Hard-Sphere Fluids with Chemical Self-Potentials
Abstract
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.
Cite
@article{arxiv.0910.0867,
title = {Hard-Sphere Fluids with Chemical Self-Potentials},
author = {Michael K. -H. Kiessling and Jerome K. Percus},
journal= {arXiv preprint arXiv:0910.0867},
year = {2015}
}
Comments
66pp. Final version, in press at J. Math. Phys. Typos and slips of pen have been corrected. Layout has been changed to accommodate the style of J. Math. Phys. Note that the numbering of equations and theorems etc. has changed as a result of the layout changes