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

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 root t + epsilon 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 similar to root 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).

Automated summary

In this paper, a theory of solid/liquid phase interface motion in an undercooled melt with nucleation and crystal growth is developed. The set of integrodifferential kinetic, heat and mass transfer equations are analytically solved to describe the two-phase and liquid layers separated by the moving phase transition interface. The main result is the propagation law of the phase interface, which is affected by crystal nucleation. The nucleation and crystal growth processes emit latent crystallization heat, reducing the melt undercooling and constraining the thickness of the two-phase layer.