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Diffusive and phase change instabilities in a ternary mushy layer

Published online by Cambridge University Press:  12 November 2014

Peter Guba  and
Daniel M. Anderson
Peter Guba
Affiliation:
Department of Applied Mathematics and Statistics, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava 4, Slovakia
Daniel M. Anderson*
Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8910, USA
*
†Email address for correspondence: danders1@gmu.edu
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Abstract

We analyse the stability of a mushy layer during the directional solidification of a ternary alloy. Our model includes diffusive and convective transport of heat and solutes, coupled by an equilibrium thermodynamic constraint of the ternary phase diagram. The model contains phase change effects due to latent-heat release, solute rejection and background solidification. We identify novel convective instabilities, both direct and oscillatory, which are present under statically stable conditions. We examine these instabilities asymptotically by simplifying to a thin mushy layer with small growth rates. We also discuss numerical results for the full problem, confirming the asymptotic predictions and providing the stability characteristics outside the small-growth-rate approximation. A physical explanation for these instabilities in terms of parcel arguments is proposed, indicating that the instability mechanisms generally involve different rates of solute diffusion, different rates of solute rejection and different background solute distributions induced by the initial alloy composition.

JFM classification

Convection: Buoyancy-driven instability Convection: Double diffusive convection Phase change: Phase change
Type
Papers
Information
Journal of Fluid Mechanics , Volume 760 , 10 December 2014 , pp. 634 - 669
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Copyright
© 2014 Cambridge University Press 

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