Generalization of Clausius-Mossotti approximation in application to short-time transport properties of suspensions

TL;DR

This paper extends the Clausius-Mossotti approximation using a ring expansion approach, applying it to short-time transport properties of suspensions, and compares its accuracy with numerical simulations and the Beenakker-Mazur method.

Contribution

The paper introduces a renormalized Clausius-Mossotti approximation based on ring expansion, enhancing the analysis of suspension transport properties.

Findings

Renormalized approximation achieves lower error than classical methods for volume fractions below 30%.

Comparison with simulations shows good accuracy of the new approximation.

Method is effective for monodisperse hard-sphere suspensions up to 45% volume fraction.

Abstract

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 $ \phi \approx 30\% $ (apart from a small range of wave vectors in hydrodynamic function). For volume fractions above $\phi \approx 30 \%$, the Beenakker-Mazur method gives in most cases lower error, than the renormalized Clausius-Mossotti approximation.