Computation of the drag force on a rough sphere close to a wall

TL;DR

This paper develops a unified method to analyze how surface roughness affects the drag force on a sphere near a wall in Stokes flow, clarifying existing models and asymptotic expressions.

Contribution

It introduces a unified methodology for deriving asymptotics of drag force considering different roughness models in Stokes flow.

Findings

Unified approach clarifies existing asymptotic expressions

Different roughness models are systematically analyzed

Provides a comprehensive framework for surface roughness effects

Abstract

We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force. In this way, we recover and clarify the various expressions that can be found in the litterature.