Density profiles and pair correlation functions of hard spheres in   narrow slits
  A hard sphere fluid confined by hard, structureless, and parallel walls is investigated using a certain version of weighted density functional theory. The density profile, the excess coverage, the finite size contribution to the free energy, the solvation force, and the total correlation function are determined as function of the slit width $L$ for various bulk number densities $\rho_b$. In quantitative agreement with rigorous results the present version of density functional theory yields a constant and large but finite number density profile for the limiting case that $L$ is reduced to the diameter of the hard spheres. Within the Derjaguin approximation the results for the slit geometry allows us to obtain the solvation force between two large hard spheres immersed into a fluid of much smaller hard spheres. 
B. Gotzelmann, S. Dietrich