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

Abstract

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 $$Z(t)=\sigma \sqrt{t}+\varepsilon \chi t^{7/2}$$ Z ( t ) = σ t + ε χ t 7 / 2 with allowance for crystal nucleation. The effect of nucleation is in the second contribution, which is proportional to $$t^{7/2}$$ t 7 / 2 whereas the first term $$\sim \sqrt{t}$$ ∼ 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 $$\chi <0$$ χ < 0 ).