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) pro- cessing, 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). 0260-8774/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 5 0 0 ) 0 0 221-1 104 A.M. Sereno et al. / Journal of Food Engineering 49 92001) 103±114 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.