  When a capillary is inserted into a liquid, the liquid will rapidly flow into
it. This phenomenon, well studied and understood on the macroscale, is
investigated by Molecular Dynamics simulations for coarse-grained models of
nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are
considered. In both cases after a transient period (of a few nanoseconds) the
meniscus rises according to a $\sqrt{\textrm{time}}$-law. For the polymer melt,
however, we find that the capillary flow exhibits a slip length $\delta$,
comparable in size with the nanotube radius $R$. We show that a consistent
description of the imbibition process in nanotubes is only possible upon
modification of the Lucas-Washburn law which takes explicitly into account the
slip length $\delta$.
