Prediction of Water Activity of Osmotic Solutions A.M

Journal of Food Engineering 49 52001) 103±114 www.elsevier.com/locate/jfoodeng

Prediction of water activity of osmotic solutions A.M. Sereno a,*, M.D. Hubinger b, J.F. Comesana~ c, A. Correa c

a Department of Chemical Engineering, University of Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal b 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 signi®cant number of theoretical thermodynamic models that are 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. Ó 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Osmotic dehydration; Vapour±liquid equilibria; Water activity; Sugars; Electrolytes; Aqueous solutions; Predictive models

1. Introduction Rios, & Raoult-Wack, 1998; Sabadini, Carvalho, So- bral, & Hubinger, 1998), as well as for fruit products, Osmotic treatments involve the contact of a material, when the correct choice of solutes and a controlled ratio usual of vegetal or animal origin, with a concentrated of water removal and impregnation allow to enhance aqueous solution and include namely osmotic dehydra- their natural ¯avour and colour retention 5Raoult-Wack tion and solute impregnation processes. These constitute et al., 1994; Guerrero, Alzamora, & Gerschenson, 1996; simple food processing operations conducted at ambient Alzamora, 1997; Forni, Sormani, Scalise, & Torregiani, or near ambient temperature, which achieve a signi®cant 1997; Spiess & Behsnilian, 1998). degree of dewatering without phase change and allowing As a preliminary step to convective air drying, some degree of product formulation and even restruc- several studies are found in the recent literature as well turing. as its in¯uence on ®nal food properties 5Lenart, 1996; A special mention should be made about the use of Del Valle, Cuadros, & Aguilera, 1998; Sa, Figueiredo, osmotic treatments in the preparation of intermediate & Sereno, 1999; Salvatori, Andres, Chiralt, & Fito, moisture foods 5IMF) and the so-called fourth genera- 1999; Lewicki & Lukaszuk, 2000; Krokida, Kiranou- tion or minimally processed foods. Such processes have dis, Maroulis, & Marinos-Kouris, 2000). The combi- been also referred to as dewatering and impregnation nation of osmotic dehydration to some less common soaking 5Raoult-Wack, Rios, Saurel, Giroux, & Guil- drying steps, such as microwave drying 5Venkatacha- bert, 1994) and are mainly being used as a pre-treatment lapathy & Raghavan, 1999) and freeze-drying 5Ka- introduced in any conventional fruit and vegetable rathanos, Anglea, & Karel, 1996) has also been processing, in order to improve quality, reduce energy described. costs or even formulate ®nal products. Applications Osmotic pre-treatments may be used before vacuum have been reported for ®sh and certain meat products frying, by immersion in solutions of high osmotic pres- 5Collignan & Raoult-Wack, 1994; Bohuon, Collignan, sure 5Spiess & Behsnilian, 1998), the eect on mass transfer rates of high hydrostatic pressure 5HPP) processing, previous to osmotic treatment of vegetable tis- * Corresponding author. Fax: +351-22-508-1440. sues was also investigated 5Rastogi & Niranjan, 1998; E-mail address: [email protected] 5A.M. Sereno). Rastogi, Angersbach, & Knorr, 2000).

Nomenclature T temperature 5K) x mole fraction a activity ARD average relative deviation 5%) Greeks f fugacity c activity coecient E FH G Gibbs free energy 5J) ti no. of non-hydrogen atoms in molecule i E À1 g molar Gibbs free energy 5J mol ) tki no. of non-hydrogen atoms in group k of component i h molar heat of mixing 5J molÀ1) Subscripts M molar mass kg molÀ1 i component i P pressure 5Pa) W water p partial pressure 5Pa) R gas constant Superscripts RH relative humidity 5%) ° reference state RMS root mean square

The transfer of mass, water and solutes observed It is usually assumed that under normal working during the contact of a solid material with an osmotic conditions of ambient temperature and atmospheric solution is due to dierences in chemical potential inside pressure, gas phases behave ideally and so the ratio of and outside the material, usually expressed in terms of fugacities can be taken as the ratio of partial pressures the corresponding activity coecients. As dehydration is 5Reid, Prausnitz, & Poling, 1987): the main objective of osmotic treatments, the activity of fW pW water in both the material and the solution and its ; 2 f 0 p0 prediction is of major importance. This relevance is W W 0 particularly emphasised when mathematical models are where pW and pW are the vapour pressures of water in used to describe the process. For cellular materials, as is the system and of pure liquid water at the same tem- the case of most foods, water transfer takes place in the perature, respectively. Under this assumption, from vicinity of the cell through the semi-permeable cell Eq. 51): membrane 5Le Maguer, 1988); again dierence of water p RH a W ; 3 activity in both sides governs its physical behaviour and W p0 100 mass transport. W The thermodynamic description of these osmotic so- where RH is the percent relative humidity of the air lutions has been the object of intense research all along layer in equilibrium with the sample. The activity coef- the last century, particularly those involving sugars and/ ®cient cW may be calculated directly from the partial E or salts. Excellent reviews of such eorts have been molar excess Gibbs energy of water, gW 5Prausnitz et al., written by Van den Berg and Bruin 51981) and Le Ma- 1986): guer 51992) to mention only two papers. Most thermo- gE RT ln c ; 4 dynamic models used to describe vapour±liquid W W E equilibrium of osmotic solutions are based on relations and for the total molar excess Gibbs energy, g : X involving Gibbs free energy of the system. Of particular E g RT xi ln c 5 E i interest is the excess Gibbs energy 5G ) and for each of i the components the partial molar excess Gibbs energy for an ideal solution all the activity coecients, 5gE), both allowing a convenient way to quantify the i c T ; P; x, are equal to one, corresponding to an excess deviations from ideal behaviour. i Gibbs energy equal to zero. From GE, a large number of physical parameters may Several approaches have been used to calculate or be calculated such as water and solute activities, partial estimate excess Gibbs energy in liquid solutions, in- equilibrium properties 5solubility, relative volatility, cluding empirical models based on solution composi- etc.) and others 5Le Maguer, 1989). tion, the use of equations of state extended to the The activity of water in aqueous solutions is de®ned description of condensed phases and probably more as 5Prausnitz, Lichtenthaler, & Azevedo, 1986): often, dierent theories developed to describe solution f T ; P; x structure and interactions among the chemical species. a T ; P; xc T ; P; xx W ; 1 W W W f 0 T ; P 0; x0 In Table 1 the major methodological groups used by W published contributions to the prediction of water ac- where aW is the water activity, xW is the mole fraction of tivity of solutions are indicated. water, cW is the activity coecient for water, fW; fW ° are Most of the models included in Table 1 are general in the fugacities of water in the system and at reference themselves and may be used with food and related sys- conditions, respectively. tems 5Prausnitz et al., 1986; Le Maguer, 1992). The A.M. Sereno et al. / Journal of Food Engineering 49 92001) 103±114 105

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 liquid±vapour and liquid±liquid equilibria; served in some cases as the basis for more complex models: Margules equation, the Wohl expansion, Van Laar equation, Redlich±Kister equation, Scatchard±Hamer equation Use of equations of state 9EOS) Hu, Liu, Soane, and Prausnitz 51991): use double lattice 5Freed & Flory-Huggins) to calculate Helmholtz energy of mixing, used to describe equilibrium in non-polar or slightly polar non-ideal systems Wu, Lin, Zhu, and Mei 51969): use modi®ed version of Pitzer 51973) virial EOS with Fowler and Guggenheim 51939) instead of the more common Debye±Huckel contribution of long-range electrostatic forces Simonin 51999): uses McMillan±Mayer theory, assuming molecules as hard bodies interacting through van der Waals short range forces; to allow for the presence of polar molecules 5alcohols) and weak electrolytes, and a volume exclusion contribution using Carnahan±Starling hard sphere EOS Solution theories Van der Waals±van Laar theory: valid only for nearly ideal systems Regular solution theory 5Hildebrand, 1929; Scatchard, Hamer, & Wood, 1938): systems without interactions among polar molecules 5athermal), e.g. hydrocarbons Debye and Huckel 51923) introduced a successful description of long-range polar and ionic forces contribution Lattice theory due mostly to Guggenheim 51935, 1952) and Eyring and Marchi 51963) Flory 51941, 1942) and Huggins 51942) extension of lattice theory to polymer solutions Local-composition models, namely Wilson 51964); NRTL model of Renon and Prausnitz 51968); UNIQUAC model of Abrams and Prausnitz 51975)

diculties usually arise from the fact that as most food a technique for aW prediction for complex systems systems are not well characterised both from a chemical without requiring parameters for each speci®c com- and structural point of view, and consequently ther- pound, but instead characteristic interaction parameters mophysical property data required to use 5and ®t) the for the chemical groups that constitute each molecule. models to such systems are not available. One way to The eect in the solution of each of such chemical group overcome these diculties in practical applications is to is assumed to be the same, irrespective of the molecule look for correlations between these thermodynamic where it is contained. properties and some easy method to measure physical The ASOG method, based on the Wilson model properties. This approach produced a series of empirical 5Wilson, 1964), has been used for this purpose by Correa and semi-empirical models which provide in many cases et al. 51994), who obtained good aW predictions for excellent results and constitute relevant contributions of aqueous solutions of both sugar/polyol and sugar/urea. widespread use in the food industry 5Table 2). Kawaguchi et al. 51981, 1982) have combined the All the models mentioned in Tables 1 and 2 refer to method with an hydration model of ionic species origi- solutions, more speci®cally aqueous solutions. A parallel nated in aqueous solutions of electrolytes; later Correa eort has been dedicated to the correlation and predic- et al. 51997) have rede®ned the groups in solution, ob- tion of sorption isotherms in solid foods; a large number taining improved predictions for several binary and of equations and models used to describe and predict multicomponent salt solutions. water activity and sorption isotherms of food systems Attempts to predict water activity using UNIFAC containing solid phases 5Van den Berg & Bruin, 1981; have also been extensively reported. Choudhury and Le

Iglesias & Chirife, 1982). Such models were not included Maguer 51986) used this method to predict aW in glucose here, as only aqueous solutions constituted the scope of solutions and Achard et al. 51992) described its use to this work. estimate activity coecients in aqueous systems con- An alternative approach to the use of empirical and taining sugars and polyols; Catte et al. 51995) used the semi-empirical equations consists in the application of same group typology as suggested by Correa et al. group contribution methods, namely ASOG 5analytical 51994) to characterise sugars, and successfully estimated solutions of groups, Derr & Deal, 1969; Kojima & several thermodynamic properties. Christensen et al. Tochigi, 1979) and UNIFAC 5UNIQUAC functional 51983) and Kikic et al. 51991) applied the same model to group activity coecients, Fredenslund, Jones, & predict equilibria in salt solutions. Very interesting ex- Prausnitz, 1975; Larsen, Rasmussen, & Fredenslund, tensions to cover organic acids 5Velezmoro & Meirelles, 1987). These two proposals probably constitute the only 1998), polyethylene glycol and other polyols 5Ninni et general accessible predictive technique for water activity al., 1999a, 2000), aminoacids 5Ninni et al., 1999b) have of osmotic solutions. Their main advantage is to provide been developed by Meirelles and co-workers. 106 A.M. Sereno et al. / Journal of Food Engineering 49 92001) 103±114

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 51940), Money and Born 51951) and Dunning, Evans, and Taylor 51951) Zdanovskii 51936) and Stokes and Robinson 51966) proposed independently, equivalent models, valid, respectively, for electrolytes and nonelectrolytes, whose merits were discussed in detail by Chen, Sangster, Teng, and Lenzi 51973) Several authors attempted to correlate water activities with freezing point depression, with moderate success: Ferro-Fontan and Chirife 51981), Lerici, Piva, and Rosa 51983) and Chen 51987) Lin, Zhu, Mei, and Yang 51996) proposed a simpli®ed formula with two parameters per solute and one additional per binary interaction; Comesana,~ Correa, and Sereno 52000) extended to sugars and salts Roa and Tapia 51998) proposed a very simple yet reasonably successful formula with a single parameter per solute in mixed multicomponent solutions 2. Semi-empirical equations A ®rst group includes empirical approximation of deviations from Raoult's law, Caurie 51985) and the very successful model by Chen 51989, 1990), which unfortunately involves three empirical parameters per solute Based on the identity between equilibrium relative humidity and thermo-dynamic activity, Norrish 51966), developed one of the most successful equations applicable to non-ionic solutes; extensions were made by Chuang and Toledo 51976) and Chirife, Ferro-Fontan, and Benmergui 51980) calculated an improved set of parameters which has been generally adopted since then Based on the Gibbs±Duhem equation for multicomponent aqueous solutions, Ross 51975) proposed a simple and successful mixing rule to predict water activity of multicomponent solutions; extensions made by Ferro-Fontan, Chirife, and Boquet 51981) and Ruegg and Blanc 51981) 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 to predict thermodynamic equilibria. Sorrentino, Voilley, and Richon 51986), used it to predict activity coecients of aroma compounds and Kawaguchi, Kanai, Kajiwara, and Arai 51981, 1982), of electrolytes; Correa, Comesana,~ and Sereno 51994) applied to sugar/polyol/urea; later Correa, Comesana,~ Correa, and Sereno 51997) applied to electrolyte solutions, introducing modi®cations to Kawaguchi's approach UNIQUAC model was used by Le Maguer 51981), Saravacos and Marino-Kouris 51990) and Sander, Fredenslund, and Rasmussen 51986), combined with Debye±Huckel contribution and applied to electrolyte systems. Le Maguer 51992) 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 51986) used it with glucose solutions; Gabas and Laguerie 51992) with sugar solutions; Achard, Gros, and Dussap 51992) with sugars and polyols; Catte, Dussap, and Gros 51995) and Peres and Macedo 51997) introduced some improvements to describe sugars; Christensen, Sander, Fredenslund, and Rasmussen 51983) and Kikic, Fermeglia, and Rasmussen 51991) applied to electrolytes. Velezmoro and Meirelles 51998) applied the concept to systems of organic acids; Ninni, Camargo, and Meirelles 51999a, 2000), to polyethylene glycol and other systems with polyols; Ninni, Camargo, and Meirelles 51999b), to aminoacids

These extensive and successful applications of the two some of the compounds found in food-related systems major group contribution methods to predict water ac- are too complex and sometimes new groups have to be tivity of osmotic solutions constitute an example, pos- identi®ed and characterised. This happened with sug- sibly one of the earliest, of the use of advanced ars. Sugars in aqueous solutions, both monosaccha- thermodynamic models to describe the behaviour of rides, like glucose and fructose, and disaccharides, like food-related systems. sucrose, adopt a cyclic structure made of pyranose and furanose unit rings 5Fig. 1). To successfully describe such compounds by the ASOG method, Correa et al. 2. How group contribution methods work 51994) de®ned three new groups named GR, FR and CPOH standing for `glucose ring', `fructose ring' and The main principle underlying this technique is the `cyclic-polyalcohol' 5OH groups linked to consecutive assumption that all chemical functional groups in solu- carbon atoms in a cyclic sugar structure). For polyhy- tion interact with other speci®c groups in a similar way, dric alcohols 5e.g. glycerol, mannitol and sorbitol) a independent of the types of groups in presence and of new group POH referring to OH groups linked to the speci®c molecules where they are contained. To use consecutive carbon atoms in a linear chain was also the method the ®rst step consists in `breaking' the adopted. A ®fth `group' de®ned was UREA for the structure of the molecule in all its basic groups, for urea molecule, as it could not be adequately repre- which interaction and individual geometric parameters sented by a combination of available ASOG groups are available. Since then, the method is applied as if the 5Table 3). solution was made of known groups instead of unknown The method uses two speci®c individual group pa- FH molecules. rameters ti and tki, and four interaction parameters for Since their development the list of identi®ed and each binary pair of groups. Table 4 lists the values of well-characterised groups is increasing. Unfortunately these parameters for some relevant compounds. A.M. Sereno et al. / Journal of Food Engineering 49 92001) 103±114 107 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 51986) where much of the published previous information including data are collected and that of Renon 51986). Loehe and Donohue 51997) 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 51923) theories and their modi®cation by Pitzer 51973), Bromley 51973) and Sandler 51977). In terms of new theoretical research on electrolyte systems, modern de- velopments follow, according to Loehe and Donohue Fig. 1. Ring structures for sugars in aqueous solution. 51997), four major lines: 5i) extensions to Debye±Huckel theories, which assume the system to be made of 3. Solutions with electrolytes charged ions in a continuous dielectric medium, and employ dierent forms of the Poisson±Boltzman equa- Although some of the general models included in tions to calculate potential energies in the system; 5ii) Tables 1 and 2 have proved to be able to describe perturbation theories that use a series expansion of the aqueous electrolyte solutions, this group of systems has Helmholtz free energy about a given reference state; 5iii) deserved, from the early stages, a special separate at- integral equation theories that include solutions of the tention. Eective empirical and semi-empirical equa- Ornstein±Zernicke equation, namely using the spherical tions were derived, but their contribution to the approximation concept and 5iv) ¯uctuation solution or

Table 3 New ASOG interaction groups

POH Polyalcohol OH groups linked to consecutive carbon atoms in a linear chain FRFructose ring Furanose cyclic structure of fructose in water GRGlucose ring Pyranose cyclic structure of glucose in water CPOH Cyclic polyalcohol OH groups linked to consecutive carbon atoms in a cyclic sugar structure UREA Urea Urea molecule

Table 4 FH Values of ti and tki for some compounds considered

FH Compound ti 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 GRFR O CPOH CH 2 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 GR0.7435 ± 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 108 A.M. Sereno et al. / Journal of Food Engineering 49 92001) 103±114

Table 5 Equations for electrolyte solutions

1. Hydration models: ion±solvent 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 51936) and Stokes and Robinson 51966): based on a linear relation existing between the molalities of isopiestic systems of single or mixed solutes Robinson and Bower 51965): use speci®c expressions to describe hydration and association of ions in solution Pitzer 51973): is a virial development of GE in terms of molalities of the solutions; is very widely used Meissner and Tester 51972): use a relation of mean ionic activity coecient and ionic force of the solution through a single parameter per salt Bromley 51973): improved previous model including extended Debye±Huckel equation Chirife et al. 51980): proposed a relation between solutions of mixed solutes and single solutes of same ttal ionic strength Heyrovska 51989): considers the association degree and hydration number as parameters for direct correlation of equilibrium data Schoenert 51990a,b) and subsequent work: used expressions of GE of hydrated and associated ions, modifying Robinson and Stokes hydration model 2. Local composition models: model ion±solvent interaction on a local basis, trying then to generalise to the whole system Chen, Britt, Boston, and Evans 51982) and Chen and Evans 51986): use NRTL + Pitzer±Debye±Huckel; good for low and moderate concentrations of strong electrolytes Liu, Wimby, and Gren 51989) and Liu and Gren 51991): use WILSON + Debye±Huckel contribution Haghtalab and Vera 51991): two parameter non-random model to calculate GE Cardoso and O'Connel 51987): combined UNIQUAC+Debye±Huckel contribution Kawaguchi et al. 51981, 1982) and Correa et al. 51997): 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 51992) and Lu and Maurer 51993): combine Debye±Huckel 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 51989), Anderko and Pitzer 51993,) and Economou, Peters, and Arons 51995): equations of state able to predict phase behaviour of electrolyte systems at high temperature Ikonomou and Donohue 51986) and Jin and Donohue 51988a,b): introduced the associated-perturbed-anisotropic-chain theory to describe aqueous halides between 200°C and 500°C Wu et al. 51969): combine Pitzer virial equation with Fowler and Guggenheim 51939), long-range contribution

Kirkhood±Bu theories, accounting for composition In spite of this elegant way of expressing temperature ¯uctuations in an open system. dependence, some empirical equations have been pro- From an applied engineering point of view recent posed 5e.g. Scott & Bernard, 1983; Kitic, Jardim, Fav- results on electrolyte systems may be divided into three etto, Resnik, & Chirife, 1986), often involving a major groups 5Loehe & Donohue, 1997): 5i) local com- considerable number system speci®c parameters. position and hydration models, 5ii) empirical and semi- Those models which involve local composition based empirical equations of state for electrolyte systems and concepts 5Wilson, NRTL, UNIQUAC) as well as 5iii) equations for mixed electrolytes and mixed solvents. equations of state have explicit dependence on temper- These are summarised in Table 5. ature 5and in some cases pressure), making this dependence automatic.

4. Temperature eect on aW 5. Comparing model predictions with experimental data Dependence of activity coecient on temperature may be expressed in terms of the excess partial molar As all the required information to apply the models enthalpy or the partial molar excess heat of mixing as included in Tables 1, 2 and 5 is detailed in the original 5Prausnitz et al., 1986): papers and some of the indicated reviews, they will not be reproduced here; the reader is invited to look at those dlnc hE i À i : 6 papers for such information. 2 dT P RT Several comparative studies have been presented in After integration between two dierent temperatures, a the past, most of them involving only a small group of form of the well-known Clausius±Clapeyron equation is models. It is apparent from these studies that for many obtained: systems of growing interest for the food industry, there a hE 1 1 is still a very important lack of reliable experimental ln W T 1 W À ; 7 data on thermophysical properties. Experimental tech- a R T T W T 2 1 2 niques to measure them are delicate and very time E when hW is constant along the path T1 to T2. consuming. A.M. Sereno et al. / Journal of Food Engineering 49 92001) 103±114 109

Table 6 Prediction of water activity in glucose±water solutions

Reference Model/Equation ARD 5%) RMS Experimental data

Norrish 51966) and Chirife et al. Norrish 51966) 0.63 0.89 Stokes and Robinson 51980) 5parameters) 51966) Chen 51989) Chen 51989) 0.65 0.95 Stokes and Robinson 51966)

Table 7 Prediction of water activity in sucrose±water solutions

Reference Model/Equation ARD 5%) RMS Experimental data

Norrish 51966) and Chirife et al. Norrish 51966) 2.8 3.9 Robinson and Stokes 51980) 5parameters) 51961) Chen 51989) Chen 51989) 2.8 3.9 Robinson and Stokes 51961) Lerici et al. 51983) Lerici et al. 51983) 12.7 14.5 Lerici et al. 51983)

Fig. 2. Water activity of aqueous glucose solution: experimental data Fig. 3. Water activity of aqueous sucrose solution: experimental data 5symbols) and predictive models 5lines). 5symbols) and predictive models 5lines).

The use of more recent techniques, like group con- ARD average relative deviation tribution methods or equations of state, has not yet been 1 Xn a À a the object of extensive comparative studies, justifying Wi calc Wi exp Ã 100; 8 n 1 À a thus this analysis targetting the case of osmotic solu- 1 wi exp tions. For such a purpose, using some of the more successful models, predictions of water activity for two RMS root mean square v sugar solutions 5glucose and sucrose, Tables 6 and 7 and u !2 u1 Xn a À a 9 Figs. 2 and 3), sodium chloride solution 5Table 8, Fig. 4) t Wi calc Wi exp Ã 100 : n 1 À a and two mixed solute solutions 5sucrose±sodium chlo- 1 Wi exp ride and glucose±sodium 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- 6. Conclusions motic treatment processes. The meaning of the statistical parameters ARD and Analysis of the comparative performance of dierent RMS in the tables is as follows: predictive models for water activity has revealed that 110 A.M. Sereno et al. / Journal of Food Engineering 49 92001) 103±114

Table 8 Prediction of water activity in sodium chloride±water solutions

Reference Model/Equation ARD 5%) RMS Experimental data

Pitzer 51973) Pitzer 51973) 0.14 0.25 Robinson and Stokes 51965) Correa et al. 51997) ASOG 1.67 2.33 Robinson and Stokes 51965) Chen 51989) Chen 51989) 2.8 3.9 Robinson and Stokes 51965) Roa and Tapia 51998) Roa and Tapia 51998) 9.35 10.7 Robinson and Stokes 51965)

good estimations may be obtained, not only from empirical equations with parameters ®tted to experimental data but also from theoretical models derived from expressions 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 components of interest. Due to these capabilities, further eort and testing should be devoted to this group of techniques. For practical applications of osmotic treatments, the most widely used equations for prediction of water activity in binary are the ones of Norrish 51966) and Ross 51975) 5see 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 Fig. 4. Water activity of aqueous sodium chloride solution: experi- electrolytes, Pitzer 51973) and Chen 51989, 1990) equa- mental data 5symbols) and predictive models 5lines).

Table 9 Prediction of water activity in sucrose±sodium chloride±water solutions

Reference Model/Equation ARD 5%) RMS Experimental data

Teng and Seow 51981) Ross 51975) 1.09 1.13 Robinson, Stokes, and Marsh 51970)a Chen 51990) Chen 51989) and Ross 51975) 1.25 1.41 Robinson et al. 51970) Comesana~ et al. 52000) Lin et al. 51996) 1.78 1.92 Robinson et al. 51970)a Correa et al. 51997) ASOG 2.48 3.54 Robinson et al. 51970)a Teng and Seow 51981) Chirife et al. 51980) 2.62 3.1 Robinson et al. 51970)a Teng and Seow 51981) Zdanovskii±Stokes±Robinson 2.99 3.3 Robinson et al. 51970)a Roa and Tapia 51998) Roa and Tapia 51998) 7.15 9.52 Robinson et al. 51970)a Chuang and Toledo 51976) Modi®ed Norrish/Ross 51975) 14.2 16.4 Chuang and Toledo 51976) a As reported by Teng and Seow 51981).

Table 10 Prediction of water activity in glucose±NaCl solutions

Reference Model/Equation ARD 5%) RMS Experimental data

Chen 51990) Chen 51990)/Ross 1.83 2.66 Comesana~ et al. 52000) Comesana~ et al. 52000) Lin et al. 51996) 1.61 2.33 Comesana~ et al. 52000) This work ASOG 8.4 9.3 Comesana~ et al. 52000) Roa and Tapia 51998) Roa and Tapia 51998) 8.9 9.7 Comesana~ et al. 52000) A.M. Sereno et al. / Journal of Food Engineering 49 92001) 103±114 111 References

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