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Effect of gravity on the dynamics of non-isothermic ultra-thin two-layer films

Published online by Cambridge University Press:  27 July 2010

ALEXANDER NEPOMNYASHCHY  and
ILYA SIMANOVSKII
ALEXANDER NEPOMNYASHCHY
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000 Haifa, Israel Minerva Center for Nonlinear Physics of Complex Systems, Technion – Israel Institute of Technology, 32000 Haifa, Israel
ILYA SIMANOVSKII*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000 Haifa, Israel
*
†Email address for correspondence: [email protected]
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Abstract

The effect of gravity on the dynamics of non-isothermic ultra-thin two-layer films is studied in this paper. The joint action of disjoining pressure and thermocapillary forces is taken into account. The problem is considered in a long-wave approximation. The linear stability of a quiescent state and thermocapillary flows is investigated. It has been found that the influence of the upper fluid density is significantly stronger than that of the difference of fluid densities. Nonlinear flow regimes are studied by means of numerical simulations. The gravity can lead to the formation of stripes or holes instead of droplets. The two-dimensional wavy patterns are replaced by one-dimensional waves with the fronts inclined or transverse to the direction of the horizontal temperature gradient.

JFM classification

Instability: Instability Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 661 , 25 October 2010 , pp. 1 - 31
Copyright
Copyright © Cambridge University Press 2010

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References

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