Planar solidification from an undercooled melt: Asymptotic solutions to a continuum model with interfacial kinetics

Planar growth of a solid germ from an undercooled melt is considered within the continuum model, accounting for kinetic effects at the interface. The paper extends previous studies of this problem by (i) analyzing not only the moving fronts but also the temperature fields in each phase and (ii) accounting for the temperature dependence of the latent heat. Explicit analytic solutions are developed both for short and long times. It is shown that, in the case of critical undercooling (at the crossover from diffusion to kinetics-dominated regimes), the nonuniformity of the solid temperature and the variation of the latent heat with temperature significantly affect the long-time (t) behavior R=γ${\mathit{t}}^{2/3}$ of the phase-change fronts R. Emergence of this law is related to the entropy production at the interface. Peculiarities of the temperature field, derived for the critical undercooling case, are clarified.