Extended Lubrication Theory: Improved Estimates of Flow in Channels with Variable Geometry

TL;DR

This paper extends lubrication theory by incorporating higher-order terms to more accurately predict fluid flow and pressure drops in channels with variable geometry, validated through experiments and numerical simulations.

Contribution

It introduces a systematic higher-order extension to lubrication theory for better flow estimates in channels with modest aspect ratio variations.

Findings

Higher-order analytical solutions align well with experimental data.

Numerical results show very good agreement with analytical predictions.

Extended theory accurately estimates pressure drops in channels with shape changes.

Abstract

Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions while numerical results are in very good agreement with the higher-order analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.