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

TL;DR

This paper rigorously derives reduced models for micropolar fluid flow in thin films with Navier slip boundary conditions, revealing how slip effects influence the pressure and flow characteristics across different slip regimes.

Contribution

It provides a rigorous asymptotic analysis and explicit reduced models for micropolar thin-film flow under various slip conditions, extending classical Reynolds equations.

Findings

Derived explicit formulas for velocity and microrotation fields.

Identified three slip regimes: perfect, partial, and no-slip.

Formulated a generalized Reynolds-type equation incorporating slip effects.

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.