STUDY OF MATHEMATICAL MODELS TO ESTIMATE THE FREEZING TEMPERATURE OF FRUIT JUICES

Several empirical and theoretical equations predict the freezing temperature of food systems through soluble solids content. In this work, we compare four models using the experimental freezing data of Auleda et al. [Journal of Food Engineering, 105 (2011), 289-294] for pear, apple and peach juices, in the range of 10-40°Brix. EMSO software estimated the parameters with a 95% confidence level. We demonstrated that model 2 is undefined for some values of soluble solids content when its parameter is positive and is converted to model 1 when the parameter is negative. On the other hand, model 3 is the most suitable model for freezing fruit juices, since it gives lower deviations and prediction errors, and higher viable range of concentration. Its parameter was rewritten as a function of the carbohydrates content and the weighted proportions of their volumes and hydroxyl groups, that is, the chemical nature of the solute was successfully inserted into the model. Based on statistical evidence, the soluble solids content of sucrose contributes most to the determination of the parameter and the prediction of the freezing temperatures. The prediction of the freezing temperatures of concentrated juices by using models 2 and 3 are challenging, once the prediction errors increase with the fourth power of the soluble solids content. To keep validating the models, freezing studies of more concentrated juices are required.