Theory of adhesion: role of surface roughness.

We discuss how surface roughness influences the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length scales. We consider two limiting cases relevant for (a) elastically hard solids with weak (or long ranged) adhesive interaction (DMT-limit) and (b) elastically soft solids with strong (or short ranged) adhesive interaction (JKR-limit). For the former cases we study the nature of the adhesion using different adhesive force laws (F ∼ u(-n), n = 1.5-4, where u is the wall-wall separation). In general, adhesion may switch from DMT-like at short length scales to JKR-like at large (macroscopic) length scale. We compare the theory predictions to results of exact numerical simulations and find good agreement between theory and simulation results.