Model development and numerical simulation of electric-stimulus-responsive hydrogels subject to an externally applied electric field.

Based on a multi-phasic mixture theory with consideration of ionic diffusion and convection, a multi-physic model, called the multi-effect-coupling electric-stimulus (MECe) model, is developed for simulation of responsive behavior of the electric-sensitive hydrogels when they are immersed into a bathing solution subject to an externally applied electric field. In the developed model, with chemo-electro-mechanical coupling effects, the convection-diffusion equations for concentration distribution of diffusive ions incorporate the influence of electric potential. The electroneutrality condition is replaced by the Poisson equation for distribution of electric potential. The steady and transient analyses of hydrogel deformation are easily carried out by the continuity and momentum equations of the mixture phase. Further, the computational domain of the present model covers both the hydrogel and the surrounding solution. In order to solve the present mathematical model consisting of multi-field coupled nonlinear partial differential governing equations, a hierarchical iteration technique is proposed and a meshless Hermite-Cloud method (HCM) is employed. The steady-state simulation of the electric-stimulus responsive hydrogel is numerically conducted when it is subjected to an externally applied electric field. The hydrogel deformation and the ionic concentrations as well as electric potentials of both the hydrogel and external solution are investigated. The parameter influences on the swelling behaviors of the hydrogel are also discussed in detail. The simulating results are in good agreement with the experimental data and they validate the presently developed model.