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Simple waves and shocks in a thin film of a perfectly soluble anti-surfactant solution

Research output: Contribution to journalArticle

  • J. J.A. Conn
  • B. R. Duffy
  • D. Pritchard
  • S. K. Wilson
  • K. Sefiane

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Original languageEnglish
Pages (from-to)167-178
Number of pages12
JournalJournal of Engineering Mathematics
Volume107
Issue number1
DOIs
Publication statusPublished - 1 Dec 2017

Abstract

We consider the dynamics of a thin film of a perfectly soluble anti-surfactant solution in the limit of large capillary and Péclet numbers in which the governing system of nonlinear equations is purely hyperbolic. We construct exact solutions to a family of Riemann problems for this system, and discuss the properties of these solutions, including the formation of both simple-wave and uniform regions within the flow, and the propagation of shocks in both the thickness of the film and the gradient of the concentration of solute.

    Research areas

  • Anti-surfactant, Hyperbolic system, Marangoni effect, Riemann problems, Shocks, Simple waves

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