An effective model for the lubrication with micropolar fluid

•Lubrication process with incompressible micropolar fluid is studied via asymptotic analysis.•New effective model in the form of the Brinkman-type system is proposed.•It explicitly acknowledges the effects of fluid microstructure.•The obtained result could be instrumental for creating more efficient numerical algorithms.

In this paper, using asymptotic analysis, we study the lubrication process with incompressible micropolar fluid. Starting from 3D micropolar equations, we derive the higher-order asymptotic model explicitly acknowledging the microstructure effects. The effective equations are similar to the Brinkman model for porous medium flow.