Where is the hydrodynamic limit?

In this paper, the classical hydrodynamic theory is compared to molecular dynamics simulation data using two different dynamical modes, namely, the transverse and longitudinal modes. The comparison is based on the dynamics of the equilibrium fluctuations for four different systems, the Lennard-Jones system, model liquids for butane, toluene, and water. Using an error estimator limit of 1%, it is found that for the transverse dynamics the classical hydrodynamic theory holds down to 5–14 nm depending on the fluidic system. For the longitudinal dynamics, this characteristic length scale is approximately doubled. From the dispersion relations, it is furthermore concluded that classical hydrodynamics qualitatively accounts for the dominating processes at even lower length scales.