Self-diffusion of spherical Brownian particles with hard-core interaction

The N-particle Smoluchowski equation is solved exactly for a system of spherical Brownian particles interacting through hard-core potentials to first order in the volume concentration φ. The self-diffusion coefficient is found to be given by Ds = D0(1−2φ), where D0 is the free diffusion constant. The hydrodynamic interaction is then taken into account in a perturbative way. Using the Oseen approximation, Ds = D0(1−0.09φ) is found, whereas the improved form for the hydrodynamic interaction due to Felderhof gives Ds = D0(1−1.89φ).