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Proceedings/Recueil Des Communications ESAIM: Proceedings and Surveys Année : 2021

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

Résumé

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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Dates et versions

hal-02570086 , version 1 (14-05-2020)

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Francois James, Meissa M’baye, Khawla Msheik, Duc Nguyen. A lubrication equation for a simplified model of shear-thinning fluid. ESAIM: Proceedings and Surveys, 70, pp.147-165, 2021, ⟨10.1051/proc/202107010⟩. ⟨hal-02570086⟩
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