From adhesion to wetting of a soft particle

TL;DR

This paper develops a thermodynamical model to analyze the deformation of soft elastic particles on rigid substrates, bridging small and large deformation regimes and providing exact energy expressions for equilibrium states.

Contribution

It introduces a unified energy expression that connects the JKR and Young-Dupré regimes and extends analysis to large deformations using fracture mechanics analogy.

Findings

Unified energy expression bridging deformation regimes

Exact energy derivation for equilibrium states

Framework applicable to very soft materials

Abstract

Using a thermodynamical approach, we calculate the deformation of a spherical elastic particle placed on a rigid substrate, under zero external load, and including an ingredient of importance in soft matter: the interfacial tension of the cap. In a first part, we limit the study to small deformation. In contrast with previous works, we obtain an expression for the energy that precisely contains the JKR and Young-Dupr\'e asymptotic regimes, and which establishes a continuous bridge between them. In a second part, we consider the large deformation case, which is relevant for future comparison with numerical simulations and experiments on very soft materials. Using a fruitful analogy with fracture mechanics, we derive the exact energy of the problem and thus obtain the equilibrium state for any given choice of physical parameters.