Velocity selection problem for combined motion of melting and solidification fronts

TL;DR

This paper develops a velocity selection theory for a complex free boundary problem involving two interacting solid-liquid interfaces during alloy melting, incorporating anisotropic surface tension and diffusion effects, relevant to liquid film migration.

Contribution

It introduces a novel velocity selection framework for coupled melting fronts considering anisotropic surface tension and diffusion interactions, extending classical dendritic growth models.

Findings

Exact steady-state solutions with parabolic fronts exist without capillary effects.

Diffusion and strain effects significantly alter growth dynamics compared to classical models.

The theory accounts for anisotropic surface tension in velocity selection.

Abstract

We discuss a free boundary problem for two moving solid-liquid interfaces that strongly interact via the diffusion field in the liquid layer between them. This problem arises in the context of liquid film migration (LFM) during the partial melting of solid alloys. In the LFM mechanism the system chooses a more efficient kinetic path which is controlled by diffusion in the liquid film, whereas the process with only one melting front would be controlled by the very slow diffusion in the mother solid phase. The relatively weak coherency strain energy is the effective driving force for LFM. As in the classical dendritic growth problems, also in this case an exact family of steady-state solutions with two parabolic fronts and an arbitrary velocity exists if capillary effects are neglected. We develop a velocity selection theory for this problem, including anisotropic surface tension effects. The strong diffusion interaction and coherency strain effects in the solid near the melting front lead to substantial changes compared to classical dendritic growth.