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Long-Wave Coupled Marangoni - Rayleigh Instabilityin a Binary Liquid Layer in the Presenceof the Soret Effect

Published online by Cambridge University Press:  17 July 2008

A. Podolny ,
A. A. Nepomnyashchy  and
A. Oron
A. Podolny
Affiliation:
Department of Mathematics, Technion - Israel Institute of Technology, Haifa, 32000, Israel
A. A. Nepomnyashchy
Affiliation:
Department of Mathematics, Technion - Israel Institute of Technology, Haifa, 32000, Israel Minerva Center for Nonlinear Physics of Complex System, Technion - Israel. Institute of Technology, Haifa, 32000, Israel
A. Oron*
Affiliation:
Department of Mechanical Engineering, Technion- Israel Institute of Technology, Haifa, Israel
*
[email protected]
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Abstract

We have explored the combined long-wave Marangoni and Rayleigh instability ofthe quiescent state of a binary- liquid layer heated from below or from above in the presenceof the Soret effect. We found that in the case of small Biot numbers there are two long-wave regions of interest k ~ Bi 1/2 and k ~ Bi 1/4. The dependence of both monotonic andoscillatory thresholds of instability in these regions on both the Soret and dynamic Bondnumbers has been investigated. The complete linear stability analysis reveals the diversityof instability types in the long-wave region, and a need in the development of the nonlineartheory of the discovered phenomena becomes obvious.

Keywords

binary liquidMarangoni instabilitybuoyancySoret effect
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 1: Interfacial phenomena in fluids , 2008 , pp. 1 - 26
Copyright
© EDP Sciences, 2008

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