Lubrication approximation for micro-particles moving along parallel walls

TL;DR

This paper derives explicit lubrication expressions for the friction of micro-particles moving between parallel walls in low-Reynolds-number flows, validating their accuracy against multipole solutions for various microchannel geometries.

Contribution

It provides explicit lubrication formulas for spherical particles in confined geometries and assesses their validity compared to detailed multipole calculations.

Findings

Lubrication expressions accurately predict particle friction in microchannels.

The formulas are valid for thin, wide, and long microchannels.

Lubrication approximation agrees well with multipole results within certain regimes.

Abstract

Lubrication expressions for the friction coefficients of a spherical particle moving in a fluid between and along two parallel solid walls are explicitly evaluated in the low-Reynolds-number regime. They are used to determine lubrication expression for the particle free motion under an ambient Poiseuille flow. The range of validity and the accuracy of the lubrication approximation is determined by comparing with the corresponding results of the accurate multipole procedure. The results are applicable for thin, wide and long microchannels, or quasi-two-dimensional systems.