VELOCITY EFFECTS IN UNSTABLE SOLIDIFICATION

The supercooled Stefan problem with surface tension is considered as a model of unstable solidification, with a general anisotropic curvature- and velocity-dependent boundary condition on the moving interface. The problem is reformulated in terms of a history-dependent singular integral equation for the velocity of the boundary. Using this equation, a new linear stability analysis of a flat interface is carried out and the smoothing role of velocity-dependence and the destabilizing effect of anisotropy are demonstrated. The results disagree with previous analyses because transient effects due to the initial temperature field are included, and numerical results are presented that confirm the analysis presented here. It is found that velocity effects cannot increase the range of unstable modes beyond that permitted by surface tension.