In some glassy polymers

the transport behavior of solvent molecules exhibits non-Fickian diffusion features which are different from the classical Fick's law

and this process is usually accompanied by swelling and large deformation of the material. In this paper

the characteristics of non-Fickian solvent diffusion and swelling deformation of gels are investigated by using a two-phase hysteresis method

which is analogous to the theory of non-Fourier effect in heat conduction analysis. In other words

two controlling parameters related to solvent concentration are introduced to describe the material properties during the glassy transition process. The governing equations for describing diffusion and swelling of different material systems

namely one-dimensional gel rod and a two-dimensional gel plate

are numerically solved by the finite difference method. Our obtained results show that the concentration distribution of solvent molecules in these two polymers is significantly different from that under the case of Fick diffusion. There is a sharp boundary between the swollen part and the non-swollen part

and its moving speed is approximately a constant. At meantime

the theoretical predictions are in good agreement with the existing experimental results

which further verifies the validity and ability of the two-phase hysteresis method to characterize the kinetics of Non-Fickian diffusion.