The swelling and shrinking of a thermo-responsive hydrogel

Thermo-responsive hydrogels are a promising new material for creating controllable actuators for use on micro-scale devices, since they expand and contract significantly (absorbing or expelling fluid) in response to relatively small temperature changes. Understanding such systems can be difficult because of the spatially- and temporally-varying properties of the gel, and the complex relationships between the fluid dynamics, elastic deformation of the gel and chemical interaction between the polymer and fluid. We address this using a poro-elastic model, considering the dynamics of a thermo-responsive spherical hydrogel after a sudden change in the temperature that should result in substantial swelling or shrinking. We typically find that swelling and shrinking have qualitatively different behaviour: swelling happens smoothly from the edge, whereas shrinking results in the formation of an inwards-travelling spherical front that separates a swollen core and shrunken shell. An approximate analytical form for the front dynamics is developed that well-approximates the numerical solutions.