Transient convective instabilities in directional solidification

TL;DR

This paper investigates the transient convective instabilities in the melt during directional solidification, providing analytical insights into the conditions leading to temporary destabilization that could influence growth mode predictions.

Contribution

It introduces an analytical dispersion relation and asymptotic analysis for large Rayleigh numbers to understand transient instabilities in directional solidification.

Findings

Identification of a transient instability regime during initial melt solidification

Analytical dispersion relation for convective instability

Asymptotic analysis for large Rayleigh number

Abstract

We study the convective instability of the melt during the initial transient in a directional solidification experiment in a vertical configuration. We obtain analytically the dispersion relation, and perform an additional asymptotic expansion for large Rayleigh number that permits a simpler analytical analysis and a better numerical behavior. We find a transient instability, i.e. a regime in which the system destabilizes during the transient whereas the final unperturbed steady state is stable. This could be relevant to growth mode predictions in solidification.