Swelling Kinetics of a Microgel Shell

Tanaka’s approach to swelling kinetics of a solid gel sphere is extended to a spherical microgel shell. The boundary condition at the inner surface is obtained from the minimization of shear elastic energy. Temporal evolution of a shell is represented in a form of expansion over eigenfunctions of the corresponding diffusion equation. The swelling of Tanaka’s solid spherical gel is recovered as a special case of our general solution if the inner radius approaches zero. In another limiting case of a thin (balloon-like) shell, the set of eigenfunctions is reduced to a single exponential term. In the general case, a solid sphere swells slightly faster than the same sphere with an internal cavity. To test our theoretical model, we prepared monodisperse poly-N-isopropylacrylamide (PNIPAM) hydrogel shells using a microfluidic device. The temporal dependence of the inner and outer radii of the shell were measured, and the data were fitted to our theoretical model. As a result, we obtained the collective diffusion...