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Nonlinear parametrically excited surface waves in surfactant-covered thin liquid films

Published online by Cambridge University Press:  29 November 2004

O. K. MATAR
Affiliation:
Department of Chemical Engineering and Chemical Technology, Imperial College London, SW7 2AZ, UK
S. KUMAR
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Ave. SE, Minneapolis, MN 55455, USA
R. V. CRASTER
Affiliation:
Department of Mathematics, Imperial College London, SW7 2AZ, UK

Abstract

The effect of gravity modulation on the nonlinear evolution of long-wavelength disturbances at the free surface of a surfactant-covered thin liquid layer is studied. The surfactants, which are assumed to be insoluble, give rise to interfacial concentration gradients and associated Marangoni flow in the underlying liquid film. A coupled system of lubrication-theory-based evolution equations for the film height and surfactant concentration is solved numerically using spectral methods. Previous work using Floquet theory had determined that small-amplitude long-wavelength disturbances are destabilized by gravity modulation in the presence of surfactant; uncontaminated films were found to be linearly stable. Our numerical results indicate that uncontaminated free surfaces are destabilized by nonlinearities and exhibit a harmonic response. The interface exhibits complex dynamics during a forcing cycle, characterized by numerous coalescence events between thickened fluid ridges leading to coarsening. The presence of surfactant-induced Marangoni flow gives rise to a harmonic response, larger scale fluid structures of reduced amplitude, less frequent coalescence events, and less complicated film dynamics.

Type
Papers
Copyright
© 2004 Cambridge University Press

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