2D to 3D transition in soap films demonstrated by microrheology

TL;DR

This study investigates how soap films transition from two-dimensional to three-dimensional behavior by analyzing colloidal particle diffusion and surface viscosity, revealing unphysical values that indicate a dimensional shift.

Contribution

It demonstrates the 2D to 3D transition in soap films through microrheology and relates diffusion constants to surface viscosity using established models.

Findings

Unphysical surface viscosity values for thick films ($h/d > 7$)

Evidence of a transition from 2D to 3D behavior in soap films

Diffusion constants linked to surface viscosity via Saffman's equation

Abstract

We follow the diffusive motion of colloidal particles of diameter $d$ in soap films of varying thickness $h$ with fluorescence microscopy. Diffusion constants are obtained both from one- and two-particle microrheological measurements of particle motion in these films. These diffusion constants are related to the surface viscosity of the interfaces comprising the soap films, by means of the Trapeznikov approximation [A. A. Trapeznikov, \emph{PICSA} (1957)] and Saffman's equation for diffusion in a 2D fluid. Unphysical values of the surface viscosity are found for thick soap films ($h/d > 7$), indicating a transition from 2D to 3D behavior.