Boundary conditions and heat resistance at the moving solid-liquid interface

Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases taken at the interface and the quantities characterizing the interfacial surface such as surface temperature and surface heat flux. Introduction of the surface temperature as an independent variable, allows us to describe the scattering energy at the interface. For the steady-state motion of the planar interface the expression for the temperature discontinuity across the phase boundary has been obtained. Effect of Kapitza resistance on interface velocity is considered. It is shown that the thermal resistance leads to non-linearity in solidification kinetics, namely, in “velocity-undercooling” relation. The conditions of the steady-state motion of the planar interface are found.