A strongly nonlinear-analysis of the morphological instability of a freezing binary alloy - solutal convection, density change, and nonequilibrium effects
IMA Journal of Applied Mathematics, 47, (2), .
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In this paper, amplitude equations for the development of morphological instability of a freezing binary alloy are derived using a strongly nonlinear analysis. The effects of density change in the system are considered. In particular, the density of the liquid phase is allowed to depend on its composition and to be different from that of the solid. Both necessarily give rise to convection in the melt when the system becomes unstable. It is found that such convection can act either to stabilize and promote supercritical behaviour or conversely to destabilize and promote subcritical behaviour, the precise behaviour being crucially dependent upon the relative densities of the solid and liquid phases. The effect of nonequilibrium segregation is also studied and it is shown that buoyancy-driven convection can act to favour the onset of instability through overstable modes.
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