Naire, S and Jensen, OE (2015) The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate. Journal of Fluid Mechanics, 554. pp. 5-24. ISSN 1469-7645

[thumbnail of paper_revision.pdf]
paper_revision.pdf - Submitted Version
Available under License Creative Commons Attribution.

Download (1MB) | Preview


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.

Item Type: Article
Uncontrolled Keywords: fingering instability, interfacial flows (free surface), thin films
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 04 May 2015 08:31
Last Modified: 26 Apr 2019 12:51

Actions (login required)

View Item
View Item