Compositional convection in the solidification of binary alloys

When a binary alloy is directionally solidified, a two-phase mushy dendritic zone is often formed. Interdendritic convection of the melt may occur, and is coupled with compositional convection of the residual melt. If fluid flow velocities are high enough, local melt-back of the dendrites may occur, leading to channel formation, and thus preferred flow paths. In order to predict the onset of convection, a coupled liquid/mush model is proposed, which includes most of the known physics. An elaborate scaling procedure leads to certain conclusions concerning the nature of convection, and points to a much simplified model, which can essentially be solved analytically. Predictions of the theory are compared quantitatively with experiments.