The contact theorem for charged fluids: from planar to curved geometries

TL;DR

This paper generalizes the contact theorem for charged fluids from flat to curved geometries, specifically concentric spheres and cylinders, providing new exact relations and insights into counter-ion behavior with validation from simulations.

Contribution

It extends the contact theorem to curved geometries and explores implications for strong Coulombic couplings and counter-ion phenomena.

Findings

Derived generalized contact relations for curved geometries.

Identified and analyzed counter-ion evaporation/condensation phenomena.

Validated theoretical results with Monte Carlo simulations.

Abstract

When a Coulombic fluid is confined between two parallel charged plates, an exact relation links the difference of ionic densities at contact with the plates, to the surface charges of these boundaries. It no longer applies when the boundaries are curved, and we work out how it generalizes when the fluid is confined between two concentric spheres (or cylinders), in two and in three space dimensions. The analysis is thus performed within the cell model picture. The generalized contact relation opens the possibility to derive new exact expressions, of particular interest in the regime of strong coulombic couplings. Some emphasis is put on cylindrical geometry, for which we discuss in depth the phenomenon of counter-ion evaporation/condensation, and obtain novel results. Good agreement is found with Monte Carlo simulation data.