Rapid growth and critical behaviour in phase field models of solidification

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Abstract

Rapid solidification fronts are studied using a phase field model. Unlike slow moving solutions which approximate the Mullins-Sekerka free boundary problem, different limiting behaviour is obtained for rapidly moving fronts. A time-dependent analysis is carried out for various cases and the leading order behaviour of solidification front solutions is derived to be one of several travelling wave problems. An analysis of these problems is conducted, leading to expressions for front speeds in certain limits. The dynamics leading to these travelling wave solutions is derived, and conclusions about stability are drawn. Finally, a discussion is made of the relationship to other solidification models.

Original languageEnglish (US)
Pages (from-to)39-56
Number of pages18
JournalEuropean Journal of Applied Mathematics
Volume12
Issue number1
DOIs
StatePublished - Dec 1 2001
Externally publishedYes

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ASJC Scopus subject areas

  • Applied Mathematics

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