Experimental Realization of an Incompressible Newtonian Fluid in Two Dimensions

TL;DR

This study demonstrates that freely suspended smectic A liquid crystal films can serve as nearly ideal two-dimensional, incompressible Newtonian fluids, especially in low-pressure environments where air effects are minimized.

Contribution

The paper provides the first experimental realization of a two-dimensional, incompressible Newtonian fluid using smectic A liquid crystal films in vacuum conditions.

Findings

Diffusion coefficient increases as air pressure decreases.

Films behave as ideal 2D Newtonian fluids in vacuum.

Air surrounding the film significantly affects micron-scale particle diffusion.

Abstract

The Brownian diffusion of micron-scale inclusions in freely suspended smectic A liquid crystal films a few nanometers thick and several millimeters in diameter depends strongly on the air surrounding the film. Near atmospheric pressure, the three-dimensionally coupled film/gas system is well described by Hughes/Pailthorpe/White hydrodynamic theory but at lower pressure (p < 70 torr), the diffusion coefficient increases substantially, tending in high vacuum toward the two-dimensional limit where it is determined by film size. In the absence of air, the films are found to be a nearly ideal physical realization of a two-dimensional, incompressible Newtonian fluid.