Condensation of Hard Spheres Under Gravity
Daniel C. Hong
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 μo ≈ 21.756 in 2 dimensions and μo≈ 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.
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