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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| Published in | European journal of applied mathematics Vol. 26; no. 1; pp. 1 - 31 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.02.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0956-7925 1469-4425 |
| DOI | 10.1017/S0956792514000291 |
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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. |
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| AbstractList | 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. |
| Author | DE BRUYN, J. R. BALMFORTH, N. J. HEWITT, I. J. |
| Author_xml | – sequence: 1 givenname: I. J. surname: HEWITT fullname: HEWITT, I. J. email: hewitt@maths.ox.ac.uk organization: 1Department of Mathematics, University of British Columbia, Vancouver, Canada email: hewitt@maths.ox.ac.uk – sequence: 2 givenname: N. J. surname: BALMFORTH fullname: BALMFORTH, N. J. email: hewitt@maths.ox.ac.uk organization: 1Department of Mathematics, University of British Columbia, Vancouver, Canada email: hewitt@maths.ox.ac.uk – sequence: 3 givenname: J. R. surname: DE BRUYN fullname: DE BRUYN, J. R. organization: 2Department of Physics and Astronomy, University of Western Ontario, London, Ontario, Canada |
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| Keywords | elastohydrodynamic lubrication theory thin film gravity current |
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| SubjectTerms | 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 |
| Title | Elastic-plated gravity currents |
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