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The role of surfactants on the mechanism of the long-wave instability in liquid film flows

Published online by Cambridge University Press:  12 February 2014

George Karapetsas  and
Vasilis Bontozoglou
George Karapetsas*
Affiliation:
Department of Mechanical Engineering, University of Thessaly, GR-38334 Volos, Greece
Vasilis Bontozoglou
Affiliation:
Department of Mechanical Engineering, University of Thessaly, GR-38334 Volos, Greece
*
†Email address for correspondence: [email protected]
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Abstract

The analysis for the physical mechanism of the long-wave instability in liquid film flow is extended to take into account the presence of a surfactant of arbitrary solubility. The Navier–Stokes equations are supplemented by mass balances for the concentrations at the interface and in the bulk, by a Langmuir model for adsorption kinetics at the interface, and are expanded in the limit of long-wave disturbances. The longitudinal flow perturbation, known to result from the perturbation shear stress which develops along the deformed interface, is shown to contribute a convective flux that triggers an interfacial concentration gradient. This gradient is, at leading order, in phase with the interfacial deformation, and as a result produces Marangoni stresses that stabilize the flow. The strength of the interfacial concentration gradient is shown to be maximum for an insoluble surfactant and to decrease with increasing surfactant solubility. The decrease is explained in terms of the spatial phase of mass transfer between interface and bulk, which mitigates the interfacial flux by the flow perturbation and leads to the attenuation of Marangoni stresses. Higher-order terms are derived, which provide corrections for disturbances of finite wavelength.

JFM classification

Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface) Convection: Marangoni convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 741 , 25 February 2014 , pp. 139 - 155
Copyright
© 2014 Cambridge University Press 

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