Theory of swelling dynamics of polyelectrolyte gels under external electric fields and geometric constraints*

Hydrogels are widely used as soft actuators owing to their stimuli sensitivity, flexibility, hydrophilicity, and high swelling ratio. In many hydrogel-based systems, precise control of gel swelling behavior is essential to realize targeted functions or motions. The swelling rate, ratio, and resultant force of given hydrogels are functions of gel size, geometric constraints, magnitude and type of external stimuli. Here, we study the swelling dynamics of polyelectrolyte hydrogel under the effects of external electric fields and geometric constraints. We theoretically model the enhancement of swelling rate and ratio owing to the electroosmotic liquid influx induced by the external electric field. We also theoretically elucidate the build-up process of stress inside geometrically constrained gels. Our theory can guide a design of hydrogel-based actuation systems that require agile response with high stiffness.