Rotational self-diffusion in suspensions of charged particles: Revised Beenakker-Mazur and Pairwise Additivity methods versus numerical simulations

TL;DR

This study evaluates a revised Beenakker-Mazur method for calculating the rotational self-diffusion coefficient in charged colloidal suspensions, comparing it with simulations and a pairwise additivity approach, revealing strengths and limitations of each method.

Contribution

The paper introduces an improved BM method for hydrodynamic interactions and compares its accuracy with simulations and a pairwise additivity approach for charged particle suspensions.

Findings

Revised BM method captures general trends but underestimates $D^r$.

PA method aligns with simulations at low concentrations but underestimates at high concentrations.

Increasing Yukawa screening enhances the rotational diffusion coefficient.

Abstract

To the present day, the Beenakker-Mazur (BM) method is the most comprehensive statistical physics approach to the calculation of short-time transport properties of colloidal suspensions. A revised version of the BM method with an improved treatment of hydrodynamic interactions is presented and evaluated regarding the rotational short-time self-diffusion coefficient, $D^r$ , of suspensions of charged particles interacting by a hard-sphere plus screened Coulomb (Yukawa) pair potential. To assess the accuracy of the method, elaborate simulations of $D^r$ have been performed, covering a broad range of interaction parameters and particle concentrations. The revised BM method is compared in addition with results by a simplifying pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a two-body level. The static pair correlation functions re- quired as input to both theoretical methods are calculated using the Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it systematically and significantly underestimates the rotational diffusion coefficient. The PA method agrees well with the simulation data at lower volume fractions, but at higher concentrations $D^r$ is likewise underestimated. For a fixed value of the pair potential at mean particle distance comparable to the thermal energy, $D^r$ increases strongly with increasing Yukawa potential screening parameter.