Capillary adhesion between elastic solids with randomly rough surfaces

TL;DR

This paper investigates how capillary bridges influence contact area and adhesion between elastic solids with rough surfaces, depending on humidity levels, revealing optimal conditions for maximum adhesion and contact.

Contribution

It provides a theoretical analysis of capillary adhesion effects on elastic solids with rough surfaces, considering different elastic properties and humidity conditions.

Findings

Maximum contact area occurs at specific humidity levels related to surface roughness.

Work of adhesion peaks at high humidity, proportional to liquid surface tension.

Elastic softness influences the humidity level at which contact area is maximized.

Abstract

I study how the contact area and the work of adhesion, between two elastic solids with randomly rough surfaces, depend on the relative humidity. The surfaces are assumed to be hydrophilic, and capillary bridges form at the interface between the solids. For elastically hard solids with relative smooth surfaces, the area of real contact and therefore also the sliding friction, are maximal when there is just enough liquid to fill out the interfacial space between the solids, which typically occurs for $d_{\rm K} \approx 3 h_{\rm rms}$, where $d_{\rm K}$ is the height of the capillary bridge and $h_{\rm rms}$ the root-mean-square roughness of the (combined) surface roughness profile. For elastically soft solids, the area of real contact is maximal for very low humidity (i.e., small $d_{\rm K}$), where the capillary bridges are able to pull the solids into nearly complete contact. In both case, the work of adhesion is maximal (and equal to $2\gamma {\rm cos}\theta$, where $\gamma$ is the liquid surface tension and $\theta$ the liquid-solid contact angle) when $d_{\rm K} >> h_{\rm rms}$, corresponding to high relative humidity.