The surface roughness power spectrum C(q), the Fourier transform of the height-height correlation function of a randomly rough surface, is the single input that governs how two solids touch. Measured height profiles show that many practical surfaces are self-affine fractal over a wave-vector range, with C(q) decaying as q^-2(H+1) and fractal dimension Df = 3 - H, often above a long-distance roll-off wave vector q0. Treating the interfacial stress distribution as diffusing in the magnification at which the interface is viewed yields a real contact area proportional to load at small load, which is the physical origin of Coulomb's friction law, and extends to viscoelastic solids whose contact area grows with contact time. The same spectrum then determines leakage through seals, the viscoelastic dissipation that produces rubber friction, and why surface roughness usually destroys adhesion between macroscopic bodies.
This 2005 topical review (J. Phys.: Condens. Matter 17, R1-R62) by Persson, Albohr, Tartaglino, Volokitin and Tosatti argues that the surface roughness power spectrum C(q) -- the Fourier transform of…