Comparative study of chemo-electro-mechanical transport models for an electrically stimulated hydrogel

Abstract

The main objective of this work is to introduce a new expression for the hydrogel’s hydration for use within the Poisson Nernst–Planck chemo electro mechanical (PNP CEM) transport models. This new contribution to the models support large deformation by considering the higher order terms in the Green–Lagrangian strain tensor. A detailed discussion of the CEM transport models using Poisson Nernst–Planck (PNP) and Poisson logarithmic Nernst–Planck (PLNP) equations for chemically and electrically stimulated hydrogels will be presented. The assumptions made to simplify both CEM transport models for electric field application in the order of 0.833 kV m−1 and a highly diluted electrolyte solution (97% is water) will be explained. This PNP CEM model has been verified accurately against experimental and numerical results. In addition, different definitions for normalizing the parameters are used to derive the dimensionless forms of both the PNP and PLNP CEM. Four models, PNP CEM, PLNP CEM, dimensionless PNP CEM and dimensionless PNLP CEM transport models were employed on an axially symmetric cylindrical hydrogel problem with an aspect ratio (diameter to thickness) of 175:3. The displacement and osmotic pressure obtained for the four models are compared against the variation of the number of elements for finite element analysis, simulation duration and solution rate when using the direct numerical solver.