On the singular nature of the elastocapillary ridge

Abstract

The functionality of soft interfaces is crucial to many applications in biology and surface science. Recent studies have used liquid drops to probe the surface mechanics of elastomeric networks. Experiments suggest an intricate surface elasticity, also known as the Shuttleworth effect, where surface tension is not constant but depends on substrate deformation. However, interpretations have remained controversial due to singular elastic deformations, induced exactly at the point where the droplet pulls the network. Here we reveal the nature of the elastocapillary singularity on a hyperelastic substrate with various constitutive relations for the interfacial energy. First, we finely resolve the vicinity of the singularity using goal-adaptive finite element simulations. This confirms the universal validity, also at large elastic deformations, of the previously disputed Neumann's law for the contact angles. Subsequently, we derive exact solutions of nonlinear elasticity that describe the singularity analytically. These solutions are in perfect agreement with numerics, and show that the stretch at the contact line, as previously measured experimentally, consistently points to a strong Shuttleworth effect. Finally, using Noether's theorem we provide a quantitative link between wetting hysteresis and Eshelby-like forces, and thereby offer a complete framework for soft wetting in the presence of the Shuttleworth effect.

17 Pages, 7 figures

References in corpus (14)

• Elastocapillarity: Surface Tension and the Mechanics of Soft Solids
• Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses
• The Deformation of an Elastic Substrate by a Three-Phase Contact Line
• Static wetting on deformable substrates, from liquids to soft solids
• Direct Measurement of Strain-dependent Solid Surface Stress
• Capillary Pressure and Contact Line Force on a Soft Solid
• Drops on soft solids: Free energy and double transition of contact angles
• Soft wetting and the Shuttleworth effect, at the crossroads between thermodynamics and mechanics
• Straight contact lines on a soft, incompressible solid
• Surface energy of strained amorphous solids
• The paradox of contact angle selection on stretched soft solids
• Dynamic solid surface tension causes droplet pinning and depinning
• Capillary fracture of soft gels
• Worst-case multi-objective error estimation and adaptivity

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• Emergence and Growth Dynamics of Wetting-induced Phase Separation on Soft Solids
• Effect of external tension on the wetting of an elastic sheet
• Unravelling the multiscale surface mechanics of soft solids