Correlation function of the velocity field of a thin suspended liquid film

TL;DR

This paper provides an exact solution for the velocity fluctuation correlation function in thin suspended liquid films, revealing how interactions with surrounding fluids affect their statistical properties at different frequencies.

Contribution

It offers a novel exact hydrodynamic solution for velocity correlations in thin liquid films considering surrounding fluid effects.

Findings

Correlation functions match 2D fluid behavior at high frequencies

Deviations occur at low frequencies due to fluid interactions

Results improve understanding of thin film hydrodynamics

Abstract

In this paper, I consider a thin suspended liquid film, surrounded by a different fluid. Examples of such a system are soap films and liquid crystal films, surrounded by air. They are considered good models for two dimensional fluid dynamics, although air drag is known to introduce strong deviations. I exactly solve the hydrodynamic equations of the system composed by the liquid layer and the surrounding fluid in order to evaluate the correlation function of the thermally excited velocity fluctuations. Both the temporal and the spatial statistical properties are the ones of a two dimensional, hypotetical fluid, only for temporal and spatial frequencies higher than critical values; at lower frequencies they show significative deviations due to the interactions of the liquid layer with the surrounding fluid.