Short-time diffusion in concentrated bidisperse hard-sphere suspensions

TL;DR

This study combines Stokesian Dynamics simulations and a semi-analytical scheme to accurately analyze short-time diffusion in concentrated bidisperse hard-sphere suspensions, extending the applicability of existing theoretical models.

Contribution

It introduces a revised $ ext{delta}\gamma$-scheme for bidisperse suspensions that accurately predicts hydrodynamic functions across a wide range of densities.

Findings

Revised $ ext{delta}\gamma$-scheme matches simulation results well.

Hydrodynamic functions are accurate up to 40% packing fraction.

Simple rescaling laws improve the scheme's applicability to mixtures.

Abstract

Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica 120A, 388 (1983) & 126A, 349 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's $\delta\gamma$-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified $\delta\gamma$ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as $40\%$.