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Longwave Marangoni convection in a surfactant solution between poorly conducting boundaries

Published online by Cambridge University Press:  08 February 2013

Sergey Shklyaev  and
Alexander A. Nepomnyashchy
Sergey Shklyaev*
Affiliation:
Department of Chemical Engineering, University of Puerto Rico – Mayagüez, Mayagüez, PR 00681, USA Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Perm 614013, Russia
Alexander A. Nepomnyashchy
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel Minerva Center for Nonlinear Physics of Complex Systems, Technion – Israel Institute of Technology, Haifa 32000, Israel
*
†Email address for correspondence: shklyaev@yandex.ru
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Abstract

We consider Marangoni convection in a heated layer of a binary liquid. The solute is a surfactant, which is present in both surface and bulk phases; the bulk gradient of the concentration is formed due to the Soret effect. Linear stability analysis demonstrates a well-pronounced stabilization of the layer due to the adsorption kinetics and advection of the surface phase. We derive nonlinear amplitude equations for longwave perturbations in the case of fast sorption kinetics (small Langmuir number) and demonstrate that with increase in the effect of the adsorption, subcritical excitation occurs. In the case of a finite Langmuir number, the weakly nonlinear problem is ill-posed. A physical mechanism of subcritical bifurcation is discussed.

JFM classification

Convection: Marangoni convection Nonlinear Dynamical Systems: Pattern formation Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , pp. 428 - 456
Copyright
©2013 Cambridge University Press

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