A Mathematical Modeling of Freezing Process in the Batch Production of Ice Cream

Abstract

This study deals with the mathematical modeling of crystallization kinetics occurring during batch production of the ice cream. The temperature decrease was recorded in-situ through a computerized wireless system. A robust pattern-recognition algorithm of the experimental cooling curves was developed to determine the initial freezing point. The theoretical freezing point was used to calibrate the whole time-temperature profile. Finally, a modified Gompertz’s function was used to describe the main steps of crystallization kinetics. Derivative analysis of the Gompertz’s function allowed to determine the time-temperature physical markers of dynamic nucleation, ice crystal growth and air whipping. Composition and freezing properties were used as input variables in multivariate analysis to classification purposes of the ice cream mixtures as a function of their ability to produce high-quality ice cream. The numerical analysis of the whole cooling curve was used to build predictive models of the ice cream quality indices.

Keywords

• Gompertz’s function
• ice cream
• initial freezing point
• supercooling
• time-temperature profile