On stickiness criteria for multiscale random rough contacts

We have just submitted a paper which solves a problem that I have been struggling to solve for many years.

Any comments are welcome to improve, while the paper goes the standard review process in the journal we submitted it.

On stickiness of multiscale randomly rough surfacesG. Violano, L. Afferrante, A. Papangelo, M. Ciavarella(Submitted on 25 Oct 2018)We derive a very simple and effective stickiness criterion for solids having random roughness using a new asymptotic theory, which we validate with that of Persson and Scaraggi and independent numerical experiments. Previous claims that stickiness may depend on small scale quantities such as rms slopes and/or curvatures, obtained by making oversimplified assumptions on the contact area geometry, are largely incorrect, as the truncation of the PSD spectrum of roughness at short wavelengths is irrelevant. We find stickiness is destroyed typically at roughness amplitudes up to three orders of magnitude larger than the range of attractive forces. With typical nanometer values of the latter, the criterion gives justification to the qualitative well known empirical Dalhquist criterion for stickiness which demands adhesives to have elastic modulus lower than about 1MPa. The results clarifies a much debated question in both the scientific and technological world of adhesion, and may serve as benchmark for better comprehension of the role of roughness.

https://arxiv.org/abs/1810.10960