Self-diffusion of a sphere in an effective medium of rods

TL;DR

This paper provides a theoretical analysis of the self-diffusion of a sphere within a rod network, deriving simple, L-independent expressions for diffusion coefficients considering hydrodynamic interactions.

Contribution

It introduces a theoretical model for sphere diffusion in rod networks, accounting for hydrodynamic interactions with assumptions that simplify the analysis.

Findings

Derived simple expressions for diffusion coefficients

Diffusion coefficients are independent of rod length L

Hydrodynamic interactions modeled using Dhont et al.'s approach

Abstract

Self-diffusion of a sphere in a network of rods is analyzed theoretically. Hydrodynamic interactions are taken into account according to the model of Dhont et al., under the assumption that $\ka << 1$ and $\bar{a}/L<<1$, where $1/\kappa$ is the network hydrodynamic screening length, $\bar{a}=a+D/2$, and $a$ is the sphere radius, while $D$ and $L$ are the diameter and length of a rod, respectively. Simple expressions for the diffusion coefficients are derived and shown to be independent of $L$.