Mean-Field Theory of Inhomogeneous Fluids

TL;DR

This paper extends the Barker-Henderson perturbation theory into a density functional framework to accurately describe inhomogeneous classical fluids in external fields, validated by numerical results matching simulations.

Contribution

It develops the first-principles Barker-Henderson density functional for inhomogeneous fluids, enabling quantitative predictions in external fields.

Findings

Good agreement with simulation data for density around a test particle

Accurate density profiles at fluid interfaces with reduced oscillation amplitude

Predictions capture decay of density oscillations near phase transition

Abstract

The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles 'Barker-Henderson density functional', thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapour interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced towards the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.