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Mullins–Sekerka stability analysis for melting-freezing waves in helium

Published online by Cambridge University Press:  26 September 2008

Joseph D. Fehribach
Joseph D. Fehribach
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA and Institute for Mathematcis & its Applications, University of Minnesota, Minneapolis, MN 55455, USA (email: bach@wpi.edu)
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Abstract

This paper considers the stability of melt-solid interfaces to eigenfunction perturbations for a system of equations which describe the melting and freezing of helium. The analysis is carried out in both planar and spherical geometries. The principal results are that when the melt is freezing, under certain far-field conditions, the interface is stable in the sense of Mullins and Sekerka. On the other hand, when the solid is melting (at least when the melting is sufficiently fast), the interface is unstable. In some circumstances these instabilities are oscillatory, with amplitude and growth rate increasing with surface tension and frequency. The last section considers the original problem of Mullins and Sekerka in the present notation.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 1 , March 1994 , pp. 21 - 37
Copyright
Copyright © Cambridge University Press 1994

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