Percolation and Reynolds Flow in Elastic Contacts of Isotropic and Anisotropic, Randomly Rough Surfaces

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.

Automated summary

In this work, 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 them, is numerically studied. The percolation threshold is found to be dependent on fluid flow direction in anisotropic systems, and a critical contact area near 0.415 is confirmed. Effective-medium treatments provide accurate expressions for Reynolds fluid flow conductances.