Contact and Adhesion of Fractal Interfaces

Experimental surfaces typically have roughness that can be described as self-affine frac-tal. Self-affine scaling has been observed on many materials and across wide range of length scales, from the atomic to the tectonic. This roughness greatly reduces the frac-tion of the area that is in intimate molecular contact and thus can contribute to friction and adhesion. The talk will describe recent numerical calculations of elastic and elasto-plastic contact between rough surfaces with nominally flat or spherical geometries on large scales. An efficient Green’s function approach allows calculations for systems with roughness on nanometer to micrometer scales. These calculations exactly reproduce contact geometries measured using contact-sensitive fluorescent markers and reveal the role of plasticity played in contact. Results for a wide range of geometries can be col-lapsed using simple scaling relations that depend on the root mean squared surface slope, sphere radius, elastic modulus and work of adhesion. The scaling relations ex-plain why adhesive interactions have little effect unless the surfaces are extremely smooth or soft.