Surface tension and contact with soft elastic solids

TL;DR

This paper investigates how solid surface tension influences contact mechanics in soft materials, revealing deviations from classical JKR theory at small scales and proposing a generalized model incorporating surface tension effects.

Contribution

It introduces a modified contact mechanics model that accounts for solid surface tension, explaining deviations from JKR theory at small scales in soft elastic solids.

Findings

JKR theory applies only above a critical lengthscale.

Solid surface tension causes size-independent contact angles.

A generalized theory accurately predicts small-scale indentation behavior.

Abstract

Johnson-Kendall-Robert (JKR) theory is the basis of modern contact mechanics. It describes how two deformable objects adhere together, driven by adhesion energy and opposed by elasticity. However, it does not include solid surface tension, which also opposes adhesion by acting to flatten the surface of soft solids. We tested JKR theory to see if solid surface tension affects indentation behaviour. Using confocal microscopy, we characterised the indentation of glass particles into soft, silicone substrates. While JKR theory held for particles larger than a critical, elastocapillary lengthscale, it failed for smaller particles. Instead, adhesion of small particles mimicked the adsorption of particles at a fluid interface, with a size-independent contact angle between the undeformed surface and the particle given by a generalised version of Young's law. A simple theory quantitatively captures this behaviour, and explains how solid surface tension dominates elasticity for small-scale indentation of soft materials.