  We present a comprehensive theoretical and computational model that explores
the behavior of a thin hydrated film bonded to a non-hydrated / impermeable
soft substrate in the context of surface and bulk elasticity coupled with
surface diffusion kinetics. This type of coupling can manifests as an integral
aspect in diverse engineering processes encountered in optical interference
coatings, tissue engineering, soft electronics, and can prove important in
design process for the next generation of sensors and actuators, especially as
the focus is shifted to systems in smaller lengthscales. The intricate
interplay between solvent diffusion and deformation of the film is governed by
surface poroelasticity, and the viscoelastic deformation of the substrate.
While existing methodologies offer tools for studying coupled poroelasticity
involving solvent diffusion and network deformation, there exists a gap in
understanding how coupled poroelastic processes occurring in a film attached to
the boundary of a highly deformable solid can influence its response. In this
study, we introduce a non-equilibrium thermodynamics formulation encompassing
the multiphysical processes of surface poroelasticity and bulk viscoelasticity,
complemented by a corresponding finite element implementation. Our approach
captures the complex dynamics between the finite deformation of the substrate
and solvent diffusion on the surface. This work contributes valuable insights,
particularly in scenarios where the coupling of surface diffusion kinetics and
substrate elasticity is an important design factor.
