Theory of adhesion: role of surface roughness

TL;DR

This paper explores how surface roughness affects adhesion between elastic solids, introducing a scale-dependent Tabor number and analyzing the transition between DMT and JKR adhesion regimes, supported by numerical simulations.

Contribution

It presents a unified theory of adhesion considering surface roughness and introduces a scale-dependent Tabor number to distinguish adhesion regimes.

Findings

Adhesion can switch from DMT-like to JKR-like depending on length scale.

Theoretical predictions agree well with numerical simulations.

Surface roughness significantly influences the adhesion behavior at different scales.

Abstract

We discuss how surface roughness influence the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length scales. We consider two limiting cases relevant for (a) elastically hard solids with weak adhesive interaction (DMT-limit) and (b) elastically soft solids or strong adhesive interaction (JKR-limit). For the former cases we study the nature of the adhesion using different adhesive force laws ($F\sim u^{-n}$, $n=1.5-4$, where $u$ is the wall-wall separation). In general, adhesion may switch from DMT-like at short length scales to JKR-like at large (macroscopic) length scale. We compare the theory predictions to the results of exact numerical simulations and find good agreement between theory and the simulation results.