The diffusion kinetics may experience either standard or anomalous behavior. In a porous medium, a transport process may distinguish between the standard and anomalous diffusion. Herein, we perform an analysis of the diffusion concentration profiles in a hierarchically porous material using the standard and the time-fractional diffusion equations. It is shown that the mass transfer regime changes from the anomalous to the standard one regarding the temporal scale of the concentration profile. Particularly, at relatively short times, the mass transfer regime corresponds to the anomalous diffusion with the superdiffusive anomalous diffusion exponent. In contrast, at relatively long times, the standard Fickian regime is obeyed. The investigated phenomenon is assigned to the diffusion in different components of a porous material. The relevant physical model of the corresponding transition is discussed based on the Cattaneo-type diffusion equation. The relaxation time for the transport of the gaseous molecules in the porous medium was found to be in the range of 10 –8 –10 –6 s.

中文翻译：

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分层多孔材料中时间分数扩散和标准扩散之间随时间变化的研究

扩散动力学可能会经历标准或异常行为。在多孔介质中，传输过程可以区分标准扩散和异常扩散。在这里，我们使用标准和时间分数扩散方程对分层多孔材料中的扩散浓度分布进行分析。结果表明，关于浓度分布的时间尺度，传质机制从异常变为标准。特别是，在相对较短的时间内，传质机制对应于具有超扩散异常扩散指数的异常扩散。相比之下，在相对较长的时间内，标准的 Fickian 制度得到遵守。所研究的现象归因于多孔材料不同组分中的扩散。基于Cattaneo型扩散方程讨论了相应转变的相关物理模型。发现多孔介质中气态分子传输的弛豫时间在 10 –8 –10 –6 s 的范围内。