Classical fluid dynamics under molecular scale confinement

This is a review of some recent developments in the theory of classical nanoscale fluid dynamics, with tagged particle dynamics as the signature of transport properties. A heuristic analysis of the time asymptotic regime in strictly one-dimensional flow is followed by an exact treatment of the same system, with arbitrary non-interacting point particle dynamics. Stretched time and space coordinates allow us to obtain a universal form the telegrapher's equation for the self-dynamics after transients have died down. Attention then shifts to one-particle diffusion in a spatially modulated tubular enclosure, which is analyzed by increasingly sophisticated approximation methods. With this background, single-file fluid flow in modulated enclosures is studied, and preliminary analysis of the "passing region" carried out as well.