A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels

We present a strategy for obtaining numerical solutions to a system of non-linear, coupled evolution equations describing volume transitions in stimulus-responsive hydrogels (SRHs). The theory underlying our sharp-interface model of phase transitions in SRHs is provided along with the assumptions leading to the specialized formulation that is the starting point for the numerical method. The discrete formulation is then developed with a hybrid eXtended Finite-Element/Level-Set Method (XFE/LSM). Domain-integral methodologies are used consistently to extract interfacial quantities such as the mechanical driving traction, the jump in the normal component of the solute flux, and requisite geometric information. Several benchmark studies are provided to demonstrate the accuracy and robustness of the numerical strategy. We then investigate various features of SRH kinetics including the regimes of unstable and stable phase transitions, surface pattern formation, and bulk phase separation.