Morphological instability in a directionally solidifying binary solution with an imposed shear flow

Abstract

The effect of an imposed shear flow on the stability of directionally solidifying binary alloys is investigated. It is shown that without the imposed shear flow the system is dominated by stationary boundary-layer-mode convection, a convection of salt-finger type confined to the solute boundary layer above the melt/mush interface. When the shear flow (no matter how small) is imposed, the boundary-layer mode becomes a longitudinal mode (roll-axis parallel to the imposed flow) propagating in the direction perpendicular to the shear flow, while the modes containing a transverse component are inhibited. As the shear flow becomes large enough, a transverse mode (roll-axis perpendicular to the imposed flow) of very unstable characteristics is induced. This mode, called the morphological mode, can exist even without buoyancy. It is triggered by the flow induced in the mushy layer through the Bernoulli force, a pressure variation resulting from the imposed flow passing along the corrugated melt/mush interface. It, nonetheless, has no relation to the boundary layer instability of the shear flow. The effect of imposed shear flow is so significant that the stability characteristics can be entirely different when the intensity of the imposed flow is larger than a critical value, which is calculated in the present paper.