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Math. Model. Nat. Phenom. Vol. 3, No. 1, 2008, pp. 1-26
DOI: 10.1051/mmnp:2008031
Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect
A. Podolny1, A.A. Nepomnyashchy1, 2 and A. Oron31 Department of Mathematics, Technion - Israel Institute of Technology, Haifa, 32000, Israel
2 Minerva Center for Nonlinear Physics of Complex System, Technion - Israel. Institute of Technology, Haifa, 32000, Israel
3 Department of Mechanical Engineering, Technion- Israel Institute of Technology, Haifa, Israel
asspekto@tx.technion.ac.il
Published online: 17 July 2008
Abstract
We have explored the combined long-wave Marangoni and Rayleigh instability of
the quiescent state of a binary- liquid layer heated from below or from above in the presence
of the Soret effect. We found that in the case of small Biot numbers there are two long-
wave regions of interest k ~ Bi1/2 and k ~ Bi1/4. The dependence of both monotonic and
oscillatory thresholds of instability in these regions on both the Soret and dynamic Bond
numbers has been investigated. The complete linear stability analysis reveals the diversity
of instability types in the long-wave region, and a need in the development of the nonlinear
theory of the discovered phenomena becomes obvious.
Mathematics Subject Classification. 76E06, 76E17
Key words: binary liquid -- Marangoni instability -- buoyancy -- Soret effect