Hydrodynamics of nanoscopic capillary waves.

The dynamics of nanoscopic capillary waves on simple liquid surfaces is analyzed using molecular dynamics simulations. Each Fourier mode of the surface is obtained from the molecular positions, and its time behavior compared with the hydrodynamic prediction. We trace the transition from propagating to overdamped modes, at short wavelengths. The damping rate is in very good agreement with the hydrodynamic theory up to surprisingly small wavelengths, of about four molecular diameters, but only if the wave number dependent surface tension is considered. At shorter scales, surface tension hydrodynamics break down and we find a transition to a molecular diffusion regime.