Xu Wenxiang, Zhu Zhigang, Jiang Yaqing, Jiao Yang
College of Mechanics and Materials, Hohai University, Nanjing 211100, People's Republic of China.
Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Phys Rev E. 2019 Mar;99(3-1):032107. doi: 10.1103/PhysRevE.99.032107.
The continuum percolation of randomly orientated overlapping polyhedral particles, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, was analyzed by Monte Carlo simulations. Two numerical strategies, (1) a Monte Carlo finite-size-scaling analysis and (2) a real-space Monte Carlo renormalization-group method, were, respectively, presented in order to determine the percolation threshold (e.g., the critical volume fraction ϕ_{c} or the critical reduced number density η_{c}), percolation transition width Δ, and correlation-length exponent ν of the polyhedral particles. The results showed that ϕ_{c} (or η_{c}) and Δ increase in the following order: tetrahedron < cube < octahedron < dodecahedron < icosahedron. In other words, both the percolation threshold and percolation transition width increase with the number of faces of the polyhedral particles as the shape becomes more "spherical." We obtained the statistical values of ν for the five polyhedral shapes and analyzed possible errors resulting in the present numerical values ν deviated from the universal value of ν=0.88 reported in literature. To validate the simulations, the corresponding excluded-volume bounds on the percolation threshold were obtained and compared with the numerical results. This paper has practical applications in predicting effective transport and mechanical properties of porous media and composites.
通过蒙特卡罗模拟分析了随机取向的重叠多面体颗粒（包括四面体、立方体、八面体、十二面体和二十面体）的连续渗流。为了确定多面体颗粒的渗流阈值（例如，临界体积分数ϕₑ或临界约化数密度ηₑ）、渗流转变宽度Δ和关联长度指数ν，分别提出了两种数值策略：（1）蒙特卡罗有限尺寸标度分析和（2）实空间蒙特卡罗重整化群方法。结果表明，ϕₑ（或ηₑ）和Δ按以下顺序增加：四面体＜立方体＜八面体＜十二面体＜二十面体。换句话说，随着形状变得更“球形”，渗流阈值和渗流转变宽度都随着多面体颗粒的面数增加而增加。我们获得了五种多面体形状的ν统计值，并分析了导致当前数值ν偏离文献报道的通用值ν = 0.88的可能误差。为了验证模拟结果，获得了渗流阈值上相应的排除体积界限，并与数值结果进行了比较。本文在预测多孔介质和复合材料的有效传输和力学性能方面具有实际应用价值。
