Screening of classical Casimir forces by electrolytes in semi-infinite geometries

TL;DR

This paper investigates how electrolytes influence the classical Casimir force between dielectric slabs, validating the separation hypothesis through models and solutions in high-temperature and special cases.

Contribution

It demonstrates the validity of the separation hypothesis in electrolyte-slab systems using microscopic Coulomb gas models and analytical solutions.

Findings

Screening of Casimir force by electrolytes confirmed under certain conditions.

Separation hypothesis validated in high-temperature Debye-Hückel limit.

Analytical solutions obtained for Coulomb gases in various geometries.

Abstract

We study the electrostatic Casimir effect and related phenomena in equilibrium statistical mechanics of classical (non-quantum) charged fluids. The prototype model consists of two identical dielectric slabs in empty space (the pure Casimir effect) or in the presence of an electrolyte between the slabs. In the latter case, it is generally believed that the long-ranged Casimir force due to thermal fluctuations in the slabs is screened by the electrolyte into some residual short-ranged force. The screening mechanism is based on a "separation hypothesis": thermal fluctuations of the electrostatic field in the slabs can be treated separately from the pure image effects of the "inert" slabs on the electrolyte particles. In this paper, by using a phenomenological approach under certain conditions, the separation hypothesis is shown to be valid. The phenomenology is tested on a microscopic model in which the conducting slabs and the electrolyte are modelled by the symmetric Coulomb gases of point-like charges with different particle fugacities. The model is solved in the high-temperature Debye-H\"uckel limit (in two and three dimensions) and at the free fermion point of the Thirring representation of the two-dimensional Coulomb gas. The Debye-H\"uckel theory of a Coulomb gas between dielectric walls is also solved.