Gravity-driven thin-film flow on a flexible substrate

P. D. Howell, J. Robinson, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We study the flow of a thin liquid film along a flexible substrate. The flow is modelled using lubrication theory, assuming that gravity is the dominant driving force. The substrate is modelled as an elastic beam that deforms in two dimensions. Steady solutions are found using numerical and perturbation methods, and several different asymptotic regimes are identified. We obtain a complete characterization of how the length and stiffness of the beam and the imposed liquid flux determine the profile of the liquid film and the resulting beam deformation.

Original languageEnglish (US)
Pages (from-to)190-213
Number of pages24
JournalJournal of Fluid Mechanics
StatePublished - Oct 2013

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • coating
  • lubrication theory
  • thin films


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