Water activity in multicomponent model food systems from thermodynamic activity coefficient equations

Water activity is an important food preservation criterion affecting various types of spoilage reactions and microbial growths. A number of empirical equations for predicting this parameter in model food systems are available in the literature. However, no attempt has thus far been made to use these thermodynamic equations for this purpose.;The present study is concerned with the application of four well known thermodynamic equations for the calculation of activity coefficients to the calculation of the water activities of model food systems. The activity coefficient is a measure of the lowering of the vapor pressure exerted in and above an aqueous mixture due to associations of the water molecules with the mixture ingredients.;The equations studied were the two-suffix Margules equation, the three-suffix Margules equation, the van Laar equation, and the Wilson equation. These activity coefficient equations were applied to the calculation of the water activities of ternary solutions at room temperature for all combinations of two of the following four ingredients plus water: glucose, fructose, sucrose, and glycerol. The calculated data were compared with measured laboratory data and with standard data calculated with the UNIQUAC equation using parameters from the literature.;The three-component forms of the activity coefficient models are compiled as combinations of the binary forms. All of the binary parameters that are present in each of the three binary activity coefficient equations relating the three components of a ternary solution are present in the ternary solutions; but, with the exception of the three-suffix Margules equation, no additional ternary parameters are involved, and this is the convenient advantage of these equations: no additional parameters other than those of the binary solutions are needed. Parameters of the binary forms are obtained by curve-fitting activity coefficient versus water mole fraction by nonlinear regression.;The results indicate very good prediction of the three-component water activities for the complete range of solubility of the solid components. In particular, it was found that the two-suffix Margules equation, which models the type of symmetric behavior of binary component versus mole fraction present in these solutions, and the Wilson equation, fit this data very well. The van Laar equation was also good, but the three-suffix Margules equation was found to need further modification for the three-component calculations, particularly when one data set was involved. (Abstract shortened by UMI.)...