Constitutive modeling of pH-sensitive hydrogel: Multi-physics coupling of electromagnetics with mechanics and thermodynamics

The field theory of pH-sensitive hydrogel deformation is presented coupling electro-magnetic (EM) field (external or internal) and diffusion (Poisson–Nernst–Planck and Maxwell equations) of mobile ionic species through irreversible thermodynamics. The evolution of fixed-charge in the hydrogel is modeled by Langmuir monolayer adsorption theory. The important contribution of present work is a derivation of Cauchy stress tensor constitutive relation with EM field and species diffusion through Maxwell's stress and spherical tensors. The EM field work done is computed in the frame-invariant settings employing Poynting vector concept, which is another novel contribution of the present work. The hydrogel deformation is finally computed by mechanical equilibrium equation coupled with the diffusion equations through traction boundary conditions. The applicability of the presented framework is successfully demonstrated by several pH-sensitive hydrogel simulations (one- and two-dimensional). The constitutive relations derived here are also verified with the other published results.