Modeling and simulation of the swelling behavior of pH-stimulus-responsive hydrogels

The modulation of the swelling ability of the hydrogel matrix by pH-stimulus enables the dynamic control of the swelling forces, thereby obtaining effective diffusivity and permeability of the solutes, or mechanical energy from the hydrogel. In this work, a chemo-electro-mechanical model describing hydrogel behavior, based on multi-field effects, is developed to simulate the swelling and shrinking of these fascinating biomaterials, and it is termed the multi-effect-coupling pH-stimulus (MECpH) model. This model accounts for the ionic fluxes within both the hydrogel and solution, the coupling between the electric field, ionic fluxes, and mechanical deformations of the hydrogel. The main contribution of this model is to incorporate the relationship between the concentrations of the ionized fixed-charge groups and the diffusive hydrogen ion, which follows a Langmuir isotherm, into the Poisson-Nernst-Planck system. To validate this MECpH model, one-dimensional steady-state simulations under varying pH solution are carried out via a meshless Hermite-Cloud methodology, and the numerical results are compared with available experimental data. It is shown that the presently developed MECpH model is accurate, efficient, and numerically stable.