Specific Mass Growth Rate of Sugar Crystals: Probabilistic Modeling

Introduction. The present research featured industrial sugar crystallization. The article introduces a generalized mathematical model of specific growth rate of sugar crystals depending on temperature, solids, and the purity of solution, as well as on the concentration and average size of crystals. The model includes the probabilistic component of growth rate of monocrystals and the reduced adjustment of the constrained crystal growth depending on the abovementioned as-pects. Study objects and methods. The research focused on mass crystallization of sucrose, including the growth rate of monocrystals and the number of crystals in the fill mass. The obtained experimental data were processed using nonlinear programming. Results and discussion. 421 experiments made it possible to develop a probabilistic mathematical model of specific mass growth rate of sugar monocrystals and its dependence on the solution temperature, purity, and solids content. Model error: ± 11.3%. The model covers the temperature range, concentration of solids, and purity of the solution. The proximity of crystals was calculated according to the dependence of the growth rate on their concentration and the average size (error: ± 1.3%). The adjustment range: concentration of crystals = 5–60%, average size = 0.25–1.50 mm. Conclusion. The present generalized mathematical model of crystallization considered the temperature, as well as the purity and solids content in the fill mass, the concentration of sucrose crystals and their average size. The research compared the effect of linear size and concentration of sugar monocrystals on the calculated and experimental sizes of specific mass growth rate and the dimensionless adjustment of growth rate. The calculated sizes proved to be close to the ex-perimental data, which showed adequacy to the developed crystallization model. The research results can be used to optimize the process of mass sugar crystallization.