Growing surfactant waves in thin liquid films driven by gravity


Journal Article

The dynamics of a gravity-driven thin film flow with insoluble surfactant are described in the lubrication approximation by a coupled system of nonlinear PDEs. When the total quantity of surfactant is fixed, a traveling wave solution exists. For the case of constantflux of surfactant from an upstream reservoir, global traveling waves no longer exist as the surfactant accumulates at the leading edge of the thin film profile. The dynamics can be described using matched asymptotic expansions for t→∞ . The solution is constructed from quasistatically evolving traveling waves. The rate of growth of the surfactant profile is shown to be O(√t) and is supported by numerical simulations.

Full Text

Duke Authors

Cited Authors

  • Witelski, TP; Shearer, M; Levy, R

Published Date

  • December 1, 2006

Published In

Volume / Issue

  • 2006 /

Electronic International Standard Serial Number (EISSN)

  • 1687-1197

International Standard Serial Number (ISSN)

  • 1687-1200

Digital Object Identifier (DOI)

  • 10.1155/AMRX/2006/15487

Citation Source

  • Scopus