Self-diffusion coefficients of charged particles: Prediction of Nonlinear volume fraction dependence

TL;DR

This paper predicts nonlinear volume fraction dependencies of self-diffusion coefficients for charged colloidal particles, highlighting differences from hard sphere suspensions and introducing an effective hard sphere model.

Contribution

It introduces new nonlinear scaling relations for self-diffusion coefficients of charged colloids considering electrostatic and hydrodynamic interactions.

Findings

Nonlinear scaling relations for $D^t_s$ and $D^r_s$ depending on volume fraction.

Charge-independent parameters $a_t$ and $a_r$ in the scaling.

Improved understanding of diffusion in charged colloidal suspensions.

Abstract

We report on calculations of the translational and rotational short-time self-diffusion coefficients $D^t_s$ and $D^r_s$ for suspensions of charge-stabilized colloidal spheres. These diffusion coefficients are affected by electrostatic forces and many-body hydrodynamic interactions (HI). Our computations account for both two-body and three-body HI. For strongly charged particles, we predict interesting nonlinear scaling relations $D^t_s\propto 1-a_t\phi^{4/3}$ and $D^r_s\propto 1-a_r\phi^2$ depending on volume fraction $\phi$, with essentially charge-independent parameters $a_t$ and $a_r$. These scaling relations are strikingly different from the corresponding results for hard spheres. Our numerical results can be explained using a model of effective hard spheres. Moreover, we perceptibly improve the known result for $D^t_s$ of hard sphere suspensions.