Fractal diffusion model used for diffusion in porous material within limited volume of stiff container

In this paper, the fractal diffusion model obtained by O’Shaugnessy and Procaccia (OP model) was used to describe the diffusion of gases in a porous material within the limited volume of a stiff container (LVSC). The theoretical solution of OP model was obtained using the method of eigenfunction expansion, and it included the theoretical solution of Fick's model. With this solution, the adsorption kinetics could be analyzed in detail. The estimating method of the pre-exponential factor of diffusivity DOPDOP was proposed. The experimental data of adsorption kinetics of N2N2 and CO2CO2 in γγ-alumina were estimated by OP model and Fick's model for comparison, respectively. The results showed that the quantitative differences could be observed in the relative adsorption amount of adsorption process calculated by these two models. There were no qualitative differences between them, but the OP model would lead to a more realistic description of the diffusion process in a porous material since the calculated results fit more the experimental curves. The diffusivity DFDF of Fick's model strongly depended on concentration, while the diffusivity DOPDOP of OP model was related to temperature, molecular weight of gases and structure of the porous material.