Porous squeeze-film flow

Knox, D.J. and Wilson, S.K. and Duffy, B.R. and McKee, S. (2015) Porous squeeze-film flow. IMA Journal of Applied Mathematics, 80 (2). pp. 376-409. ISSN 1464-3634 (https://doi.org/10.1093/imamat/hxt042)

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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.

  • Item type:Article
    ID code:49194
    Dates:
    Date
    Event
    2015
    Published
    14 November 2013
    Published Online
    8 October 2013
    Accepted
    Notes:This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record D. J. Knox, S. K. Wilson, B. R. Duffy, and S. McKee, Porous squeeze-film flow, IMA J Appl Math first published online November 2013, is available online at: http://dx.doi.org/10.1093/imamat/hxt042
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:12 Sep 2014 12:53
    Last modified:19 Apr 2024 00:14
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/49194
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