# Hard-Sphere Fluids with Chemical Self-Potentials

Source: [Hard-Sphere Fluids with Chemical Self-Potentials](<https://www.sota2.com/research/paper/68fa2f1d1e209131ce868f88>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:53:35.482Z

Authors: Michael K.-H. Kiessling, Jerome K. Percus

Published: 2009-10-05T21:19:57.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0910.0867>)

[PDF](<https://arxiv.org/pdf/0910.0867.pdf>)