Justification of lubrication approximation: an application to fluid/solid interactions

TL;DR

This paper derives precise asymptotic solutions for the stationary Stokes problem in fluid domains with small gaps, validating the lubrication approximation in fluid/solid interaction scenarios.

Contribution

It provides rigorous asymptotic analysis of the Stokes flow in domains with narrow gaps, supporting the justification of lubrication approximation.

Findings

Sharp asymptotics for Stokes solutions in narrow gaps

Validation of lubrication approximation in fluid/solid interactions

Mathematical framework for small gap asymptotics

Abstract

We consider the stationary Stokes problem in a three-dimensional fluid domain $\mathcal F$ with non-homogeneous Dirichlet boundary conditions. We assume that this fluid domain is the complement of a bounded obstacle $\mathcal B$ in a bounded or an exterior smooth container $\Omega$. We compute sharp asymptotics of the solution to the Stokes problem when the distance between the obstacle and the container boundary is small.