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Contact in a viscous fluid. Part 1. A falling wedge

Published online by Cambridge University Press:  08 March 2010

C. J. CAWTHORN  and
N. J. BALMFORTH
C. J. CAWTHORN
Affiliation:
DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
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
*
†Email address for correspondence: [email protected]
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Abstract

Computations are presented of the upward force on a two-dimensional wedge descending towards a plane surface due to the Stokes flow of an intervening viscous fluid. The predictions are compared with those of lubrication theory and an approximate analytical solution; all three predict a logarithmic divergence of the force with the minimum separation. An object falling vertically under gravity will therefore make contact with an underlying plane surface in finite time if roughened by asperities with sharp corners (with smooth surfaces, contact is made only after infinite time). Contact is still made in finite time if the roughened object also moves horizontally or rotates as it falls.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 646 , 10 March 2010 , pp. 327 - 338
Copyright
Copyright © Cambridge University Press 2010

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References

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