Shear flow, phase change and matched asymptotic expansions: Pattern formation in mushy layers

Neufeld, J. A. and Wettlaufer, J.S. (2011) Shear flow, phase change and matched asymptotic expansions: Pattern formation in mushy layers. Physica D: Nonlinear Phenomena, 240 (2). pp. 140-149. ISSN 0167-2789 DOI doi:doi:10.1016/j.physd.2010.10.007

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Abstract

In many scientific and engineering problems the solidification of an alloy leads to a highly convoluted crystalline matrix modeled as a thermodynamically controlled reactive porous medium called a mushy layer. We analyze the interaction of an external shear flow with a solidifying mushy layer through a corrugated mush–liquid interface. We find that the external flow can drive forced convective motions within the mushy layer resulting in the formation of a pattern of dissolution and solidification features transverse to the overall flow. Here we seek to lay bare the underlying processes through a systematic comparison of matched asymptotic expansions and numerical solutions. The success of our modeling effort draws substantially upon understanding gleaned from the fluid mechanics of boundary layers and the theory of multi-component solidification. The results have a broad range of implications in geophysics and materials science.

Item Type: Article
Uncontrolled Keywords: 2010AREP;
Subjects: 99 - Other
Divisions: 99 - Other
Journal or Publication Title: Physica D: Nonlinear Phenomena
Volume: 240
Page Range: pp. 140-149
Identification Number: doi:doi:10.1016/j.physd.2010.10.007
Depositing User: Sarah Humbert
Date Deposited: 06 Dec 2011 11:08
Last Modified: 23 Jul 2013 10:02
URI: http://eprints.esc.cam.ac.uk/id/eprint/2261

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