Finite-size effects in presence of gravity: The behavior of the susceptibility in $^3He$ and $^4He$ films near the liquid-vapor critical point

TL;DR

This paper investigates how gravity and long-range interactions influence the susceptibility of helium films near their critical points, revealing significant deviations from short-range models and providing analytical expressions for susceptibilities.

Contribution

It introduces a comprehensive analysis of finite-size effects in helium films considering gravity and van der Waals forces, with exact mean-field solutions for susceptibilities.

Findings

Gravity and van der Waals forces cause substantial deviations from short-range models.

Analytical mean-field expressions for susceptibilities are derived.

Predictions are made for helium films near critical points.

Abstract

We study critical point finite-size effects on the behavior of susceptibility of a film placed in the Earth's gravitational field. The fluid-fluid and substrate-fluid interactions are characterized by van der Waals-type power law tails, and the boundary conditions are consistent with bounding surfaces that strongly prefer the liquid phase of the system. Specific predictions are made with respect to the behavior of $^3$He and $^4$He films in the vicinity of their respective liquid-gas critical points. We find that for all film thicknesses of current experimental interest the combination of van der Waals interactions and gravity leads to substantial deviations from the behavior predicted by models in which all interatomic forces are very short ranged and gravity is absent. In the case of a completely short-ranged system exact mean-field analytical expressions are derived, within the continuum approach, for the behavior of both the local and the total susceptibilities.