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REVIEW ARTICLES: Solidification

Long–Wave Morphologies in Directional Solidification

[+] Author and Article Information
D. S. Riley

School of Mathematics, University of Bristol, Bristol BS8 1TW

Appl. Mech. Rev 43(5S), S85-S88 (May 01, 1990) doi:10.1115/1.3120857 History: Online April 30, 2009

Abstract

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.

Copyright © 1990 by American Society of Mechanical Engineers
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