Geometry of contact between self-affine surfaces

Abstract

We study the geometry of the contact between two rigid self-affine surfaces. We investigate the mean shape of the surface in the vicinity of the contact point as well as the probability distribution of apertures a as a function of the distance to the contact point. The latter reveals two distinct scaling regimes which are characterized. We show that as the two surfaces are shifted with respect to each other, the contact point on one surface undergoes a “Levy walk”. If u is the relative shift of the surfaces, the distance d between the two contact points (before and after the shift), scales as d ∝ uα where the exponent α is shown to be equal to the roughness exponent of the surfaces.