Journal
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
Volume 26, Issue -, Pages 1-31Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0956792514000291
Keywords
elastohydrodynamic lubrication theory; thin film; gravity current
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Funding
- Killam Foundation
- NSERC
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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.
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