  A quasi-two-dimensional system of hard spheres strongly confined between two
parallel plates is considered. The attention is focussed on the macroscopic
self-diffusion process observed when the system is looked from above or from
below. The transport equation, and the associated self-diffusion coefficient,
are derived from a Boltzmann-Lorentz kinetic equation, valid in the dilute
limit. Since the equilibrium state of the system is inhomogeneous, this
requires the use of a modified Chapman-Enskog expansion that distinguishes
between equilibrium and non-equilibrium gradients of the density of labelled
particles. The self-diffusion coefficient is obtained as a function of the
separation between the two confining plates. The theoretical predictions are
compared with molecular dynamics simulation results and a good agreement is
found.
