Elastocapillarity: Surface Tension and the Mechanics of Soft Solids

Abstract

It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play an central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresses play an important role. We highlight how surface stresses causes dramatic departures from classic theories for wetting (Young-Dupré), adhesion (Johnson-Kendall-Roberts), and composites (Eshelby). A common thread is the importance of the ratio of surface stress to an elastic modulus, which defines a length scale below which surface stresses can dominate.

Strain-Dependent Solid Surface Stress and the Stiffness of Soft Contacts

“…The transition between these domains is determined by the elastocapillary length, which is usually assumed to be a material constant [30]. Here, the dramatic increase of ΔS with sphere displacement suggests a concomitant increase in the elastocapillary length with deformation.…”

Analogies between elastic and capillary interfaces

“…Solid interfaces exhibit an excess surface free energy, just like liquid interfaces. However, only fairly recently has it been appreciated that the resulting surface tension γ s , often called surface stress in solid mechanics [21,22,24], has important mechanical consequences: It implies a jump in normal stress γ s κ, where κ is the interface curvature, and this can dramatically change the mechanics of very soft elastic materials. Here we highlight a few striking consequences of solid surface tension.…”

“…currently being actively explored [20][21][22]. In the second part of the paper we therefore highlight some striking features of elastocapillary interfaces and discuss some deep connections between between the adhesion of solids and the wetting of liquids.…”

“…Interestingly, when considering exceedingly soft matter, the wetting and lubrication becomes even more intricate and the analogy with liquid interfaces takes on a whole new meaning. Namely, gels and elastomers themselves possess a solid surface tension γ s and as a consequence share common mechanical features with liquid interfaces [17][18][19][20][21][22]. Indeed, surface effects can compete with, and even dominate over, bulk elastic effects when Young's modulus E of the solid is sufficiently small.…”

Role reversal: Liquid “Cheerios” on a solid sense each other

“…Collectively, these phenomena are being referred to as elastocapillarity (8,9). Two important (static) problems that involve a contact line are wetting of a compliant solid by drops (two fluids, one solid) and adhesive contact between a particle and a compliant solid (two solids, one fluid).…”