Local orientations of fluctuating fluid interfaces

TL;DR

This paper investigates the local orientations of fluctuating fluid interfaces using theoretical models, deriving probability distributions and correlations for tilt angles, and compares predictions from different models to highlight the importance of surface tension variations.

Contribution

It introduces a detailed theoretical framework for characterizing local interface orientations and compares different models to improve understanding of interfacial fluctuations.

Findings

The mean tilt angle varies with temperature and model assumptions.

The tilt angle distribution distinguishes between theoretical approaches.

Two-point correlation functions provide structural insights into interface fluctuations.

Abstract

Thermal fluctuations cause the local normal vectors of fluid interfaces to deviate from the vertical direction defined by the flat mean interface position. This leads to a nonzero mean value of the corresponding polar tilt angle which renders a characterization of the thermal state of an interface. Based on the concept of an effective interface Hamiltonian we determine the variances of the local interface position and of its lateral derivatives. This leads to the probability distribution functions for the metric of the interface and for the tilt angle which allows us to calculate its mean value and its mean square deviation. We compare the temperature dependences of these quantities as predicted by the simple capillary wave model, by an improved phenomenological model, and by the microscopic effective interface Hamiltonian derived from density functional theory. The mean tilt angle discriminates clearly between these theoretical approaches and emphasizes the importance of the variation of the surface tension at small wave lengths. Also the tilt angle two-point correlation function is determined which renders an additional structural characterization of interfacial fluctuations. Various experimental accesses to measure the local orientational fluctuations are discussed.