Diffusion in randomly dispersed, spherical, and ellipsoidal composite systems is studied using the random walk simulations. The outcome of the computational analysis is validated by finite element analyses. A Monte Carlo scheme is applied to generate the particulate system. The composite is assumed to have a lower diffusivity in the inclusions and a higher diffusivity in the matrix. The effective diffusion coefficient is found to agree with the theory relating volume fractions of permeable and impermeable inclusions to the diffusion coefficient. The effect of the particle aspect ratio is investigated numerically and compared with the closed-form, effective medium solutions. In the case of ellipsoidal inclusions, it is found that the effective diffusion coefficient is strongly dependent on the particle aspect ratio and that it rapidly decreases with the volume fraction of inclusions. The interfacial effect in the setting of anomalous diffusion for permeable systems is also tentatively investigated.

中文翻译：

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球和椭球复合材料中基于随机Walk扩散的随机建模

使用随机游走模拟研究了随机分散的，球形和椭圆形复合系统中的扩散。计算分析的结果通过有限元分析得到验证。应用蒙特卡洛方案产生微粒系统。假定该复合材料在夹杂物中具有较低的扩散率，并且在基质中具有较高的扩散率。发现有效扩散系数与将可渗透和不可渗透夹杂物的体积分数与扩散系数相关的理论相一致。数值研究了颗粒长径比的影响，并与封闭形式的有效介质溶液进行了比较。如果是椭圆形夹杂物，结果发现，有效扩散系数在很大程度上取决于颗粒的长径比，并且随着夹杂物的体积分数而迅速减小。还尝试研究了渗透系统异常扩散的界面效应。