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The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate

Published online by Cambridge University Press:  07 May 2015

J. V. Goddard  and
S. Naire
J. V. Goddard
Affiliation:
School of Computing and Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK
S. Naire*
Affiliation:
School of Computing and Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK
*
†Email address for correspondence: s.naire@keele.ac.uk
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Abstract

We consider a viscous drop, loaded with an insoluble surfactant, spreading over an inclined plane that is covered initially with a thin surfactant-free liquid film. Lubrication theory is employed to model the flow using coupled nonlinear evolution equations for the film thickness and surfactant concentration. Exploiting high-resolution numerical simulations, we describe the late-time multi-region asymptotic structure of the spatially one-dimensional spreading flow. A simplified differential–algebraic equation model is derived for key variables characterising the spreading process, using which the late-time spreading and thinning rates are determined. Focusing on the neighbourhood of the drop’s leading-edge effective contact line, we then examine the stability of this region to small-amplitude disturbances with transverse variation. A dispersion relationship is described using long-wavelength asymptotics and numerical simulations, which reveals physical mechanisms and new scaling properties of the instability.

JFM classification

Interfacial Flows (free surface): Fingering instability Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , pp. 535 - 568
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Copyright
© 2015 Cambridge University Press 

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