Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption

TL;DR

This paper derives exact analytical results for the thermodynamic Casimir force in a mean-field model with strong boundary adsorption, analyzing its behavior near critical points and in capillary condensation regimes.

Contribution

It provides the first exact analytical solutions for the Casimir force in a model with strong boundary adsorption, covering temperature and field dependence.

Findings

Exact analytical expressions for the Casimir force near critical points.

Numerical maps of the force in temperature-field space.

Behavior of the force in capillary condensation regime.

Abstract

When massless excitations are limited or modified by the presence of material bodies one observes a force acting between them generally called Casimir force. Such excitations are present in any fluid system close to its true bulk critical point. We derive exact analytical results for both the temperature and external ordering field behavior of the thermodynamic Casimir force within the mean-field Ginzburg-Landau Ising type model of a simple fluid or binary liquid mixture. We investigate the case when under a film geometry the boundaries of the system exhibit strong adsorption onto one of the phases (components) of the system. We present analytical and numerical results for the (temperature-field) relief map of the force in both the critical region of the film close to its finite-size or bulk critical points as well as in the capillary condensation regime below but close to the finite-size critical point.