The present work explores water permeability of uniformly graded irregular grains using 3D printing with controlled shapes and fractal morphological features at low Reynold's number for viscous flow. From large amount of real 3D granular morphological data, a scaling law, in terms of fractal dimension, is found to be followed. With this universal law, sand grains with controlled fractal morphological features are generated using Spherical Harmonics, and then created using 3D printing technique for water permeability tests. A modified Kozeny‐Carman equation is proposed through more accurate determination of specific area, as a function of relative roughness and fractal dimension, than approximation using the volume‐equivalent sphere. By isolating the contributions from specific area, the shape coefficient is found to be insensitive to particle morphology. Through benchmarking the model prediction against experiments from both this work and past literature, we demonstrate the validity and wide applicability of the modified Kozeny‐Carman equation.

中文翻译：

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均匀渐变的3D打印颗粒介质的磁导率

本工作使用具有低粘性的低雷诺数的具有受控形状和分形形态特征的3D打印方法，探索均匀梯度不规则晶粒的透水性。从大量真实的3D颗粒形态数据中，发现遵循分形维数的缩放定律。利用此通用定律，可使用球谐函数生成具有可控的分形形态特征的沙粒，然后使用3D打印技术进行水渗透性测试。通过相对于粗糙度和分形维数的比面积的精确计算，比使用体积当量球的近似值更精确地确定了比面积，从而提出了一种改进的Kozeny-Carman方程。通过从特定领域中分离出贡献，发现形状系数对颗粒形态不敏感。通过对照本工作和过去的文献中的实验对模型预测进行基准测试，我们证明了改进的Kozeny-Carman方程的有效性和广泛的适用性。