Simple waves and shocks in a thin film of a perfectly soluble antisurfactant solution

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Abstract

We consider the dynamics of a thin film of a perfectly soluble anti-surfactant solution in the limit of large capillary and Peclet 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.
Original languageEnglish
Pages (from-to)167-178
Number of pages12
JournalJournal of Engineering Mathematics
Volume107
Issue number1
Early online date3 Aug 2017
DOIs
Publication statusPublished - 31 Dec 2017

Keywords

  • hyperbolic system
  • Riemann problems
  • simple waves
  • shocks
  • anti-surfactants
  • Marangoni effect

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