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Publications [#244233] of Thomas P. Witelski


Papers Published

  1. Levy, R; Shearer, M; Witelski, TP, Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves, European Journal of Applied Mathematics, vol. 18 no. 6 (2007), pp. 679-708, ISSN 0956-7925 [S0956792507007218], [doi]
    (last updated on 2018/02/25)

    The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerate-parabolic, and admits traveling wave solutions in which the free-surface height is piecewise constant, and the surfactant concentration is piecewise linear and continuous. The jumps and corners in the traveling waves are regularized when the small parameters are nonzero; their structure is revealed through a combination of analysis and numerical simulation. © 2007 Cambridge University Press.
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