Long–wave instabilities in a directionally–solidified binary mixture may occur in several limits. Sivashinsky identified a small–segregation–coefficient limit and obtained a weakly–nonlinear evolution equation governing subcritical two–dimensional bifurcation. Brattkus and Davis identified a near–absolute–stability limit and obtained a strongly–nonlinear evolution equation governing supercritical two–dimensional bifurcation. In this presentation these previous analyses are set into a logical framework, and a third distinguished (small–segregation–coefficient, large–surface–energy) limit identified. The corresponding strongly–nonlinear, evolution equation equation links both of the previous and describes the change from sub– to super–critical bifurcations.

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