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

  • O. E. JENSEN (a1) and S. NAIRE (a2)
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.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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