  We study a lattice model for the spreading of fluid films, which are a few
molecular layers thick, in narrow channels with inert lateral walls. We focus
on systems connected to two particle reservoirs at different chemical
potentials, considering an attractive substrate potential at the bottom,
confining side walls, and hard-core repulsive fluid-fluid interactions. Using
kinetic Monte Carlo simulations we find a diffusive behavior. The corresponding
diffusion coefficient depends on the density and is bounded from below by the
free one-dimensional diffusion coefficient, valid for an inert bottom wall.
These numerical results are rationalized within the corresponding continuum
limit.
