Mathematical modeling of binary compounds with the presence of a phase transition layer

Abstract

When looking for solutions to nonstationary problems in the field of binary melts or solutions, the scientific community regularly faces the need to transform the classical Stefan‐type approach in order to obtain both new analytical results and explicit solutions. Within the framework of the current paper, we present the analysis of the problem of directional crystallization of binary solutions or melts in the presence of a mushy layer, based on the consideration of field data under the prism of a modified formulation, which made it possible to obtain such characteristics of the behavior of the mushy zone as the thickness and growth rate of the solid phase, temperature distribution, and also to determine heat‐conducting and latent heat flows. The simulation results are presented, including in the form of illustrative material; a good agreement was noted between the predicted values of the growth rates and temperature profiles of the mushy zone and the area of solid matter with the existing observations of young sea ice dynamics.