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.

We study the flow around the tip of a dendritic crystal by an inclined stream of viscous incompressible liquid. The tip shape is chosen accordingly to recent theory[Phil. Trans. R. Soc. A 2020, 378, 20190243] confirmed by a number of experiments and computations [Phil. Trans. R. Soc. A 2021, 379, 20200326]. Our simulations have been carried out for a 0, 30, 60, and 90-degree flow slope to the dendrite axis. We show that the stream inclination has a significant effect on the hydrodynamic flow and shear stress. In particular, a transition from laminar to turbulent currents on the upstream side of the dendritic crystal may occur in an inclined hydrodynamic flow. This leads to the fact that the heat and mass transfer mechanisms on the upstream and downstream sides of a growing dendritic crystal may be different.

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