Mathematical Modeling of Crystallization Process from a Supercooled Binary Melt

The article is concerned with the analytical solution to the integro-differential system of balance and kinetic equations that describe the crystal growth phenomenon in a binary system for various nucleation kinetics. The effect of impurity concentration on the evolutionary behavior of crystals is shown. The nonlinear dynamics of a supercooled binary melt is studied with allowance for the withdrawal mechanism of product crystals from a metastable liquid of the crystallizer. © 2020 John Wiley & Sons, Ltd.This study comprises different parts of research work including (i) the model formulation, approximate analytical solution using the saddle-point technique, and separation of variables method and (ii) numerical simulations based on the analytical solutions obtained. Different parts of the present study were supported by different grants and programs. With this in mind, the authors are grateful to the following foundations, programs, and grants. Theoretical part (i) was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (20-1-5-82-1). Numerical part (ii) based on the developed analysis was made possible due to the financial support of the Russian Science Foundation (project no. 19-71-10044)