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Pattern selection in ternary mushy layers

Published online by Cambridge University Press:  24 July 2017

Peter Guba  and
Daniel M. Anderson Open the ORCID record for Daniel M. Anderson [Opens in a new window]
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 consider finite-amplitude convection in a mushy layer during the primary solidification of a ternary alloy. Previous linear stability theories applied to ternary alloy primary-solidification models have identified an exceptional class of direct convective instability when all the individual stratifying agencies (one thermal and two solutal) were statically stabilizing. A reduced model, in which the effects of latent heat, solute rejection and background solidification are neglected, contains the essential interactions that admit qualitatively the same instability. We examine pattern selection for steady convection in this model. We find that roll, square or hexagonal convection patterns can be nonlinearly stable, depending on the relative importance of a number of physical effects, namely the solutal diffusion rates, the liquidus slopes and the background thermal and solutal density stratifications. The results for a special case are found to isolate a purely double-diffusive phase-change mechanism of pattern selection. Subcritical behaviour is identified inside the domain of individual static stability. A physical system is proposed that may be a promising one in which to experimentally identify these novel instabilities.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection Phase change: Phase change
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 853 - 886
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Copyright
© 2017 Cambridge University Press 

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