Numerical analysis of adhesion of rough surfaces shows that there exist one unique parameter determining whether the surface is sticky or not.
It is well known that neutral bodies attract each other by van der Waals forces. However, adhesive forces in macroscopic systems often are negligible. Kendall expressed this with his famous statement “solids are expected to adhere; the question is to explain why they do not, rather than why they do!” It is often believed that the reason for the weakness of adhesion in macroscopic contacts is the roughness of surfaces. It is the roughness which prevents intimate contact on the atomic scale. However, it was shown already 30 years ago – both theoretically and experimentally – that roughness sometimes can even enhance adhesion!
When the surfaces are smooth and when rough – the answer to this question was given, using simplified model roughness in form of regular waviness by Kenneth Johnson in 1995. He introduced a dimensionless parameter governing the adhesion behavior and found that above a critical value of this “Johnson parameter”, surfaces jump into complete contact even at zero load.
Since the classical work of Johnson, the situation in contact mechanics has changed drastically. Now researchers have a possibility to numerically simulate contacts of arbitrary complexity, even in the presence of adhesive interactions. In a recent paper, researchers from Technische Universität Berlin repeated analytical calculations by Johnson numerically and then extended them to contacts of curved rough bodies. They found that the resulting force of adhesion has a very simple structure: it is given by the solution of the corresponding smooth contact multiplied with a function depending only on the Johnson parameter. In all cases, researchers observed that the adhesive force increases at small roughness amplitudes while it sharply decreases after achieving some critical roughness. This confirming the old experiments by Briggs and Briscoe (1977) and Guduru (2007). Numerical simulations show that such unique “switching parameter” between adhesive and non-adhesive cases does exist also for randomly rough fractal surfaces.
Further details: Li Q, Pohrt R and Popov VL (2019) Adhesive Strength of Contacts of Rough Spheres. Front. Mech. Eng. 5:7. doi: 10.3389/fmech.2019.00007