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The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer

Published online by Cambridge University Press:  04 January 2007

DAVID PRITCHARD  and
CHRIS N. RICHARDSON
DAVID PRITCHARD
Affiliation:
Department of Mathematics, University of Strathclyde, 26 Richmond St, Glasgow G1 1XH, UKdtp@maths.strath.ac.uk.
CHRIS N. RICHARDSON
Affiliation:
B.P. Institute for Multiphase Flow, Department of Earth Sciences, University of Cambridge, Madingley Rise, Madingley Road, Cambridge CB3 0EZ, UK
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Abstract

We consider the onset of thermosolutal (double-diffusive) convection of a binary fluid in a horizontal porous layer subject to fixed temperatures and chemical equilibrium on the bounding surfaces, in the case when the solubility of the dissolved component depends on temperature. We use a linear stability analysis to investigate how the dissolution or precipitation of this component affects the onset of convection and the selection of an unstable wavenumber; we extend this analysis using a Galerkin method to predict the structure of the initial bifurcation and compare our analytical results with numerical integration of the full nonlinear equations. We find that the reactive term may be stabilizing or destabilizing, with subtle effects particularly when the thermal gradient is destabilizing but the solutal gradient is stabilizing. The preferred spatial wavelength of convective cells at onset may also be substantially increased or reduced, and strongly reactive systems tend to prefer direct to subcritical bifurcation. These results have implications for geothermal-reservoir management and ore prospecting.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 59 - 95
Copyright
Copyright © Cambridge University Press 2007

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