Geodesic
A lubrication equation for a simplified model of shear-thinning fluid
Francois James1 ; Meissa M’Baye2 ; Khawla Msheik3 ; Duc Nguyen4
1Institut Denis Poisson, Université d’Orléans, Université de Tours & CNRS UMR 7013, BP 6759, F-45067 Orléans Cedex 2, France
2Laboratoire Jean Leray, Université de Nantes & CNRS UMR 6629, BP 92208, F-44322 Nantes Cedex 3, France
3LAMA, Université Savoie Mont-Blanc & CNRS UMR 5127, F-73376 Le Bourget du Lac, France
4LAMA, Université Paris-Est Marne-la-Vallée & CNRS UMR 8050, F-77454 Marne-la-Vallée cedex 2, France
ESAIM. Proceedings, Tome 70 (2021), pp. 147-165
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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.
DOI : 10.1051/proc/202107010

Francois James  1   ; Meissa M’Baye  2   ; Khawla Msheik  3   ; Duc Nguyen  4

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 
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     author = {Francois James and Meissa M{\textquoteright}Baye and Khawla Msheik and Duc Nguyen},
     title = {A lubrication equation for a simplified model of shear-thinning fluid},
     journal = {ESAIM. Proceedings},
     pages = {147--165},
     year = {2021},
     volume = {70},
     doi = {10.1051/proc/202107010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202107010/}
}
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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, Tome 70 (2021), pp. 147-165. doi: 10.1051/proc/202107010

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