Analysis of the thin film flow in a rough domain filled with micropolar fluid
Inspired by the lubrication framework, in this paper a micropolar fluid flow through a rough thin domain is studied. The domains thickness is considered as the small parameter ? ? , while the roughness is defined by a periodical function with period of order ?2 ? 2 . Starting from three-dimensional micropolar equations and using asymptotic analysis with respect to ? ? , we formally derive the macroscopic model clearly detecting the effects of the specific rugosity profile and fluid microstructure. We provide the rigorous justification of our formally obtained asymptotic model by deriving the effective system by means of the two-scale convergence.
micropolar fluid two-scale convergence thin-film flow rough boundary different scales asymptotic expansion