsequent work: used expressions ofGE of hydrated and associated ions, modifying Robinson and Stokes hydrationmodel

2. Local composition models: model ionsolvent interaction on a local basis, trying then to generalise to the whole system

Chen, Britt, Boston, and Evans (1982) and Chen and Evans (1986): use NRTL + PitzerDebyeHuckel; good for low and moderateconcentrations of strong electrolytes

Liu, Wimby, and Gren (1989) and Liu and Gren (1991): use WILSON+ DebyeHuckel contribution

Haghtalab and Vera (1991): two parameter non-random model to calculate GE

Cardoso and O'Connel (1987): combined UNIQUAC+DebyeHuckel contribution

Kawaguchi et al. (1981, 1982) and Correa et al. (1997): use WILSON based ASOG group contribution coupled with hydration model for cations

3. Aqueous mixed electrolytes: concentrates in developing mixing rules that can be used with single solute models Clegg and Pitzer (1992) and Lu and Maurer (1993): combine DebyeHuckel with UNIQUAC for mean ionic activity and osmotic coecient,proposing a mixing rule for mixed systems

4. Equation of state models: used mostly to predict the behaviour at high temperature and pressures

Pitzer and Tanger (1989), Anderko and Pitzer (1993,) and Economou, Peters, and Arons (1995): equations of state able to predict phasebehaviour of electrolyte systems at high temperature

Ikonomou and Donohue (1986) and Jin and Donohue (1988a,b): introduced the associated-perturbed-anisotropic-chain theory to describeaqueous halides between 200C and 500C

Wu et al. (1969): combine Pitzer virial equation with Fowler and Guggenheim (1939), long-range contribution



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The use of more recent techniques, like group con-

tribution methods or equations of state, has not yet been

the object of extensive comparative studies, justifying

thus this analysis targetting the case of osmotic solu-tions. For such a purpose, using some of the more

successful models, predictions of water activity for two

sugar solutions (glucose and sucrose, Tables 6 and 7 and

Figs. 2 and 3), sodium chloride solution (Table 8, Fig. 4)

and two mixed solute solutions (sucrosesodium chlo-

ride and glucosesodium chloride, Tables 9 and 10 and

Figs. 5 and 6) were made and compared. These systems

are believed to be the most common solutions for os-

motic treatment processes.

The meaning of the statistical parameters ARD and

RMS in the tables is as follows:

ARD average relative deviation

1

nXn

1

aWicalc aWiexp

1 awiexp 100; 8

RMS root mean square1

n

Xn1

aWicalc aWiexp1 aWiexp

100

!2vuut:

9

6. Conclusions

Analysis of the comparative performance of dierent

predictive models for water activity has revealed that

Table 6

Prediction of water activity in glucosewater solutions

Reference Model/Equation ARD (%) RMS Experimental data

Norrish (1966) and Chirife et al.

(1980) (parameters)

Norrish (1966) 0.63 0.89 Stokes and Robinson

(1966)

Chen (1989) Chen (1989) 0.65 0.95 Stokes and Robinson

(1966)

Table 7

Prediction of water activity in sucrosewater solutions


Norrish (1966) and Chirife et al.

(1980) (parameters)

Norrish (1966) 2.8 3.9 Robinson and Stokes

(1961)

Chen (1989) Chen (1989) 2.8 3.9 Robinson and Stokes

(1961)

Lerici et al. (1983) Lerici et al. (1983) 12.7 14.5 Lerici et al. (1983)

Fig. 2. Water activity of aqueous glucose solution: experimental data

(symbols) and predictive models (lines).

Fig. 3. Water activity of aqueous sucrose solution: experimental data

(symbols) and predictive models (lines).



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good estimations may be obtained, not only from em-

pirical equations with parameters tted to experimental

data but also from theoretical models derived from ex-

pressions of the excess Gibbs free energy and from

equations of state.

It is somehow surprising how good the predictions

made from group contribution models are. These truly

predictive models use group interaction parameters not

necessarily calculated from data involving the compo-

nents of interest. Due to these capabilities, further eortand testing should be devoted to this group of tech-

niques.

For practical applications of osmotic treatments, the

most widely used equations for prediction of water ac-

tivity in binary are the ones of Norrish (1966) and Ross

(1975) (see also Lopez-Malo, Palou, Welti, Corte, &

Argaiz, 1994; Guerrero et al., 1996; Alzamora, 1997;

Nieto, Salvatori, Castro, & Alzamora, 1998). Parame-

ters calculated by Chirife et al., 1980 should be preferred

for use with Norrish equation. For solutions containing

electrolytes, Pitzer (1973) and Chen (1989, 1990) equa-

Table 9

Prediction of water activity in sucrosesodium chloridewater solutions


Teng and Seow (1981) Ross (1975) 1.09 1.13 Robinson, Stokes, and Marsh (1970)a

Chen (1990) Chen (1989) and Ross (1975) 1.25 1.41 Robinson et al. (1970)

Comesa~na et al. (2000) Lin et al. (1996) 1.78 1.92 Robinson et al. (1970)a

Correa et al. (1997) ASOG 2.48 3.54 Robinson et al. (1970)a

Teng and Seow (1981) Chirife et al. (1980) 2.62 3.1 Robinson et al. (1970)a

Teng and Seow (1981) ZdanovskiiStokesRobinson 2.99 3.3 Robinson et al. (1970)a

Roa and Tapia (1998) Roa and Tapia (1998) 7.15 9.52 Robinson et al. (1970)a

Chuang and Toledo (1976) Modied Norrish/Ross (1975) 14.2 16.4 Chuang and Toledo (1976)

a As reported by Teng and Seow (1981).

Fig. 4. Water activity of aqueous sodium chloride solution: experi-

mental data (symbols) and predictive models (lines).

Table 8

Prediction of water activity in sodium chloridewater solutions


Pitzer (1973) Pitzer (1973) 0.14 0.25 Robinson and Stokes (1965)

Correa et al. (1997) ASOG 1.67 2.33 Robinson and Stokes (1965)

Chen (1989) Chen (1989) 2.8 3.9 Robinson and Stokes (1965)

Roa and Tapia (1998) Roa and Tapia (1998) 9.35 10.7 Robinson and Stokes (1965)

Table 10

Prediction of water activity in glucoseNaCl solutions


Chen (1990) Chen (1990)/Ross 1.83 2.66 Comesa~na et al. (2000)

Comesa~na et al. (2000) Lin et al. (1996) 1.61 2.33 Comesa~na et al. (2000)

This work ASOG 8.4 9.3 Comesa~na et al. (2000)

Roa and Tapia (1998) Roa and Tapia (1998) 8.9 9.7 Comesa~na et al. (2000)



9/12

tions are recommended. For water activity of multi-component mixtures good results are obtained using

Ross (1975) equation with any of the already mentioned

single solute models. Recently Roa and Tapia (1998)

have proposed a simple equation, based on the rst-

order sum of molalities, with a reasonable predictive

accuracy.

The use of UNIFAC and ASOG models as well as

equations of state, although constituting a good and

accurate tool to estimate the activity coecients of non-

electrolyte and electrolyte mixtures, are not yet widely

used in everyday practical application of osmotic treat-

ments. The development of computer-aided tools al-lowing a simpler manipulation of such complex models

may contribute to their popularity and should be en-

couraged.

Acknowledgements

The authors acknowledge the support of project

XI.12, Programme CYTED, and EU project FAIR-

CT96-1118 and of project XUGA 30101B98 of Xunta

de Galicia.

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