Coupled convective instabilities at crystal-melt interfaces

The stability of the parallel flow between a vertical crystal-melt interface and a vertical wall held at a temperature above the melting point of the crystal is analyzed for Prandtl numbers, P, ranging from 10 -2 to 10 2. Three modes of instability occur: (1) a bouyant mode, (2) a shear mode, and (3) a coupled crystal-melt mode. The bouyant and shear modes are similar to those that occur for flow between two vertical rigid walls held at different temperatures. For Prandtl numbers greater than approximately two, the coupled crystal-melt mode occurs at a lower Grashof number than the other two modes. Specific results are given for succinonitrile ( P = 22.8) and lead ( P = 0.0225). These calculations and similar calculations for a cylindrical geometry were motivated by and are in general agreement with recent experiments on succinonitrile.