Linear stability of planar solidification fronts

Abstract

We review, extend and modify the classical linear stability theory of planar solidification fronts in Langer's moving symmetric model. Using a new integral equation for the front position, we compute an exact linear stability equation and solve it exactly for an important special case. The classical theory is seen to be the long-time limit of the exact solution. Finally, we show how to treat a general planar front, using a short-time approximation. Our conclusions generalize those of previous analyses, by treating initial temperature field perturbations and the resulting transient growth phenomena.