Contact mechanics of and Reynolds flow through saddle points: On the coalescence of contact patches and the leakage rate through near-critical constrictions

TL;DR

This study numerically investigates how contact patches between rough surfaces coalesce at saddle points, affecting fluid flow and potentially influencing friction and aging, with a focus on the critical load threshold and flow resistance divergence.

Contribution

It introduces a detailed numerical analysis of contact patch coalescence at saddle points, revealing the critical behavior and flow resistance scaling near the percolation threshold.

Findings

Flow resistance diverges as (L_c - L)^-3.45 near critical load

Contact patches coalesce continuously without adhesion

Adhesion or short-range repulsion causes discontinuous contact merging

Abstract

We study numerically local models for the mechanical contact between two solids with rough surfaces. When the solids softly touch either through adhesion or by a small normal load $L$, contact only forms at isolated patches and fluids can pass through the interface. When the load surpasses a threshold value, $L_c$, adjacent patches coalesce at a critical constriction, i.e., near points where the interfacial separation between the undeformed surfaces forms a saddle point. This process is continuous without adhesion and the interfacial separation near percolation is fully defined by scaling factors and the sign of $L_c-L$. The scaling factors lead to a Reynolds flow resistance which diverges as $(L_c-L)^\beta$ with $\beta = 3.45$. Contact merging and destruction near saddle points becomes discontinuous when either short-range adhesion or specific short-range repulsion are added to the hard-wall repulsion. These results imply that coalescence and break-up of contact patches can contribute to Coulomb friction and contact aging.