Inspired by the lubrication framework, in this paper we consider a micropolar fluid flow through a rough thin domain, whose thickness is considered as the small parameter ε while the roughness at the bottom is defined by a periodical function with period of order $$ and amplitude ε$$, with δ> ℓ >1. Assuming nonzero boundary conditions on the rough bottom and by means of a version of the unfolding method, we identify a critical case and obtain three macroscopic models coupling the effects of the rough bottom and the nonzero boundary conditions. In every case we provide the corresponding micropolar Reynolds equation. We apply these results to carry out a numerical study of a model of squeeze-film bearing lubricated with a micropolar fluid. Our simulations reveal the impact of the roughness coupled with the nonzero boundary conditions on the performance of the bearing, and suggest that the introduction of a rough geometry may contribute to enhancing the mechanical properties of the device.
Keywords: Thin-film flow, micropolar fluid, rough boundary, homogenization, unfolding method
@article{M2AN_2022__56_4_1255_0,
author = {Bonnivard, Matthieu and Pa\v{z}anin, Igor and Su\'arez-Grau, Francisco J.},
title = {A generalized {Reynolds} equation for micropolar flows past a ribbed surface with nonzero boundary conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1255--1305},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {4},
doi = {10.1051/m2an/2022039},
mrnumber = {4444534},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022039/}
}
TY - JOUR AU - Bonnivard, Matthieu AU - Pažanin, Igor AU - Suárez-Grau, Francisco J. TI - A generalized Reynolds equation for micropolar flows past a ribbed surface with nonzero boundary conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 1255 EP - 1305 VL - 56 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022039/ DO - 10.1051/m2an/2022039 LA - en ID - M2AN_2022__56_4_1255_0 ER -
%0 Journal Article %A Bonnivard, Matthieu %A Pažanin, Igor %A Suárez-Grau, Francisco J. %T A generalized Reynolds equation for micropolar flows past a ribbed surface with nonzero boundary conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 1255-1305 %V 56 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022039/ %R 10.1051/m2an/2022039 %G en %F M2AN_2022__56_4_1255_0
Bonnivard, Matthieu; Pažanin, Igor; Suárez-Grau, Francisco J. A generalized Reynolds equation for micropolar flows past a ribbed surface with nonzero boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 4, pp. 1255-1305. doi: 10.1051/m2an/2022039
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