Interfacial fluid flow for systems with anisotropic roughness

I discuss fluid flow at the interface between solids with anisotropic roughness. I show that the Bruggeman effective medium theory and the critical junction theory give nearly the same results for the fluid flow conductivity. This shows that, in most cases, the surface roughness observed at high magnification is irrelevant for fluid flow problems such as the leakage of static seals, and fluid squeeze-out. The effective medium theory predicts that the fluid flow conductivity vanishes at the relative contact area A/A₀ = 0.5 independent of the anisotropy. However, the effective medium theory does not solve the elastic contact mechanics problem but is based on a purely geometric argument. Thus, for anisotropic roughness the contact area may percolate at different values of A/A₀ depending on the direction. We discuss how this may be taken into account in the effective medium and critical junction theories.