Tricritical Casimir forces and order parameter profiles in wetting films of $^3\text{He}$ -$^4\text{He}$ mixtures

TL;DR

This paper investigates tricritical Casimir forces and order parameter profiles in $^3$He-$^4$He$ wetting films using a mean field lattice gas model that incorporates superfluid symmetry and vapor phase, aligning theory with experiments.

Contribution

It introduces a lattice gas model accounting for superfluid symmetry and vapor phase, enhancing the theoretical understanding of tricritical Casimir forces in helium mixtures.

Findings

Model successfully describes experimental data

Wetting films exhibit specific order parameter profiles

Casimir forces show characteristic dependence on film thickness

Abstract

Tricritical Casimir forces in $^3\text{He}$ -$^4\text{He}$ wetting films are studied, within mean field theory, in therms of a suitable lattice gas model for binary liquid mixtures with short--ranged surface fields. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with $^4\text{He}$ and it allows, inter alia, for the occurrence of a vapor phase. As a result, the model facilitates the formation of wetting films, which provides a strengthened theoretical framework to describe available experimental data for tricritical Casimir forces acting in $^3\text{He}$ -$^4\text{He}$ wetting films.