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A new oscillatory instability in a mushy layer during the solidification of binary alloys

Published online by Cambridge University Press:  26 April 2006

D. M. Anderson  and
M. Grae Worster
D. M. Anderson
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Present address: Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
M. Grae Worster
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

We consider the solidification of a binary alloy in a mushy layer and analyse the linear stability of a quiescent state with specific interest in identifying an oscillatory convective instability. We employ a near-eutectic approximation and consider the limit of large far-field temperature. These asymptotic limits allow us to examine the dynamics of the mushy layer in the form of small deviations from the classical case of convection in a horizontal porous layer of uniform permeability. We consider also the limit of large Stefan number, which incorporates a key balance necessary for the existence of the oscillatory instability. The model we consider here contains no double-diffusive effects and no region in which a statically stable density gradient exists. The mechanism underlying the oscillatory instability we discover is instead associated with a complex interaction between heat transfer, convection and solidification.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 307 , 25 January 1996 , pp. 245 - 267
Copyright
© 1996 Cambridge University Press

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