On stickiness of multiscale randomly rough surfaces

A new stickiness criterion for solids having random fractal roughness is derived using Persson’s theory with DMT-type adhesion. As expected, we find that stickiness, i.e. the possibility to sustain macroscopic tensile pressures or else non-zero contact area without load, is not affected by the truncation of the PSD spectrum of roughness at short wavelengths and can persist up to roughness amplitude orders of magnitude larger than the range of attractive forces. With typical nanometre values of the latter, the criterion gives justification to the well-known empirical Dalhquist criterion for stickiness that demands adhesives to have elastic modulus lower than about 1 MPa.