Porous squeeze-film flow

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Abstract

The squeeze-film flow of a thin layer of Newtonian fluid filling the gap between a flat impermeable surface moving under a prescribed constant load and a flat thin porous bed coating a stationary flat impermeable surface is considered. Unlike in the classical case of an impermeable bed, in which an infinite time is required for the two surfaces to touch, for a porous bed contact occurs in a finite contact time. Using a lubrication approximation an implicit expression for the fluid layer thickness and an explicit expression for the contact time are obtained and analysed. In addition, the fluid particle paths are calculated, and the penetration depths of fluid particles into the porous bed are determined. In particular, the behaviour in the asymptotic limit of small permeability, in which the contact time is large but finite, is investigated. Finally, the results are interpreted in the context of lubrication in the human knee joint, and some conclusions are drawn about the contact time of the cartilage-coated femoral condyles and tibial plateau and the penetration of nutrients into the cartilage.
Original languageEnglish
Pages (from-to)376-409
Number of pages34
JournalIMA Journal of Applied Mathematics
Volume80
Issue number2
Early online date14 Nov 2013
DOIs
Publication statusPublished - 2015

Keywords

  • porous squeeze-film flow
  • finite contact time
  • fluid particle paths
  • penetration depths

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