Wave vector and frequency dependent longitudinal viscosity of systems of interacting Brownian particles

Using linear response theory the memory function of the concentration-autocorrelation function of interacting Brownian particles is related directly to the change of the longitudinal stress due to fluctuations of the local velocity gradient. This derivation is valid for arbitrary frequencies and wavevectors and defines an intrinsic longitudinal viscosity of the system. It is further shown that the dynamical properties of interacting Brownian particles can be described by generalized hydrodynamic equations and that deviations of the concentration-autocorrelation function from an exponential form can be understood as a visco-elastic effect.