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.

    ORCID iDs

    Conn, J. J. A. ORCID logoORCID: https://orcid.org/0000-0002-1772-1539, Duffy, B. R. ORCID logoORCID: https://orcid.org/0000-0003-2687-7938, Pritchard, D. ORCID logoORCID: https://orcid.org/0000-0002-9235-7052, Wilson, S. K. ORCID logoORCID: https://orcid.org/0000-0001-7841-9643 and Sefiane, K.;