title: Crossover between 2D and 3D fluid dynamics in the diffusion of islands in ultrathin freely suspended smectic films.
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 D∼ -ln(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.
authors.affiliation: Department of Physics and LCMRC, University of Colorado, Boulder, Colorado, USA.
authors.forename: Zoom Hoang
authors.initials: ZH
authors.lastname: Nguyen
authors.forename: Markus
authors.initials: M
authors.lastname: Atkinson
authors.forename: Cheol Soo
authors.initials: CS
authors.lastname: Park
authors.forename: Joseph
authors.initials: J
authors.lastname: Maclennan
authors.forename: Matthew
authors.initials: M
authors.lastname: Glaser
authors.forename: Noel
authors.initials: N
authors.lastname: Clark
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D057446:Hydrodynamics; D050866:Liquid Crystals / Q000737:chemistry*; D013535:Suspensions
chemical_list: D013535:Suspensions