凝聚连续渗流模型中电导率的数值计算
Numerical Computations of Conductivities over Agglomerated Continuum Percolation Models
摘要：
为了阐明渗流理论如何支配由小导电颗粒组成的实际材料中的导电性，例如，纳米粒子，在绝缘体中具有随机配置，我们使用有限差分法数值研究了由重叠粒子组成的连续渗流模型的电导率，作为我们先前文章的续集（Int. J. Mod. Phys. 21（2010），709）。由于前一篇文章显示了每个颗粒的形状效应，通过处理不同的长径比的球体，在这篇文章中，我们数值显示的颗粒团聚对电导率的影响后，我们采用一个简单的数值算法，模拟团聚配置的颗粒由一个自然参数的团聚配置建模。我们的结论是，占主导地位的凝聚效应的电导率可以解释为分析区域的尺寸效应。我们还讨论了团簇形状对其普适性的影响。
英文摘要：
In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the conductivities of continuum percolation models consisting of overlapped particles using the finite difference method as a sequel of our previous article (Int. J. Mod. Phys. 21 (2010), 709). As the previous article showed the shape effect of each particle by handling different aspect ratios of spheroids, in this article we numerically show influences of the agglomeration of the particles on conductivities after we model the agglomerated configuration by employing a simple numerical algorithm which simulate an agglomerated configuration of particles by a natural parameter. We conclude that the dominant agglomeration effect on the conductivities can be interpreted as the size effect of an analyzed region. We also discuss an effect of shape of the agglomerated clusters on its universal property.
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