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    Porous squeeze-film flow

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    Type
    Article
    Authors
    Knox, D. J.
    Wilson, S. K.
    Duffy, B. R.
    McKee, S.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2013-11-14
    Online Publication Date
    2013-11-14
    Print Publication Date
    2015-04-01
    Permanent link to this record
    http://hdl.handle.net/10754/599340
    
    Metadata
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    Abstract
    © 2013 © The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. 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.
    Citation
    Knox DJ, Wilson SK, Duffy BR, McKee S (2013) Porous squeeze-film flow. IMA Journal of Applied Mathematics 80: 376–409. Available: http://dx.doi.org/10.1093/imamat/hxt042.
    Sponsors
    This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Oxford University Press (OUP)
    Journal
    IMA Journal of Applied Mathematics
    DOI
    10.1093/imamat/hxt042
    ae974a485f413a2113503eed53cd6c53
    10.1093/imamat/hxt042
    Scopus Count
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