Hard-Sphere Fluids with Chemical Self-Potentials

TL;DR

This paper investigates the mathematical properties of self-consistent models of hard-sphere fluids, establishing existence, uniqueness, stability, and phase transitions using statistical mechanics and nonlinear fixed point equations.

Contribution

It introduces a rigorous analysis of hydrostatic equilibria in hard-sphere fluids with chemical self-potentials, including phase transition proofs.

Findings

Existence of grand canonical phase transition.

Existence of petit canonical phase transition.

Stability and uniqueness results for equilibrium solutions.

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.