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 vi a the gradient expansion. The solutions exist only when beta mu less than o r 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 th e underlying packing, When this inequality breaks down, a fraction of parti cles condenses from the bottom toward the surface. (C) 1999 Published by El sevier Science B.V. All rights reserved.