Swelling kinetics of polymer gels: comparison of linear and nonlinear theories

The swelling of a polymer gel is a kinetic process coupling mass transport and mechanical deformation. Both linear and nonlinear theories have been used to describe the swelling kinetics. Here we present a comparison between a nonlinear theory for polymer gels and the classical theory of linear poroelasticity. We show that the two theories are consistent within the linear regime under the condition of small perturbation from an isotropically swollen state of the gel. The relationship between the material properties in the linear theory and those in the nonlinear theory is established by a linearization procedure. Both linear and nonlinear solutions are presented for swelling kinetics of substrate-constrained and freestanding hydrogel layers. Although the linear poroelasticity theory can be used to fit experimental data, it is cautioned that the applicability of the linear theory should be limited to relatively small swelling ratios. To remove the linear limitation, a new procedure is suggested to fit the experimental data with the nonlinear theory. Finally, we discuss the indentation experiment as an effective method for characterizing the mechanical and transport properties of polymer gels along with possible extensions of the method.