Condensation of Hard Spheres Under Gravity

Details Condensation of Hard Spheres Under Gravity Condensation of Hard Spheres Under Gravity

1998-06-21

arxiv.org/abs/cond-mat/9806253v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, one figure

Scientific paper

10.1016/S0378-4371(99)00181-8

Starting from Enskog equation of hard spheres of mass m 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 \le \mu_o \approx 21.756 in 2 dimensions and \mu_o\approx 15.299 in 3 dimensions, where \mu is the dimensionless initial layer thickness and \beta=mgD/T. When this inequality breaks down, a fraction of particles condense from the bottom up to the Fermi surface.

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