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

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.