Contact lines on stretched soft solids: Modeling anisotropic surface stresses

Abstract

We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu et al, Soft Matter 2018). Following a Green's function approach, we extend the surface-stress regularized Flamant-Cerruti problem to account for uniaxial pre-strains of the substrate. Surface profiles, including the heights and opening angles of wetting ridges, are provided for linearized and finite kinematics. We fit experimental wetting ridge shapes as a function of applied strain using two free parameters, the surface Lame coefficients. In comparison with experiments, we find that observed opening angles are more accurately captured using finite kinematics, especially with increasing levels of applied pre-strain. These fits qualitatively agree with the results of Xu et al, but revise values of the surface elastic constants.