Abstract Fractal geometry has been successfully applied to the study of structures and transport properties of porous media due to its scale invariant property. A new fractal probability density (FPD) model is developed to characterize the pore structures of porous media in this paper. Mechanical press filtration (MPF) is performed on pre-dewatered sludge samples in order to achieve different porous structures. The pore structures and water contents of the dewatered porous sludge cakes are then measured by low-field nuclear magnetic resonance (NMR). The pore fractal dimensions are determined with the proposed FPD model based on NMR results. It has been found that the pore fractal dimension increases with porosity under fixed pore size range. The value of the pore fractal dimension of porous samples is larger than 2.6, which indicates highly heterogeneous pore structures. The present work may provide insight on the multiscale structures of porous media based on NMR technique.

中文翻译：

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基于低场核磁共振的多孔介质分形新模型

摘要 分形几何由于其尺度不变性，已成功应用于多孔介质结构和输运性质的研究。本文开发了一种新的分形概率密度 (FPD) 模型来表征多孔介质的孔隙结构。对预先脱水的污泥样品进行机械压滤 (MPF)，以获得不同的多孔结构。然后通过低场核磁共振 (NMR) 测量脱水多孔污泥饼的孔隙结构和含水量。孔隙分形维数由基于核磁共振结果的拟议 FPD 模型确定。已经发现，在固定孔径范围内，孔隙分形维数随着孔隙度的增加而增加。多孔样品孔隙分形维数大于2.6，这表明高度异质的孔隙结构。目前的工作可以提供基于核磁共振技术的多孔介质的多尺度结构的见解。