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.

中文翻译：

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用于量化多孔介质中非菲克扩散的时间分数织物：先前研究的新愿景


不同物质在多孔介质中的扩散动力学是由第二菲克扩散定律先验描述的。在这里，我们证明这种描述有时会产生不稳定的结果。相反，时间分数扩散方程可以反映菲克定律失效情况下的扩散动力学。时间分数扩散方程的解析解基于 Mittag-Leffler 函数。大多数时候，结果表明，利用 Mittag-Leffler 函数的大值近似来描述实验数据，得到的结果几乎与使用 Mittag-Leffler 函数本身获得的结果相同。时间分数扩散是在现象学基础上应用的。尽管如此，我们推测与菲克定律的偏差可能是由多孔材料小微孔内扩散物质的强烈吸附决定的。