Abstract Gas slip flow in micro- and nano- porous media with rough surfaces is investigated by the fractal geometry theory with a focus on the effect of surface roughness of capillaries. Based on the assumption that the pore size distribution of the porous media and rough elements of the wall surfaces of capillaries follow the fractal scaling law, apparent gas permeability and gas slippage factor are derived. According to the Klinkenberg equation, the key to the calculation of apparent gas permeability is the determination of gas slippage factor. In this paper, we established an analytical relationship between the gas slippage factor and the structural parameters of porous media. We first validated the model with available experimental data, then analyzed the effect of the relative roughness, porosity, the tortuosity fractal dimension and the pore fractal dimension on the gas slippage factor. With our fractal model, the physical mechanisms of gas slip flow are better elucidated.

中文翻译：

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粗糙表面形貌对微纳米多孔介质中气体滑移影响的分形分析

摘要 利用分形几何理论研究了粗糙表面微纳米多孔介质中的气体滑移流动，重点研究了毛细管表面粗糙度的影响。假设多孔介质的孔径分布和毛细管壁面的粗糙元素遵循分形标度规律，推导出表观气体渗透率和气体滑脱因子。根据Klinkenberg方程，气体表观渗透率计算的关键是气体滑脱因子的确定。在本文中，我们建立了气体滑移因子与多孔介质结构参数之间的解析关系。我们首先用可用的实验数据验证了模型，然后分析了相对粗糙度、孔隙度、曲折分形维数和孔隙分形维数对气体滑脱因子的影响。通过我们的分形模型，可以更好地阐明气体滑移的物理机制。