Hydrodynamic stability of the melt during the solidification of a binary alloy with small segregation coefficient

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We consider the convective flow present during the directional solidification of a dilute binary alloy having small segregation coefficient k. The constitutional undercooling is set to zero, so that morphological instabilities of the melt-crystal interface are suppressed and the interface is planar. In the linearized stability theory, the critical wave number of the convective mode ac is found to behave like ac ≈ k 1 4 as k → 0, which is identical in behavior to the morphological mode. The weakly nonlinear theory gives rise to a Sivashinsky equation governing the spatial structure of the convection. Unlike previous long-wave evolution equations governing convective processes, this one arises in a geometrically unbounded domain with system boundaries that are neither fixed heat flux nor small Biot number; here the equivalent Biot number is of unit order.

Original languageEnglish (US)
Pages (from-to)231-238
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Volume39
Issue number2-3
DOIs
StatePublished - Oct 2 1989

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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