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Rapid growth and critical behaviour in phase field models of solidification

Published online by Cambridge University Press:  16 May 2001

KARL GLASNER
KARL GLASNER
Affiliation:
Department of Mathematics, University of UT, Salt Lake City, Utah 84112-0090, USA; Email: [email protected]
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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.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 12 , Issue 1 , February 2001 , pp. 39 - 56
Copyright
2001 Cambridge University Press

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