  We simulate a hard-sphere liquid in confined geometry where the separation of
the two parallel, hard walls is smaller than two particle diameters. By
systematically reducing the wall separation we analyze the behavior of
structural and thermodynamic properties, such as inhomogeneous density
profiles, structure factors, and compressibilities when approaching the
two-dimensional limit. In agreement with asymptotic predictions, we find for
quasi-two-dimensional fluids that the density profile becomes parabolic and the
structure factor converges towards its two-dimensional counterpart. To extract
the compressibility in polydisperse samples a perturbative expression is used
which qualitatively influences the observed non-monotonic dependence of the
compressibility with wall separation. We also present theoretical calculations
based on fundamental-measure theory and integral-equation theory, which are in
very good agreement with the simulation results.
