Buoyancy effects on morphological instability during directional solidification

The onset of morphological instability during the directional solidification of a single-phase binary alloy at constant velocity vertically upwards is treated by a linear stability analysis. The case in which a heavier solute is rejected at the solidifying interface is considered, and the effect of natural convection on the critical concentration for the onset of instability is studied. For tin containing lead, a small destabilization of the system at low growth velocities, and a large increase in the wavelength of the instability at the onset are found. Calculations show that the destabilization is enhanced as the variation of density with solute concentration is reduced, and in the limit of neutrally-dense solute, there is a long wavelength instability for which the critical solute concentration is several orders of magnitude lower than that predicted by the Mullins and Sekerka (1964) analysis in the absence of convection. For the neutrally-dense solute, a simplified analysis indicates the roles played by the interface deformation and thermal convection in promoting the instability. In particular, the destabilization is very sensitive to the ratio of crystal and melt thermal conductivities.