Condensation of Hard Spheres Under Gravity
arXiv:cond-mat/9806253 · doi:10.1016/S0378-4371(99)00181-8
Abstract
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 βμ\le μ_o \approx 21.756 in 2 dimensions and μ_o\approx 15.299 in 3 dimensions, where μis the dimensionless initial layer thickness and β=mgD/T. When this inequality breaks down, a fraction of particles condense from the bottom up to the Fermi surface.
9 pages, one figure
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