Microscopic determination of correlations in the fluid interfacial region in the presence of liquid-gas asymmetry

TL;DR

This paper extends microscopic analysis of fluid interfacial correlations to asymmetric liquid-gas systems, providing exact expressions and analytical approximations that match numerical solutions and reveal how asymmetry influences correlation structures.

Contribution

It generalizes previous symmetric models to asymmetric systems, deriving exact correlation functions as averages of symmetric contributions and offering analytical approximations validated by numerical solutions.

Findings

Exact correlation function expressed as average of symmetric contributions

Analytical approximations closely match numerical solutions

Asymmetry influences the transition from Goldstone mode to local density effects

Abstract

In a recent article, we showed how the properties of the density-density correlation function and its integral, the local structure factor, in the fluid interfacial region, in systems with short-ranged forces, can be understood microscopically by considering the resonances of the local structure factor [Nat.Phys.~{\bf 15}, 287 (2019)]. Here we illustrate, using mean-field square-gradient theory and the more microscopic Sullivan density functional model, how this approach generalises when there is liquid-gas asymmetry, i.e. when the bulk correlation lengths of the coexisting liquid and gas phases are different. In particular, we are able to express the correlation function \textit{exactly} as a simple average of contributions arising from two effective Ising-symmetric systems referred to as the symmetric gas and symmetric liquid. When combined with our earlier results, this generates analytical approximations for the correlation function and the local structure factor, which are near indistinguishable from the numerical solution to the Ornstein-Zernike equations over the whole range of wave-vectors. Our results highlight how asymmetry affects the correlation function structure, and describes the crossover from a long-ranged Goldstone mode to short-ranged properties determined by the local density, as the wave-vector increases.