Retarded hydrodynamic interactions in suspensions

We extend the method to determine the grand mobility matrix presented in a previous article to the problem of two particles in an unbounded fluid satisfying the time dependent linear incompressible Navier-Stokes equations. Use of this method combined with a generalization of the fluctuation dissipation theorem results in the determination of the correlation matrix. We determine the effect of hydrodynamic interactions on the time dependent diffusion coefficients D11(τ) and D12(τ). Finally we study the effects of the correlation functions on Brownian motion.