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

TL;DR

This paper derives boundary conditions for the solid-liquid interface during solidification, incorporating surface temperature and heat resistance effects, revealing non-linear solidification kinetics and conditions for steady-state interface motion.

Contribution

It introduces a model using Gibbs interface to include surface temperature and heat resistance, providing new expressions for interface temperature discontinuity and steady-state conditions.

Findings

Kapitza resistance affects interface velocity.

Heat resistance causes non-linearity in solidification.

Steady-state motion conditions for planar interface are established.

Abstract

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 are taken at the interface and the quantities characterizing interfacial surface such as the surface temperature and the 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 the interface velocity is considered. It is shown that heat resistance leads to non-linearity in solidification kinetics, namely, in "velocity-undercooling" relationship. The conditions of the steady--state motion of the planar interface has been found.