Dynamical law of the phase interface motion in the presence of crystals nucleation

Abstract

In this paper, we develop a theory of solid/liquid phase interface motion into an undercooled melt in the presence of nucleation and growth of crystals. A set of integrodifferential kinetic, heat and mass transfer equations is analytically solved in the two-phase and liquid layers divided by the moving phase transition interface. To do this, we have used the saddle-point method to evaluate a Laplace-type integral and the small parameter method to find the law of phase interface motion. The main result is that the phase interface Z propagates into an undercooled melt with time t as Z(t)=sigma sqrt{t}+varepsilon chi t^{7/2} with allowance for crystal nucleation. The effect of nucleation is in the second contribution, which is proportional to t^{7/2} whereas the first term sim sqrt{t} represents the well-known self-similar solution. The nucleation and crystal growth processes are responsible for the emission of latent crystallization heat, which reduces the melt undercooling and constricts the two-phase layer thickness (parameter chi <0).