Two-Scale Models for Liquid-Solid Phase Transitions in Binary Material with Equiaxed Microstructure

Abstract

In many liquid-solid phase transitions, a specific dendritic microstructure of the phase interface is observed. In this contribution we present two-scale models capable to describe the evolution of equiaxed microstructure. The models are based either on a sharp interface model or on a phase field model for phase transitions in binary alloys. In both cases, a formal asymptotic expansion in terms of a scale parameter ε for the microstructure is carried out, with solute diffusivity scaling proportional to ε². In the limit ε→0 we obtain a two scale-model consisting of a macroscopic heat transport equation and, at each point of the macroscopic domain, of a local cell problem modeling the microsegregation and the evolution of the microstructure.