The mechanical equilibrium of soft solids with surface elasticity

Abstract

Recent experiments have shown that surface stresses in soft materials can have a significant strain-dependence. Here we explore the implications of this surface elasticity to show how, and when, we expect it to arise. We develop the appropriate boundary condition, showing that it simplifies significantly in certain cases. We show that surface elasticity's main role is to stiffen a solid surface's response to in-plane tractions, in particular at length-scales smaller than a characteristic elastocapillary length. We also investigate how surface elasticity affects the Green's-function problem of a line force on a flat, incompressible, linear-elastic substrate. There are significant changes to this solution, especially in that the well-known displacement singularity is regularised. This raises interesting implications for soft phenomena like wetting contact lines, adhesion and friction. Finally, we discuss open questions, future directions, and close ties with existing fields of research.

Droplets on Soft Surfaces Exhibit a Reluctance to Coalesce due to an Intervening Wetting Ridge

“…The solution procedure employed here has been previously developed and described in detail by Style and Xu. [33] The surface stress is represented by a linear-elastic constitutive relationship…”

“…The solution procedure employed here has been previously developed and described in detail by Style and Xu. [ 33 ] The surface stress is represented by a linear‐elastic constitutive relationship where ϒ 0 is the residual stress in the absence of any strain, µ s and λ s are the two surface Lamé constants, is the infinitesimal surface strain tensor, is its trace, and is the identity tensor. The surface Lamé constants are different from the bulk Lamé constants; the latter are known functions of the bulk Young's modulus and Poisson's ratio for a linear elastic material.…”

Chemomechanical equilibrium at the interface between a simple elastic solid and its liquid phase

“…Similar to externally applied surface loads, surface tension will equally deform the interior of a soft solid. This is the subject of the new and fascinating field of elasto-capillarity [45][46][47] . Solid nucleation will be a more ambitious goal.…”

Elasticity and damping ratio measurement of droplets on super-hydrophobic surfaces

“…For verifying the relationship between the elasticity of droplets and viscosity, we prepared three different concentrations of glycerol solution (AR, Shanghai Hushi Laboratorial Equipment Co., Ltd.): 0 wt%, 50 wt% and 75 wt%. The viscosity of glycerol solution with different concentrations varies greatly, but the difference of surface tension can be neglected [29]. For example, the surface tension values of 0 wt%, 50 wt% and 75 wt% glycerol solutions are 72.8 mN m −1 , 68.3 mN m −1 and royalsocietypublishing.org/journal/rsos R. Soc.…”

“…For verifying the relationship between the elasticity of droplets and viscosity, we prepared three different concentrations of glycerol solution (AR, Shanghai Hushi Laboratorial Equipment Co., Ltd.): 0 wt%, 50 wt% and 75 wt%. The viscosity of glycerol solution with different concentrations varies greatly, but the difference of surface tension can be neglected [ 29 ]. For example, the surface tension values of 0 wt%, 50 wt% and 75 wt% glycerol solutions are 72.8 mN m −1 , 68.3 mN m −1 and 65.3 mN m −1 , respectively, but the viscosity has a big disparity of 1.0 mPa s, 6.0 mPa s and 60.0 mPa s. We can assess how the viscosity affects the droplet elasticity by measuring the elasticity of the same volume but with different concentrations of glycerol droplets under the same compression distance.…”