Phase field model simulations of hydrogel dynamics under chemical stimulation

Abstract

Two decades ago, it has been observed experimentally that hydrogels immersed in a bath solution swells or shrinks under external stimulations (Ricka et al., Macromolecules 17:2916–2921, 1984). Recently, this fact has received renewed interest, since understanding the precise mechanisms underlying that kind of behavior has the potential to tailor most sensitive drug delivery systems based on hydrogels (Segalman and Witkowski, Mater Sci Eng C 2:243–249, 1995). Here we contribute to a precise understanding of the mechanisms responsible for the hydrogels’ swelling kinetics as well as dynamics by proposing for the first time a model approach that can resolve the inherent short-range correlation effects along the hydrogel–solution interface jointly with the long-range ionic transport fields. To that end, we investigate the swelling dynamics of hydrogels, which is a moving boundary problem, by a phase field model, which couples the Nernst–Planck equation for the concentration of mobile ions, Poisson equation for the electric potential, mechanical equation for the displacement, and an equation for the phase field variable. Simulation for two-dimensional case reveals that under the chemical stimulation, the hydrogel will swell or shrink if the concentration of mobile ions inside bath solution decreases or increases. This is in agreement with the experimental results qualitatively and validates our new model approach.