Computational analysis of smart soft hydrogels subjected to pH-electrical coupled stimuli: Effects of initial geometry

A chemo-electro-mechanical formulation, referred to as the multi-effect-coupling pH-stimulus (MECpH) model, is presented in this paper for the analysis of the effects of the initial geometrical size on the responsive behavior of pH-sensitive hydrogels subject to the coupled stimuli of environmental solution pH and externally applied electric voltage. The model is composed of coupled nonlinear partial differential equations, and it accounts for the diffusion of ionic species, distributive electric potential and large mechanical deformation. In addition, the correlation between the diffusive hydrogen ion within the hydrogel and charge groups fixed to the polymeric network chains is incorporated quantitatively into this MECpH model. For the simulation of the response characteristics of the smart hydrogel, we solve the one-dimensional steady-state problem using the Hermite–Cloud meshless technique. For the MECpH model, the present numerical simulations were compared with experimental data available from literature to validate the accuracy and robustness of the model, and good agreement was observed. Several parameter studies were then carried out in the analysis of the hydrogel swelling when immersed in solution, and it was observed that the initial geometrical size has significant influence on the volume variations of these pH-responsive hydrogels.