Shailesh Naire s.naire@keele.ac.uk
The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate
Naire
Authors
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.
Acceptance Date | Apr 7, 2015 |
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Publication Date | May 7, 2015 |
Publicly Available Date | Mar 28, 2024 |
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 |
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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
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