  Although continuum theories have been proven quite robust to describe
confined fluid flow at molecular length scales, molecular dynamics (MD)
simulations reveal mechanistic insights into the interfacial dissipation
processes. Most MD simulations of confined fluids have used setups in which the
lateral box size is not much larger than the gap height, thus breaking
thin-film assumptions usually employed in continuum simulations. Here, we
explicitly probe the long wavelength hydrodynamic correlations in confined
simple fluids with MD and compare to gap-averaged continuum theories as
typically applied in e.g. lubrication. Relaxation times obtained from
equilibrium fluctuations interpolate between the theoretical limits from bulk
hydrodynamics and continuum formulations with increasing wavelength. We show
how to exploit this characteristic transition to measure viscosity and slip
length in confined systems simultaneously from equilibrium MD simulations.
Moreover, the gap-averaged theory describes a geometry-induced dispersion
relation that leads to overdamped sound relaxation at large wavelengths, which
is confirmed by our MD simulations. Our results add to the understanding of
transport processes under strong confinement and might be of technological
relevance for the design of nanofluidic devices due to the recent progress in
fabrication methods.
