Percolation and Reynolds flow in elastic contacts of isotropic and anisotropic, randomly rough surface

TL;DR

This study numerically investigates elastic contact and Reynolds flow between rough surfaces, revealing anisotropy effects on percolation thresholds and providing accurate models for fluid conductance based on surface properties.

Contribution

It introduces a detailed numerical analysis of elastic contact and fluid flow in anisotropic rough surfaces, including new insights into percolation thresholds and effective-medium models.

Findings

Percolation threshold depends on flow direction in anisotropic surfaces.

Critical contact area is approximately 0.415.

Derived closed-form expressions for Reynolds flow conductance.

Abstract

In this work, we numerically study the elastic contact between isotropic and anisotropic, rigid, randomly rough surfaces and linearly elastic counterfaces as well as the subsequent Reynolds flow through the gap between the two contacting solids. We find the percolation threshold to depend on the fluid-flow direction when the Peklenik number indicates anisotropy unless the system size clearly exceeds the roll-off wave length parallel to the easy flow direction. A critical contact area near 0.415 is confirmed. Heuristically corrected effective-medium treatments satisfactorily provide Reynolds fluid-flow conductances, e.g., for isotropic roughness, we identify accurate closed-form expressions, which only depend on the mean gap and the relative contact area.