Solutal convection and morphological instability in directional solidification of binary alloys

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Abstract
We study the effect of the coupling between front deformation and solutal convection on the position of the bifurcation from the planar quiescent state of a dilute binary alloy submitted to directional solidification. We set up a perturbation treatment of the coupling between the « bare » (Mullins-Sekerka and solutal convective) bifurcations. We show that the shift of the Mullins-Sekerka bifurcation is extremely small at usual values of the applied thermal gradient, and is accurately predicted by the first order perturbation expression. The shift of the convective bifurcation, though much larger, can also be calculated with very good accuracy in the same range of values of the thermal gradient with the help of the first order approximation. We give a qualitative interpretation of these results in terms of an effective Rayleigh number and of the mismatch between the critical wavevectors of the uncoupled system

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