The rapid advance and slow retreat of a mushy zone

Abstract

We discuss a model for the evolution of a mushy zone which forms during the solidification of a binary alloy cooled from below in a tank with finite height. Our focus is on behaviours of the system that do not appear when either a semi-infinite domain or negligible solute diffusion is assumed. The problem is simplified through an assumption of negligible latent heat, and we develop a numerical scheme that will permit insights that are critical for developing a more general procedure. We demonstrate that a mushy zone initially grows rapidly, then slows down and eventually retreats slowly. The mushy zone vanishes after a long time, as it is overtaken by a slowly growing solid region at the base of the tank.