A note on the possibility of roughness enhancement of adhesion in Persson's theory

In an attempt to model the observed enhancement of adhesion in some classical experiments in the 1970-1980's, Persson introduced in his theory of adhesion between rough solids an "effective adhesion energy" term which is increased due to roughness-induced area increase. In the old experiments, the adhesion enhancement was measured to be up to one order of magnitude in terms of rolling resistance (and hence adhesion hysteresis), whereas it is generally smaller (up to 30-40%) for pull-off force. Here, an estimate the area increase in those experiments shows Persson's postulate is not supported since a discrepancy of at least one order of magnitude is found. Other explanations of adhesion enhancement come from more recent studies involving special axisymmetric indenters confirmed by experimental findings with negligible area increase, or by a model with well separated gaps in a fully random surface contact. However, even these models are very limited by their assumptions, and in the most general case of adhesion of random rough surfaces a comprehensive model remains elusive, and many questions remain open, requiring a detailed understanding of loading and unloading processes, of the possible effects of range of adhesive forces, of effects of roughness anisotropy, and so on.