Exact results for the temperature-field behavior of the thermodynamic Casimir force in a model of film system with a strong surface adsorption

TL;DR

This paper derives exact analytical results for the thermodynamic Casimir force in a film system with strong surface adsorption, analyzing its behavior near critical points and in capillary condensation regimes.

Contribution

It provides the first exact analytical solutions for the temperature and field dependence of the Casimir force in a mean-field model with strong surface adsorption.

Findings

Exact analytical expressions for the Casimir force near critical points.

Numerical results illustrating force behavior in different regimes.

Insights into surface effects on thermodynamic forces in confined systems.

Abstract

When masless excitations are limited or modified by the presence of material bodies one observes a force atcing 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) surface 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 the finite-size critical point.