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A lubrication equation for a simplified model of shear-thinning fluid

Abstract : 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 illustations are provided, bringing to light the different possible behaviours.
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Contributor : Francois James <>
Submitted on : Thursday, May 14, 2020 - 11:23:17 AM
Last modification on : Wednesday, November 4, 2020 - 3:52:59 PM


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  • HAL Id : hal-02570086, version 1


Francois James, Meissa M'Baye, Khawla Msheik, Duc Nguyen. A lubrication equation for a simplified model of shear-thinning fluid. 2020. ⟨hal-02570086⟩



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