Capillary-Wave Model for the Solidification of Dilute Binary Alloys

TL;DR

This paper develops a phase-field model for the solidification of dilute binary alloys, incorporating capillary wave interactions and non-equilibrium effects, providing insights into instabilities during rapid growth.

Contribution

It introduces a novel capillary-wave model that does not rely on sharp-interface assumptions and accounts for non-equilibrium effects in alloy solidification.

Findings

Analytical evaluation of the model reveals an instability similar to Cahn's grain-boundary motion.

The model captures interactions between solidification front waves and solute diffusion.

It extends understanding of rapid-growth solidification regimes.

Abstract

Starting from a phase-field description of the isothermal solidification of a dilute binary alloy, we establish a model where capillary waves of the solidification front interact with the diffusive concentration field of the solute. The model does not rely on the sharp-interface assumption, and includes non-equilibrium effects, relevant in the rapid-growth regime. In many applications it can be evaluated analytically, culminating in the appearance of an instability which, interfering with the Mullins-Sekerka instability, is similar to that, found by Cahn in grain-boundary motion.