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Elastic-plated gravity currents

Published online by Cambridge University Press:  10 October 2014

I. J. HEWITT ,
N. J. BALMFORTH  and
J. R. DE BRUYN
I. J. HEWITT
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada email: hewitt@maths.ox.ac.uk
N. J. BALMFORTH
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada email: hewitt@maths.ox.ac.uk
J. R. DE BRUYN
Affiliation:
Department of Physics and Astronomy, University of Western Ontario, London, Ontario, Canada
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Abstract

We consider a nonlinear diffusion equation describing the planar spreading of a viscous fluid injected between an elastic sheet and an underlying rigid plane. The dynamics depends sensitively on the physical conditions at the contact line where the sheet is lifted off the plane by the fluid. We explore two possibilities for these conditions (or “regularisations”): a pre-wetted film and a constant-pressure fluid lag (a gas-filled gap between the fluid edge and the contact line). For both flat and inclined planes, we compare numerical and asymptotic solutions, identifying the distinct stages of evolution and the corresponding characteristic rates of spreading.

Keywords

elastohydrodynamic lubrication theorythin filmgravity current
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 1 , February 2015 , pp. 1 - 31
Copyright
Copyright © Cambridge University Press 2014 

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