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• W2076292803 startingPage "679" @default.
• W2076292803 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 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." @default.
• W2076292803 created "2016-06-24" @default.
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• W2076292803 date "2007-12-01" @default.
• W2076292803 modified "2023-09-24" @default.
• W2076292803 title "Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves" @default.
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• W2076292803 doi "https://doi.org/10.1017/s0956792507007218" @default.
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