Single-asperity contact mechanics with positive and negative work of adhesion: Influence of finite-range interactions and a continuum description for the squeeze-out of wetting fluids

In this work, single-asperity contact mechanics is investigated for positive and negative work of adhesion Δγ. In the latter case, finite-range repulsion acts in addition to hard-wall constraints. This constitutes a continuum model for a contact immersed in a strongly wetting fluid, which can only be squeezed out in the center of the contact through a sufficiently large normal load F N. As for positive work of adhesion, two stable solutions can coexist in a finite range of normal loads. The competing solutions can be readily interpreted as contacts with either a load-bearing or a squeezed-out fluid. The possibility for coexistence and the subsequent discontinuous wetting and squeeze-out instabilities depend not only on the Tabor coefficient μT but also on the functional form of the finite-range repulsion. For example, coexistence and discontinuous wetting or squeeze-out do not occur when the repulsion decreases exponentially with distance. For positive work of adhesion, the normal displacement mainly depends on F N, Δγ, and μT but – unlike the contact area – barely on the functional form of the finite-range attraction. The results can benefit the interpretation of atomic force microscopy in liquid environments and the modeling of multi-asperity contacts.