  Thermo-responsive hydrogels are a promising material for creating
controllable actuators for use in 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 focus on two model examples, with
equilibrium parameters extracted from data in the literature. We find a range
of qualitatively different behaviours when swelling and shrinking, including
cases where swelling and shrinking happen smoothly from the edge, and other
situations which result in the formation of an inwards-travelling spherical
front that separates a core and shell with markedly different degrees of
swelling. We then characterise when each of these scenarios is expected to
occur. An approximate analytical form for the front dynamics is developed, with
two levels of constant porosity, that well-approximates the numerical
solutions. This system can be evolved forward in time, and is simpler to solve
than the full numerics, allowing for more efficient predictions to be made,
such as when deciding dosing strategies for drug-laden hydrogels.
