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We study numerically local models for the mechanical contact between twosolids with rough surfaces. When the solids softly touch either throughadhesion or by a small normal load $L$, contact only forms at isolated patchesand fluids can pass through the interface. When the load surpasses a thresholdvalue, $L_c$, adjacent patches coalesce at a critical constriction, i.e., nearpoints where the interfacial separation between the undeformed surfaces forms asaddle point. This process is continuous without adhesion and the interfacialseparation 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 divergesas $(L_c-L)^\beta$ with $\beta = 3.45$. Contact merging and destruction nearsaddle points becomes discontinuous when either short-range adhesion orspecific short-range repulsion are added to the hard-wall repulsion. Theseresults imply that coalescence and break-up of contact patches can contributeto Coulomb friction and contact aging.

europhysics letters

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