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

Naire

Abstract

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.

Citation

Naire. (2015). The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate. Journal of Fluid Mechanics, 5-24. https://doi.org/10.1017/S0022112005008104

• 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
• DOI: https://doi.org/10.1017/S0022112005008104
• Keywords: fingering instability, interfacial flows (free surface), thin films
• Publisher URL: https://doi.org/10.1017/S0022112005008104