The two-region (“Kärger”) model of diffusion in complex pore spaces is exploited for quantitating mass transfer in hierarchically organized nanoporous materials, consisting of a continuous microporous bulk phase permeated by a network of transport pores. With the implications that the diffusivity in the transport pores significantly exceeds the diffusivity in the micropores and that the relative population of the transport pores is far below that of the micropores, overall transport depends on only three independent parameters. Depending on their interrelation, enhancement of the overall mass transfer is found to be ensured by two fundamentally different mechanisms. They are referred to as the limiting cases of fast and slow exchange, with the respective time constants of molecular uptake being controlled by different parameters. Complemented with reaction terms, the two-region model may equally successfully be applied to the quantitation of the combined effect of diffusion and reaction in terms of the effectiveness factor. Generalization of the classical Thiele concept is shown to provide an excellent estimate of the effectiveness factor of a chemical reaction in hierarchically porous materials, solely based on the intrinsic reaction rate and the time constant of molecular uptake relevant to the given conditions.

利用在复杂的孔空间中扩散的两区域（“Kärger”）模型来量化在分级组织的纳米孔材料中的传质，该材料由连续的微孔本体相组成，该相通过传输孔网络渗透。暗示着传输孔中的扩散率大大超过了微孔中的扩散率，并且传输孔的相对数量远低于微孔的扩散率，因此总体传输仅取决于三个独立的参数。取决于它们之间的相互关系，发现通过两种根本不同的机制可以确保整体传质的增强。它们被称为快速和缓慢交换的极限情况，分子摄取的各个时间常数由不同的参数控制。补充有反应项的两区域模型可以等效地有效地用于根据有效性因子对扩散和反应的组合效应进行定量。仅基于固有反应速率和与给定条件相关的分子吸收时间常数，经典Thiele概念的泛化被证明可以很好地估计分层多孔材料中化学反应的效率因子。