Fractal model of gas diffusion in porous nanofibers with rough surfaces is derived, in which the porous structure is assumed to be composed of a bundle of tortuous capillaries whose pore size distribution and surface roughness follow the fractal scaling laws. The analytical expression for gas relative diffusion coefficient is a function of the relative roughness and the other microstructural parameters (porosity, the fractal dimension for pore size distribution and tortuosity, the maximum and minimum pore diameter and the characteristic length). The proposed fractal model is validated by comparison with available experimental data and correlations. At the same time, the effect of microstructural parameters of porous fibrous materials on gas diffusion has been studied in detail. It is believed that the current model may be extended to porous materials other than fibrous materials.

中文翻译：

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表面粗糙度对多孔纳米纤维气体扩散影响的分形分析

推导了具有粗糙表面的多孔纳米纤维中气体扩散的分形模型，其中假设多孔结构由一束曲折的毛细管组成，其孔径分布和表面粗糙度遵循分形比例定律。气体相对扩散系数的解析表达式是相对粗糙度和其他微观结构参数（孔隙率、孔径分布和曲折度的分形维数、最大和最小孔径以及特征长度）的函数。通过与可用的实验数据和相关性进行比较来验证所提出的分形模型。同时，详细研究了多孔纤维材料的微观结构参数对气体扩散的影响。