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Roll convection of binary fluid mixtures in porous media

Published online by Cambridge University Press:  13 April 2010

R. UMLA*
Affiliation:
Institut für Theoretische Physik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
M. AUGUSTIN
Affiliation:
Institut für Theoretische Physik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
B. HUKE
Affiliation:
Institut für Theoretische Physik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
M. LÜCKE
Affiliation:
Institut für Theoretische Physik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
*
Email address for correspondence: rudolfumla@gmx.de

Abstract

We investigate theoretically the nonlinear state of ideal straight rolls in the Rayleigh–Bénard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck–Boussinesq approximation, binary mixtures with positive separation ratio are studied and compared with one-component fluids. Our results for the structural properties of roll convection resemble qualitatively the situation in the Rayleigh–Bénard system without porous medium except for the fact that the streamlines of binary mixtures are deformed in the so-called Soret regime. The deformation of the streamlines is explained by means of the Darcy equation which is used to describe the transport of momentum. In addition to the properties of the rolls, their stability against arbitrary infinitesimal perturbations is investigated. We compute stability balloons for the pure fluid case as well as for a wide parameter range of Lewis numbers and separation ratios that are typical for binary gas and fluid mixtures. The stability regions of rolls are found to be restricted by a crossroll, a zigzag and a new type of oscillatory instability mechanism, which can be related to the crossroll mechanism.

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Papers
Copyright
Copyright © Cambridge University Press 2010

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