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Publications [#244233] of Thomas P. Witelski
search www.ams.org.Papers Published
 Levy, R; Shearer, M; Witelski, TP, Gravitydriven thin liquid films with insoluble surfactant: Smooth traveling waves,
European Journal of Applied Mathematics, vol. 18 no. 6
(2007),
pp. 679708, ISSN 09567925 [S0956792507007218], [doi]
(last updated on 2018/09/19)
Abstract: 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 freesurface fluid height and the surfactant concentration. The oneparameter 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 gravitydriven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerateparabolic, and admits traveling wave solutions in which the freesurface 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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