Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Levy, R; Shearer, M; Witelski, TP

Published Date

  • December 1, 2007

Published In

Volume / Issue

  • 18 / 6

Start / End Page

  • 679 - 708

Electronic International Standard Serial Number (EISSN)

  • 1469-4425

International Standard Serial Number (ISSN)

  • 0956-7925

Digital Object Identifier (DOI)

  • 10.1017/S0956792507007218

Citation Source

  • Scopus