We developed a random walk model for solving the diffusion problem arising from composite materials of particulate inclusions with different shapes. Our two-phase material system contains circular or elliptical impermeable inclusions that are randomly embedded in a matrix material. A computational algorithm was developed for random walk simulation of molecules and to estimate the effective diffusion coefficient of the composites. The random walk model has been validated by solutions from finite element analysis and effective medium theories. Our computational results show that the density of random distribution and the volume fraction of inclusions have significant effects on effective diffusion coefficients. Moreover, the aspect ratio of inclusions can significantly reduce diffusion speed when the volume fraction of inclusions is greater than ∼ 30%.

中文翻译：

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圆形和椭圆形颗粒复合材料中扩散的随机行走模拟模型

我们开发了一种随机游走模型，用于解决由不同形状的颗粒夹杂物复合材料引起的扩散问题。我们的两相材料系统包含随机嵌入基质材料中的圆形或椭圆形不可渗透夹杂物。为分子的随机游走模拟和估计复合材料的有效扩散系数开发了一种计算算法。随机游走模型已通过有限元分析和有效介质理论的解决方案进行验证。我们的计算结果表明，随机分布的密度和夹杂物的体积分数对有效扩散系数有显着影响。而且，