Soap films as two-dimensional fluids: Diffusion and flow fields

TL;DR

This study investigates soap films as two-dimensional fluids by measuring tracer particle diffusion and flow fields, revealing a transition from 2D to 3D diffusion with increasing film thickness and validating theoretical models.

Contribution

It introduces a comprehensive analysis of soap film dynamics, linking particle diffusion and flow fields to film thickness and validating 2D fluid theories across different regimes.

Findings

Diffusivity relates to film thickness in thin films but deviates in thicker films.

Transition from 2D to 3D diffusion occurs at h/d ≈ 5.2.

Flow fields agree with 2D fluid theory across all film thicknesses.

Abstract

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. We make soap films with a variety of water-glycerol mixtures and of differing thicknesses. The single-particle diffusivity relates closely to parameters of the film (such as thickness $h$) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the transition at $h/d = 5.2 \pm 0.9$ using the tracer particle diameter $d$. This indicates a transition from purely 2D diffusion to diffusion that is more three-dimensional. Additionally, we measure larger length scale flow fields from correlated particle motions and find good agreement with what is expected from theory of 2D fluids for all our films, thin and thick. We measure the effective 2D viscosity of a soap film using single-particle diffusivity measurements in thin films, and using the two-particle correlation measurements in all films.