Elastic-plated gravity currents

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 expl...

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Bibliographic Details
Published inEuropean journal of applied mathematics Vol. 26; no. 1; pp. 1 - 31
Main Authors HEWITT, I. J., BALMFORTH, N. J., DE BRUYN, J. R.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2015
Subjects
Applied mathematics
Asymptotic properties
Computational fluid dynamics
Contact
Elastohydrodynamic lubrication
Fluid dynamics
Fluid flow
Fluids
Mathematical analysis
Mathematical models
Nonlinear equations
Planes
Spreading
Thin films
Viscosity
elastohydrodynamic lubrication theory
thin film
gravity current
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792514000291