Clausius-Mossotti近似在悬浮液短时输运中的推广
Generalization of Clausius-Mossotti approximation in application to short-time transport properties of suspensions
摘要：
1983年，Felderhof、Ford和Cohen对非极性电介质介电常数的著名的Clausius-Mossotti公式作了微观解释。他们的考虑基于介电常数的团簇膨胀，这将这种宏观性质与系统的微观特征联系起来。在这篇文章中，我们分析了Felderhof，Ford和Cohen的集群扩展通过执行其重正化（重整化）。我们的分析导致了环展开的宏观系统的特点，这是一种表达替代集团展开。利用团簇展开和环展开结构的相似性，我们推广（重整化）Clausius-Mossotti近似。我们应用我们的重整化Clausius-Mossotti近似的悬浮液的短时输运性质的情况下，计算的有效粘度和流体动力学函数的平移自扩散和集体扩散系数。我们进行计算的单分散硬球悬浮液在平衡与体积分数高达45%。为了评估重整化的克劳修斯-莫索蒂近似，将其与数值模拟和Beenakker-Mazur方法进行了比较。对于低于$ ϕ\approx 30\% $的体积分数（除了流体力学函数中的小范围波矢量），我们的重整化Clausius-Mossotti近似的结果导致与Beenakker-Mazur方法相当或更小的误差（相对于数值模拟）。对于高于$ϕ\approx 30 \%$的体积分数，Beenakker-Mazur方法在大多数情况下给出比重整化Clausius-Mossotti近似更低的误差。
英文摘要：
In 1983 Felderhof, Ford and Cohen gave microscopic explanation of the famous Clausius-Mossotti formula for the dielectric constant of nonpolar dielectric. They based their considerations on the cluster expansion of the dielectric constant, which relates this macroscopic property with the microscopic characteristics of the system. In this article, we analyze the cluster expansion of Felderhof, Ford and Cohen by performing its resummation (renormalization). Our analysis leads to the ring expansion for the macroscopic characteristic of the system, which is an expression alternative to the cluster expansion. Using similarity of structures of the cluster expansion and the ring expansion, we generalize (renormalize) the Clausius-Mossotti approximation. We apply our renormalized Clausius-Mossotti approximation to the case of the short-time transport properties of suspensions, calculating the effective viscosity and the hydrodynamic function with the translational self-diffusion and the collective diffusion coefficient. We perform calculations for monodisperse hard-sphere suspensions in equilibrium with volume fraction up to 45%. To assess the renormalized Clausius-Mossotti approximation, it is compared with numerical simulations and the Beenakker-Mazur method. The results of our renormalized Clausius-Mossotti approximation lead to comparable or much less error (with respect to the numerical simulations), than the Beenakker-Mazur method for the volume fractions below $ ϕ\approx 30\% $ (apart from a small range of wave vectors in hydrodynamic function). For volume fractions above $ϕ\approx 30 \%$, the Beenakker-Mazur method gives in most cases lower error, than the renormalized Clausius-Mossotti approximation.
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