A lattice model for continuum percolation by cylindrical rods is generalized to account for inhomogeneities in the volume fraction that are indicative of particle clustering or aggregation. The percolation threshold is evaluated from a formalism that uses two different categories of occupied sites (denoting particles) with different occupation probabilities that represent large and small local volume fractions. Our modeling framework enables independent variations in (i) the strength of the correlation that adjacent particles experience high (or low) effective volume fractions, (ii) the disparity between the macroscopically averaged volume fraction and (say) the volume fraction characterizing the regions with high effective particle concentrations, and (iii) the overall proportion of particles that are located in regions with either high or low volume fraction. Calculations performed for monodisperse cylinders show that enhancement in each of the above factors leads to reduction in the macroscopically averaged volume fraction at the percolation threshold.

中文翻译：

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体积分数波动对圆柱体渗流影响的晶格模型

概括了用于通过圆柱棒进行连续渗滤的晶格模型，以说明体积分数中的不均匀性，该不均匀性指示粒子聚集或聚集。渗透阈值是根据形式主义评估的，形式主义使用两种不同类别的占位点（表示粒子），它们具有不同的占位率，分别代表局部和局部的体积分数。我们的建模框架可实现以下方面的独立变化：（i）相邻粒子经历高（或低）有效体积分数的相关强度；（ii）宏观平均体积分数与（例如）表征具有以下特征的区域的体积分数之间的差异有效粒子浓度高，（iii）位于体积分数高或低的区域中的颗粒的总比例。对单分散圆柱体进行的计算表明，上述每个因素的增强会导致在渗透阈值处的宏观平均体积分数降低。