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

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. [J. Chem. Phys. 122, 044905 (2005); ibid.124, 044907 (2006); ibid.126, 214501 (2007)] based on the Debye-Bueche-Brinkman equation. The hydrodynamic screening length of the effective medium is assumed to be much larger than the sphere radius and the rod thickness. The self-diffusion coefficient, given by Dhont et al. in terms of four-dimensional integrals, is in this work expressed in terms of a single integral only and therefore evaluated numerically with a high precision. Moreover, simple expressions for the self-diffusion coefficient are derived and shown to be independent of the rod length. They can be useful for experimental verification of the model.