  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.
