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

Conn, J. J. A. and Duffy, B. R. and Pritchard, D. and Wilson, S. K. and Sefiane, K. (2017) Simple waves and shocks in a thin film of a perfectly soluble antisurfactant solution. Journal of Engineering Mathematics, 107 (1). pp. 167-178. ISSN 0022-0833

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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.