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Three-dimensional dynamics of falling films in the presence of insoluble surfactants

Published online by Cambridge University Press:  13 November 2020

Assen Batchvarov
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Lyes Kahouadji
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Cristian R. Constante-Amores
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Gabriel Farah Norões Gonçalves
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Seungwon Shin
Affiliation:
Department of Mechanical and System Design Engineering, Hongik University, Seoul 121-791, Republic of Korea
Jalel Chergui
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), CNRS, Université Paris Saclay, Bât. 507, Rue du Belvédère, Campus Universitaire, 91405 Orsay, France
Damir Juric
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), CNRS, Université Paris Saclay, Bât. 507, Rue du Belvédère, Campus Universitaire, 91405 Orsay, France
Richard V. Craster
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Omar K. Matar
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Corresponding

Abstract

We study the effect of insoluble surfactants on the wave dynamics of vertically falling liquid films. We use three-dimensional numerical simulations and employ a hybrid interface-tracking/level-set method, taking into account Marangoni stresses induced by gradients of interfacial surfactant concentration. Our numerical predictions for the evolution of the surfactant-free, three-dimensional wave topology are validated against the experimental work of Park & Nosoko (AIChE J., vol. 49, 2003, pp. 2715–2727). The addition of surfactants is found to influence significantly the development of horseshoe-shaped waves. At low Marangoni numbers, we show that the wave fronts exhibit spanwise oscillations before eventually acquiring a quasi-two-dimensional shape. In addition, the presence of Marangoni stresses is found to suppress the peaks of the travelling waves and preceding capillary wave structures. At high Marangoni numbers, a near-complete rigidification of the interface is observed.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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