Nonlinear Reynolds equation for hydrodynamic lubrication

TL;DR

This paper introduces a new nonlinear correction to the classical Reynolds equation to account for pressure-dependent viscosity, improving the accuracy of hydrodynamic lubrication predictions.

Contribution

It derives a rigorous nonlinear Reynolds equation considering pressure-dependent viscosity, extending classical models with new shear-rate related terms.

Findings

Modified equation predicts higher pressures and viscosities in flow domain

Numerical comparison shows significant differences from classical Reynolds equation

Enhanced model captures effects of pressure-dependent viscosity more accurately

Abstract

We derive a novel and rigorous correction to the classical Reynolds lubrication approximation for fluids with viscosity depending upon the pressure. Our analysis shows that the pressure dependence of viscosity leads to additional nonlinear terms related to the shear-rate and arising from a non negligible cross-film pressure. We present a numerical comparison between the classical Reynolds equation and our modified equation and conclude that the modified equation leads to the prediction of higher pressures and viscosities in the flow domain.