Abstract
The Stokes paradox, that moving a disk at finite velocity through an infinite two-dimensional (2D) viscous fluid requires no force, leads, via the Einstein relation, to an infinite diffusion coefficient for the disk. Saffman and Delbrück proposed that if the 2D fluid is a thin film immersed in a 3D viscous medium, then the film should behave as if it were of finite size, and , where is the inclusion radius and is the viscosity of the 3D medium. By studying the Brownian motion of islands in freely suspended smectic liquid crystal films a few molecular layers thick, we verify this dependence using no free parameters, and confirm the subsequent prediction by Hughes, Pailthorpe, and White of a crossover to 3D Stokes-like behavior when the diffusing island is sufficiently large.
- Received 1 September 2010
DOI:https://doi.org/10.1103/PhysRevLett.105.268304
© 2010 The American Physical Society