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Dynamics of ultra-thin two-layer films under the action of inclined temperature gradients

Published online by Cambridge University Press:  17 July 2009

ALEXANDER A. NEPOMNYASHCHY  and
ILYA B. SIMANOVSKII
ALEXANDER A. NEPOMNYASHCHY
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000, Haifa, Israel Minerva Centre for Nonlinear Physics of Complex Systems, Technion – Israel Institute of Technology, 32000, Haifa, Israel
ILYA B. SIMANOVSKII*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000, Haifa, Israel Minerva Centre for Nonlinear Physics of Complex Systems, Technion – Israel Institute of Technology, 32000, Haifa, Israel
*
†Email address for correspondence: yuri11@inter.net.il
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Abstract

The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film in the presence of an inclined temperature gradient is investigated. The problem is solved by means of a linear stability theory and nonlinear simulations. It has been found that for sufficiently large values of the ratio between the longitudinal and transverse Marangoni numbers, the real part of the linear growth rate does not depend on the direction of the wavenumber, except the case of nearly longitudinal disturbances. Numerous types of nonlinear evolution have been observed, among them are ordered systems of droplets, ‘splashes’, oblique waves, modulated transverse and longitudinal structures.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 631 , 25 July 2009 , pp. 165 - 197
Copyright
Copyright © Cambridge University Press 2009

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