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Contact in a viscous fluid. Part 2. A compressible fluid and an elastic solid

Published online by Cambridge University Press:  08 March 2010

N. J. BALMFORTH ,
C. J. CAWTHORN  and
R. V. CRASTER
N. J. BALMFORTH*
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada Department of Earth and Ocean Science, University of British Columbia, 6339 Stores Road, Vancouver, BC V6T 1Z4, Canada
C. J. CAWTHORN
Affiliation:
DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
R. V. CRASTER
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
*
†Email address for correspondence: [email protected]
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Abstract

A lubrication theory is presented for the effect of fluid compressibility and solid elasticity on the descent of a two-dimensional smooth object falling under gravity towards a plane wall through a viscous fluid. The final approach to contact, which takes infinite time in the absence of both effects, is determined by numerical and asymptotic methods. Compressibility can lead to contact in finite time either during inertially generated oscillations or if the viscosity decreases sufficiently quickly with increasing pressure. The approach to contact is invariably slowed by allowing the solids to deform elastically; specific results are presented for an underlying elastic wall modelled as a foundation, half-space, membrane or beam.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 646 , 10 March 2010 , pp. 339 - 361
Copyright
Copyright © Cambridge University Press 2010

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