Hard-Sphere Fluids with Chemical Self-Potentials

Details Hard-Sphere Fluids with Chemical Self-Potentials Hard-Sphere Fluids with Chemical Self-Potentials

2009-10-05

arxiv.org/abs/0910.0867v2

Journal of Mathematical Physics, vol. 51 (2010), no. 1, 015206, 42 pp

Physics

Mathematical Physics

66pp. Final version, in press at J. Math. Phys. Typos and slips of pen have been corrected. Layout has been changed to accommo

Scientific paper

Existence, uniqueness and stability of solutions is studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container and in contact with either a heat and a matter reservoir, or just a heat reservoir. The local thermodynamics is furnished by the statistical mechanics of a system of hard balls, in the approximation of Carnahan-Starling. The fluid's local chemical potential per particle at is the sum of the matter reservoir's contribution and a self contribution which is computed by convoluting the fluid density distribution with a van der Waals, a Yukawa, or a Newton kernel. We prove the existence of a grand canonical phase transition, and a petit canonical phase transition which is embedded in the former.

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