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Marangoni instabilities associated with heated surfactant-laden falling films

Published online by Cambridge University Press:  28 January 2020

S. J. D. D’Alessio Open the ORCID record for S. J. D. D’Alessio [Opens in a new window] ,
J. P. Pascal ,
E. Ellaban  and
C. Ruyer-Quil
S. J. D. D’Alessio*
Affiliation:
Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
J. P. Pascal
Affiliation:
Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada
E. Ellaban
Affiliation:
Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada
C. Ruyer-Quil
Affiliation:
Université de Savoie Mont Blanc, CNRS, LOCIE 73000 Chambéry, France
*
†Email address for correspondence: [email protected]
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Abstract

Investigated in this paper is the stability of the gravity-driven flow of a liquid layer laden with soluble surfactant down a heated incline. A mathematical model incorporating variations in surface tension with surfactant concentration and temperature has been formulated. A linear stability analysis is carried out both asymptotically for small wavenumbers and numerically for arbitrary wavenumbers. An expression for the critical Reynolds number has been derived which accounts for thermocapillary and solutocapillary effects, and reduces to known documented results for special cases. Also, a nonlinear reduced model has been derived using weighted residuals, and solved numerically to simulate the instability of the equilibrium flow and the development of permanent surface waves that arise. The nonlinear simulations were found to be in good agreement with the linear stability analysis.

JFM classification

Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , A20
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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