A microscopic theory of tracer diffusivity: crossover to the hydrodynamic limit

A microscopic approach is developed for the tracer diffusivity in fluids based on the concepts of mode coupling theory. The calculated numerical results for the tracer diffusivity in a Lennard-Jones (LJ) fluid are shown to be in good agreement with the corresponding simulation results. The hydrodynamic limit is found to be reached at higher mass and larger size of the solute particle which is consistent with the results of simulation studies.