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Finite-sample-size effects on convection in mushy layers

Published online by Cambridge University Press:  02 July 2012

J.-Q. Zhong ,
A. T. Fragoso ,
A. J. Wells  and
J. S. Wettlaufer
J.-Q. Zhong
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA
A. T. Fragoso
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA Department of Physics, Yale University, New Haven, CT 06520, USA
A. J. Wells
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA Program in Applied Mathematics, Yale University, New Haven, CT 06520, USA
J. S. Wettlaufer*
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA Program in Applied Mathematics, Yale University, New Haven, CT 06520, USA Department of Physics, Yale University, New Haven, CT 06520, USA NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden
*
†Email address for correspondence: john.wettlaufer@yale.edu
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Abstract

We report theoretical and experimental investigations of the flow instability responsible for mushy-layer convection with chimneys, drainage channels devoid of solid, during steady-state solidification of aqueous ammonium chloride. Under certain growth conditions a state of steady mushy-layer growth with no flow is unstable to the onset of convection, resulting in the formation of chimneys. We present regime diagrams to quantify the state of the flow as a function of the initial liquid concentration, the porous-medium Rayleigh number, and the sample width. For a given liquid concentration, increasing both the porous-medium Rayleigh number and the sample width drove a transition from a weakly convecting chimney free state to a state of mushy-layer convection with fully developed chimneys. Increasing the concentration ratio stabilized the system and suppressed the formation of chimneys. As the initial liquid concentration increased, onset of convection and formation of chimneys occurred at larger values of the porous-medium Rayleigh number, but the critical cell widths for chimney formation are far less sensitive to the liquid concentration. At the highest liquid concentration, the mushy-layer mode of convection did not occur in the experiment. The formation of multiple chimneys and the morphological transitions between these states are discussed. The experimental results are interpreted in terms of a previous theoretical analysis of finite amplitude convection with chimneys, with a single value of the mushy-layer permeability consistent with the liquid concentrations considered in this study.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection in porous media Phase change: Solidification/melting
Type
Papers
Information
Journal of Fluid Mechanics , Volume 704 , 10 August 2012 , pp. 89 - 108
Copyright
Copyright © Cambridge University Press 2012

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