Crossover between 2D and 3D Fluid Dynamics in the Diffusion of Islands in Ultrathin Freely Suspended Smectic Films

Zoom Hoang Nguyen, Markus Atkinson, Cheol Soo Park, Joseph Maclennan, Matthew Glaser, and Noel Clark
Phys. Rev. Lett. 105, 268304 – Published 30 December 2010

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 D 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 Dln(aη), where a is the inclusion radius and η 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 1 September 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.268304

© 2010 The American Physical Society

Authors & Affiliations

Zoom Hoang Nguyen, Markus Atkinson, Cheol Soo Park, Joseph Maclennan, Matthew Glaser, and Noel Clark

  • Department of Physics and LCMRC, University of Colorado, Boulder, Colorado, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 105, Iss. 26 — 31 December 2010

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×