Fluid flow at the interface between elastic solids with randomly rough surfaces

TL;DR

This paper models fluid flow at elastic solid interfaces with random roughness, integrating contact mechanics and effective medium theories to predict leak rates and anisotropy effects.

Contribution

It extends perturbation methods to arbitrary order and introduces a matrix D(Zeta) to describe surface anisotropy at different scales.

Findings

Calculated flow tensor and pressure flow factor for rough surfaces.

Extended perturbation treatment to higher orders in roughness amplitude.

Analyzed anisotropy effects for specific surface types.

Abstract

I study fluid flow at the interface between elastic solids with randomly rough surfaces. I use the contact mechanics model of Persson to take into account the elastic interaction between the solid walls and the Bruggeman effective medium theory to account for the influence of the disorder on the fluid flow. I calculate the flow tensor which determines the pressure flow factor and, e.g., the leak-rate of static seals. I show how the perturbation treatment of Tripp can be extended to arbitrary order in the ratio between the root-mean-square roughness amplitude and the average interfacial surface separation. I introduce a matrix D(Zeta), determined by the surface roughness power spectrum, which can be used to describe the anisotropy of the surface at any magnification Zeta. I present results for the asymmetry factor Gamma(Zeta) (generalized Peklenik number) for grinded steel and sandblasted PMMA surfaces.