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Generation of nonlinear Marangoni waves in a two-layer film by heating modulation

Published online by Cambridge University Press:  17 April 2015

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: yuri11@inter.net.il
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Abstract

Longwave Marangoni convection in two-layer films under the action of heating modulation is considered. The analysis is carried out in the lubrication approximation. The capillary forces are assumed to be sufficiently strong, and they are taken into account. Periodic or symmetric boundary conditions are applied on the boundaries of the computational region. Numerical simulations are performed by means of a finite-difference method. Two regions of parametric instabilities have been found. In the first region, one observes the competition or coexistence of standing waves parallel to the boundaries of the computational region. The multistability of the flow regimes is revealed. In the second region, the regimes found in the case of periodic boundary conditions are more diverse than in the case of symmetric boundary conditions.

JFM classification

Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 771 , 25 May 2015 , pp. 159 - 192
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Copyright
© 2015 Cambridge University Press 

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