Crossover between 2D and 3D fluid dynamics in the diffusion of islands in ultrathin freely suspended smectic films |
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Authors: | Nguyen Zoom Hoang Atkinson Markus Park Cheol Soo Maclennan Joseph Glaser Matthew Clark Noel |
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Institution: | Department of Physics and LCMRC, University of Colorado, Boulder, Colorado, USA. |
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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. |
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