Inhomogeneous swelling behavior of a bi-layered spherical hydrogel containing a hard core

Hydrogels can absorb a significant amount of water and swell greatly. When the swelling is constrained, hydrogels exhibit inhomogeneous deformation, stress, and water concentration fields. This paper studies the swelling behavior of a bi-layered spherical hydrogel containing a hard core after imbibing sufficient water. By adopting a continuum field theory of hydrogels, the governing differential equation of the hydrogel radial deformation is derived, which is further solved numerically at proper mixed boundary conditions and inner field continuity conditions across the hydrogel interface. Effects of material properties and the presence of the hard core on the deformation, stress, and water concentration fields of the hydrogels are examined. It shows that the inner hard core can remarkably reduce the water concentration near the core surface and simultaneously induce large stresses. In addition, the water concentration in the bi-layered hydrogel heavily depends upon the stiffness of the individual hydrogel. The study offers a rational route to design and regulate hydrogels with tailorable swelling behavior for practical applications in drug delivery, leakage blocking, etc.