Dynamics of Poro-viscoelastic Wetting with Large Swelling
The deposition of droplets onto a swollen polymer network induces the formation of a wetting ridge at the contact line. Current models typically consider either viscoelastic effects or poroelastic effects, while polymeric gels often exhibit both properties. In this study, we investigate the growth of the wetting ridge using a comprehensive large deformation theory that integrates both dissipative mechanisms - viscoelasticity and poroelasticity. In the purely poroelastic case, following an initial instantaneous incompressible deformation, the growth dynamics exhibit scale-free behavior, independent of the elastocapillary length or system size. A boundary layer of solvent imbibition between the solid surface (in contact with the reservoir) and the region of minimal chemical potential is created. At later times, the ridge equilibrates on the diffusion timescale given by the elastocapillary length. When viscoelastic properties are incorporated, our findings show that, during the early stages (prior to the viscoelastic relaxation timescale), viscoelastic effects dominate the growth dynamics of the ridge and solvent transport is significantly suppressed. Beyond the relaxation time, the late-time dynamics closely resemble those of the purely poroelastic case. These findings are discussed in light of recent experiments, showing how our approach offers a new interpretation framework for wetting of polymer networks of increasing complexity.