  We investigate experimentally and theoretically thin layers of colloid
particles held adjacent to a solid substrate by gravity. Epifluorescence,
confocal, and holographic microscopy, combined with Monte Carlo and
hydrodynamic simulations, are applied to infer the height distribution function
of particles above the surface, and their diffusion coefficient parallel to it.
As the particle area fraction is increased, the height distribution becomes
bimodal, indicating the formation of a distinct second layer. In our theory we
treat the suspension as a series of weakly coupled quasi-two-dimensional layers
in equilibrium with respect to particle exchange. We experimentally,
numerically, and theoretically study the changing occupancies of the layers as
the area fraction is increased. The decrease of the particle diffusion
coefficient with concentration is found to be weakened by the layering. We
demonstrate that particle polydispersity strongly affects the properties of the
sedimented layer, because of particle size segregation due to gravity.
