Long-time tails in the solid-body motion of a sphere immersed in a suspension

Long-time tails in the translational and rotational motion of a sphere imme rsed in a suspension of spherical particles are discussed on the basis of t he linear, time-dependent Stokes equations of hydrodynamics. It is argued t hat the coefficient of the t(-3/2) long-time tail of translational motion d epends only on the effective mass density and shear viscosity of the suspen sion. A similar expression holds for the coefficient of the t(-5/2) long-ti me tail of rotational motion. In particular, the long-time tails are indepe ndent of the sphere radius, and therefore the expressions hold also for a p article of the suspension. On account of the fluctuation-dissipation theore m the lung-time tails of the velocity autocorrelation function and the angu lar velocity autocorrelation function of interacting Brownian particles are also given by these expressions.