A pinned or free-floating rigid plate on a thin viscous film

Philippe H. Trinh, Stephen K. Wilson, Howard A. Stone

Research output: Contribution to journalArticle

2 Citations (Scopus)
52 Downloads (Pure)


A pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work is to describe how the competing effects of the speed of the substrate, surface tension, viscosity, and, in the case of a pinned plate, the prescribed pressure in the reservoir of fluid at its upstream end, determine the possible equilibrium positions of the plate, the free surface, and the flow within the film. The present problems are of interest both in their own right as paradigms for a range of fluid–structure interaction problems in which viscosity and surface tension both play an important role, and as a first step towards the study of elastic effects.
Original languageEnglish
Pages (from-to)407-430
Number of pages24
JournalJournal of Fluid Mechanics
Early online date11 Nov 2014
Publication statusPublished - 10 Dec 2014


  • capillary flows
  • lubrication theory
  • thin films
  • rigid plate
  • free boundary problem
  • fluid structure interaction problem

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