Geodesic
Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect
A. Podolny1 ; A. A. Nepomnyashchy1, 2 ; A. Oron3
1 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
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 1, pp. 1-26.

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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.
DOI : 10.1051/mmnp:2008031

A. Podolny 1 ; A. A. Nepomnyashchy 1, 2 ; A. Oron 3

1 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 
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     author = {A. Podolny and A. A. Nepomnyashchy and A. Oron},
     title = {Long-Wave {Coupled} {Marangoni} - {Rayleigh} {Instability} in a {Binary} {Liquid} {Layer} in the {Presence} of the {Soret} {Effect}},
     journal = {Mathematical modelling of natural phenomena},
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     doi = {10.1051/mmnp:2008031},
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A. Podolny; A. A. Nepomnyashchy; A. Oron. Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 1, pp. 1-26. doi : 10.1051/mmnp:2008031. http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008031/

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