Diffusion of particles in simple fluids: A joint theory of kinetics and   hydrodynamics
  The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are derived analytically, and the hydrodynamics effect on the particle diffusion is analyzed in detail. Unlike previous studies, the ring-collision effect is exhaustively considered in our treatment, and the hydrodynamics approach is extended to the whole time range. Large scale molecular dynamics simulations for the hard-disk fluid show that our analytical results are valid up to the density close to the crystallization point. 
Hanqing Zhao, Hong Zhao
physics.flu-dyn cond-mat.stat-mech