Navier slip effects in micropolar thin-film flow: a rigorous derivation of Reynolds-type models

Abstract: We study the stationary flow of incompressible micropolar fluid in a thin three-dimensional domain under Navier slip boundary condition for the velocity and no-spin condition for microrotation. After rescaling the governing equations, we perform a rigorous asymptotic analysis as the film thickness tends to zero, considering a friction coefficient dependent on the small parameter. According to the scaling of the slip coefficient, we identify three distinct regimes: perfect slip, partial slip, and no-slip. For each regime, we derive the corresponding reduced micropolar system and obtain explicit expressions for the velocity and microrotation fields. This leads to a generalized Reynolds-type equation for the pressure, highlighting the impact of slip effects on the micropolar thin-film flow.