Long-wave morphological instabilities in the directional solidification of a dilute binary mixture

D. S. Riley*, S. H. Davis

*Corresponding author for this work

Research output: Contribution to journalArticle

24 Scopus citations

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. The present investigation identifies a third, strongly-nonlinear, evolution equation, arising in the small-segregation-coefficient, large-surface-energy limit. This equation links both of the former and describes the change from the sub- to super-critical bifurcations. This study sets the previous long-wave analyses into a logical framework.

Original languageEnglish (US)
Pages (from-to)420-436
Number of pages17
JournalSIAM Journal on Applied Mathematics
Volume50
Issue number2
DOIs
StatePublished - Jan 1 1990

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint Dive into the research topics of 'Long-wave morphological instabilities in the directional solidification of a dilute binary mixture'. Together they form a unique fingerprint.

  • Cite this