Measures of Fluctuations for a Liquid Near Critical Drying

TL;DR

This paper examines density fluctuations near a critical drying transition in a liquid using density functional theory, revealing similar behavior of different fluctuation measures and their ratios, supported by a scaling thermodynamics approach.

Contribution

It introduces and compares three measures of density fluctuations near critical drying, showing their similar behavior and ratio constancy, supported by a scaling thermodynamics framework.

Findings

All three fluctuation measures exhibit similar scaled forms near critical drying.

The ratio of thermal susceptibility to compressibility remains constant at fixed distances.

Scaling analysis explains the observed fluctuation behavior on general thermodynamic grounds.

Abstract

We investigate density fluctuations in a liquid close to a solvophobic substrate at which a surface critical drying transition occurs. Using classical density functional theory, we determine three measures of the spatial extent and strength of the fluctuations, i.e., the local compressibility $\chi_{\mu}(z)$, the local thermal susceptibility $\chi_T(z)$ and the reduced density $\chi_*(z)$; $z$ is the distance from the substrate. Whilst the first measure is frequently used, the second and third were introduced very recently by Eckert et.al., Phys. Rev. Lett. 125, 268004 (2020). For state points in the critical drying regime, all three measures, each scaled by its bulk value, exhibit very similar forms and the ratio of $\chi_T(z)$ to $\chi_{\mu}(z)$, for fixed $z$ in the vapour-liquid transition region, is constant. Using a scaling treatment of surface thermodynamics we show that such behaviour is to be expected on general grounds.