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


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



We consider a viscous drop, loaded with an insoluble surfactant, spreading over a flat plane that is covered initially with a thin liquid film. Lubrication theory allows the flow to be modelled using coupled nonlinear evolution equations for the film thickness and surfactant concentration. Exploiting high-resolution numerical simulations, we describe the multi-region asymptotic structure of the spatially one-dimensional spreading flow and derive a simplified ODE model that captures its dominant features at large times. The model includes a version of Tanner's law accounting for a Marangoni flux through the drop's effective contact line, the magnitude of which is influenced by a rarefaction wave in the film ahead of the contact line. Focusing on the neighbourhood of the contact line, we then examine the stability of small-amplitude disturbances with spanwise variation, using long-wavelength asymptotics and numerical simulations to describe the growth-rate/wavenumber relationship. In addition to revealing physical mechanisms and new scaling properties, our analysis shows how initial conditions and transient dynamics have a long-lived influence on late-time flow structures, spreading rates and contact-line stability.

Acceptance Date Apr 7, 2015
Publication Date May 7, 2015
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Publisher Cambridge University Press
Pages 5-24
Keywords fingering instability, interfacial flows (free surface), thin films
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