Condensation of hard spheres under gravity

Starting from the Enskog equation of hard spheres of mass nt and diameter D under the gravity g, we first derive the exact equation of motion for the equilibrium density profile at a temperature T and examine its solutions via the gradient expansion. The solutions exist only when beta mu less than or equal to mu(0), where mu is the dimensionless initial layer thickness and beta = mgD/T, and the precise value of the upper bound mu(0) depends on the underlying packing, When this inequality breaks down, a fraction of particles condenses from the bottom toward the surface. (C) 1999 Published by Elsevier Science B.V. All rights reserved.