Volume 70, 2021CEMRACS 2019 - Geophysical Fluids, Gravity Flows
|Page(s)||147 - 165|
|Published online||01 June 2021|
A lubrication equation for a simplified model of shear-thinning fluid
1 Institut Denis Poisson, Université d’Orléans, Université de Tours & CNRS UMR 7013, BP 6759, F-45067 Orléans Cedex 2, France
2 Laboratoire Jean Leray, Université de Nantes & CNRS UMR 6629, BP 92208, F-44322 Nantes Cedex 3, France
3 LAMA, Université Savoie Mont-Blanc & CNRS UMR 5127, F-73376 Le Bourget du Lac, France
4 LAMA, Université Paris-Est Marne-la-Vallée & CNRS UMR 8050, F-77454 Marne-la-Vallée cedex 2, France
A lubrication equation is obtained for a simplified shear-thinning fluid. The simplified rheology consists of a piecewise linear stress tensor, resulting in a two-viscosity model. This can be interpreted as a modified Bingham fluid, which can be recovered in a specific limit. The lubrication equation is obtained in two steps. First two scalings are performed on the incompressible Navier-Stokes equations, namely the long-wave scaling and the slow motion scaling. Second, the resulting equations are averaged along the vertical direction. Numerical illustrations are provided, bringing to light the different possible behaviours.
© EDP Sciences, SMAI 2021
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