Makuch Karol
Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042317. doi: 10.1103/PhysRevE.92.042317. Epub 2015 Oct 30.
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≈30% (apart from a small range of wave vectors in hydrodynamic function). For volume fractions above ϕ≈30%, the Beenakker-Mazur method gives in most cases lower error than the renormalized Clausius-Mossotti approximation.
1983年，费尔德霍夫、福特和科恩对著名的非极性电介质介电常数的克劳修斯 - 莫索蒂公式给出了微观解释。他们的考虑基于介电常数的团簇展开，该展开将这一宏观性质与系统的微观特征联系起来。在本文中，我们通过对费尔德霍夫、福特和科恩的团簇展开进行求和（重整化）来分析它。我们的分析得出了系统宏观特征的环展开，这是一种与团簇展开不同的表达式。利用团簇展开和环展开结构的相似性，我们推广（重整化）了克劳修斯 - 莫索蒂近似。我们将重整化的克劳修斯 - 莫索蒂近似应用于悬浮液的短时间输运性质的情况，计算有效粘度以及具有平移自扩散和集体扩散系数的流体动力学函数。我们对体积分数高达45%的单分散硬球悬浮液处于平衡态的情况进行了计算。为了评估重整化的克劳修斯 - 莫索蒂近似，将其与数值模拟和贝纳克尔 - 马祖尔方法进行了比较。对于体积分数低于ϕ≈30%的情况（除了流体动力学函数中一小范围的波矢外），我们重整化的克劳修斯 - 莫索蒂近似的结果相对于数值模拟产生的误差与贝纳克尔 - 马祖尔方法相当或更小。对于体积分数高于ϕ≈30%的情况，在大多数情况下，贝纳克尔 - 马祖尔方法产生的误差比重整化的克劳修斯 - 莫索蒂近似更低。
