Long-time tails of translational and rotational Brownian motion in a suspension of hard spheres

The long-time translational and rotational Brownian motion of a sphere in a suspension of hard spheres is studied on the basis of the linearized Navier-Stokes equations and the fluctuation-dissipation theorem. It is shown that for the rotational long-time coefficient an effective medium conjecture is incorrect. There are short-range velocity correlations that decay at the same rate as the macroscopic flow pattern used in the effective medium conjecture. An estimate of the short-range correction is made on the basis of the pair term in the cluster expansion of the rotational admittance.