Solidification fronts with unusual long-time behavior

Effects of nonlinear interfacial kinetics and interfacial thermal resistance in planar solidification

Large temperature discontinuities were recently measured at a solid-liquid interface during heat transport processes. These observations suggest that when heat flows between two phases, the interface is not well characterized by assuming thermal equilibrium. This can be of importance in rapid solidification processes. In this paper we consider a planar front model that solidifies from its undercooled melt. We use a generalized interfacial boundary condition that includes nonlinear kinetic effects and allows for a temperature discontinuity. The effects of the new boundary condition on the solidification rates and the temperature profile are reported as a function of time. Our analysis shows that the undercooling regime where constant phase-front velocities are observed at steady states (traveling-wave solutions) are unaffected by the new boundary conditions. These solutions arise when the Stephan number is larger than 1. On the other hand, the solidification rates and the steady-state velocities are greatly affected by the assumed conditions at the interface. Incorporation of an interface thermal resistance, or Kapitza resistance, generates temperature discontinuities at the interface, leads to reduced solidification rates and the Mullins-Sekerka instability arises at longer wavelengths deformation of the planar front.

Eighth-order phase-field-crystal model for two-dimensional crystallization

We present a derivation of the recently proposed eighth-order phase-field crystal model [A. Jaatinen, Phys. Rev. E 80, 031602 (2009)] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two-dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase-field crystal models. We find that among the phase-field crystal models studied, the eighth-order fitting scheme gives results in good agreement with the density functional theory for both static and dynamic properties, suggesting it is an accurate and computationally efficient approximation to the density functional theory.