Time-fractional fabric to quantify non-Fickian diffusion in porous media: New vision from previous studies

Abstract

The diffusion kinetics of different substances in porous media is a priori described by the second Fick's law of diffusion. Herein, we demonstrate that such a description sometimes yields erratic results. In contrast, the time-fractional diffusion equation is found to reflect the diffusion kinetics in the case of Fick's law failure. The analytic solutions of the time-fractional diffusion equation are based on the Mittag–Leffler function. At large times, it is shown that the utilization of the approximation of the Mittag–Leffler function for the large values of its argument for the description of the experimental data gives almost the same results as those obtained using the Mittag–Leffler function itself. The time-fractional diffusion is applied on a phenomenological basis. Nevertheless, we speculate that the deviations from Fick's law may be governed by strong adsorption of the diffusing species inside the small micropores of a porous material.