Fluid dynamics at the interface between contacting elastic solids with randomly rough surfaces

We study fluid dynamics at the interface between elastic solids with randomly rough surfaces. The contact mechanics model of Persson is used to take into account the elastic interaction between the solid walls, and the Bruggeman effective medium theory to account for the influence of the disorder on the fluid flow. We calculated the flow tensor which determines the pressure flow factor and, for example, the leak rate of static seals. It is shown how the perturbation treatment of Tripp can be extended to arbitrary order in the ratio between the root-mean-square roughness amplitude and the average interfacial surface separation. We introduce a matrix D(zeta), determined by the surface roughness power spectrum, which can be used to describe the anisotropy of the surface at any magnification zeta. Results are presented for the asymmetry factor gamma (zeta) ( generalized Peklenik number) for grinded steel and sandblasted PMMA surfaces.