Mathematical modeling of nonlinear growth rates of crystals with allowance for Meirs kinetics

Abstract

In this paper, we study the process of nonlinear growth of spherical crystals in supercooled single-component melts with the Meirs nucleation kinetics. The balance and Fokker-Planck equations are solved with allowance for the power-dependent law for the crystal growth rate. It is shown that the melt supercooling is a decreasing function of time due to the latent heat release by the growing solid phase particles.In this paper, we study the process of nonlinear growth of spherical crystals in supercooled single-component melts with the Meirs nucleation kinetics. The balance and Fokker-Planck equations are solved with allowance for the power-dependent law for the crystal growth rate. It is shown that the melt supercooling is a decreasing function of time due to the latent heat release by the growing solid phase particles.