Abstract Particle morphology is a crucial factor of influencing the prediction of percolation threshold in the study of continuum percolation of particle systems. Previous works on the percolation of particle synthesis mainly focused on spheres, ellipsoids and spherocylinders. In this paper, the newly synthesized superballs which smoothly interpolate between octahedrons, spheres and cubes are introduced, and a simple contact detection algorithm for superballs is proposed. By combing Monte Carlo method and percolation theory, the continuum percolation of randomly orientated congruent overlapping superballs is investigated in detail. The global percolation threshold ψc for superballs with shape parameter m in [0.5, +∞) are obtained in terms of a finite-size scaling technique. Finally, an analytical approximation for percolation threshold ψc of superballs is derived and verified by existing data from literature. It is found from the study that when the parameter m varies between 0.5 and 1.0, the percolation threshold ψc significantly increases with the increasing m, whereas the value of m continues to increase from 1.0 to +∞, ψc will gradually decrease. We hope this study can provide good guidance for the development of percolation theory about non-spherical particle packing systems.

中文翻译：

---

颗粒形态对颗粒多孔介质渗透的影响：超球研究

摘要 在颗粒系统连续渗流研究中，颗粒形态是影响渗流阈值预测的关键因素。以前关于粒子合成渗透的工作主要集中在球体、椭球体和圆柱体上。本文介绍了在八面体、球体和立方体之间平滑插值的新合成的超级球，并提出了一种简单的超级球接触检测算法。结合蒙特卡罗方法和渗流理论，详细研究了随机定向全等重叠超球的连续渗流问题。形状参数 m 在 [0.5, +∞) 中的超级球的全局渗透阈值 ψc 是根据有限尺寸缩放技术获得的。最后，超级球的渗透阈值 ψc 的解析近似值是由文献中的现有数据导出和验证的。研究发现，当参数m在0.5和1.0之间变化时，渗流阈值ψc随着m的增加而显着增加，而m的值从1.0继续增加到+∞，ψc会逐渐减小。希望本研究能为非球形颗粒填料系统渗流理论的发展提供良好的指导。