Microscopic theory for interface fluctuations in binary liquid mixtures

TL;DR

This paper develops a microscopic theoretical framework for understanding interface fluctuations in binary liquid mixtures, incorporating density and composition variations, and providing explicit formulas for physical parameters relevant to scattering experiments.

Contribution

It introduces a density functional theory-based effective Hamiltonian that extends the standard capillary-wave model to include composition fluctuations in binary mixtures.

Findings

Derived explicit expressions for surface tension and bending rigidities.

Predicted scattering signatures for grazing-incidence x-ray experiments.

Extended the capillary-wave model to account for compositional effects.

Abstract

Thermally excited capillary waves at fluid interfaces in binary liquid mixtures exhibit simultaneously both density and composition fluctuations. Based on a density functional theory for inhomogeneous binary liquid mixtures we derive an effective wavelength dependent Hamiltonian for fluid interfaces in these systems beyond the standard capillary-wave model. Explicit expressions are obtained for the surface tension, the bending rigidities, and the coupling constants of compositional capillary waves in terms of the profiles of the two number densities characterizing the mixture. These results lead to predictions for grazing-incidence x-ray scattering experiments at such interfaces.