Transient swelling response of pH-sensitive hydrogels: A monophasic constitutive model and numerical implementation

Due to their ability to swell/deswell under alternating pH conditions, pH-sensitive hydrogels present themselves as a potential candidate for controlled drug delivery. In this paper, a coupled electro-chemo-mechanical transient large deformation homogeneous and inhomogeneous swelling theory is developed for pH-sensitive hydrogels. The hydrogel is treated as a single-phase compressible isotropic hyperelastic material. The Nernst-Planck equation is used for the flux of the ionic species inside the hydrogel through its boundaries. The main reason which causes the hydrogel to swell is the osmotic pressure. The osmotic pressure is treated as external stress to the hydrogel. As soon as the concentration of the ions inside the hydrogel is known one may compute the osmotic pressure. Finally, the mechanical equilibrium equations give the deformation of the hydrogel. After presenting the swelling theory, the theory is implemented into the finite element method, and the experimental data is used in order to validate the theory. The simulation matches closely the experimental data which shows the accuracy of the proposed theory. The free swelling and constrained swelling of the pH-sensitive hydrogel are also simulated to show the capabilities of the proposed formulation and well as its numerical counterpart.