2010
DOI: 10.1103/physrevlett.105.268304
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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 fr… Show more

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Cited by 52 publications
(54 citation statements)
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“…Since S is about two orders of magnitude smaller than the film radius in these experiments, contributions to the island mobility from confinement should be negligible. The observations are consistent with an extensive earlier study of the Brownian diffusion of islands in ultra-thin 8CB films, which showed that the islands have mobilities that follow SD/HPW theory over a wide range of ε [7]. Although they have fluid interiors, circulatory flow inside the islands induced by their motion through the background film is expected to be strongly suppressed, so that they behave hydrodynamically like solid discs.…”
supporting
confidence: 90%
See 1 more Smart Citation
“…Since S is about two orders of magnitude smaller than the film radius in these experiments, contributions to the island mobility from confinement should be negligible. The observations are consistent with an extensive earlier study of the Brownian diffusion of islands in ultra-thin 8CB films, which showed that the islands have mobilities that follow SD/HPW theory over a wide range of ε [7]. Although they have fluid interiors, circulatory flow inside the islands induced by their motion through the background film is expected to be strongly suppressed, so that they behave hydrodynamically like solid discs.…”
supporting
confidence: 90%
“…Most rheological investigations of membranes have been made by observing Brownian motion in flat lipid membranes and spherical vesicles [3,5,6] as well as in liquid crystal films [7,8], with the mobility of the inclusions calculated from the diffusion coefficient by means of the Einstein relation. This approach requires a model describing the relation between the mobility and such physical parameters as the inclusion size and the viscosities of the membrane and the surrounding fluid.…”
mentioning
confidence: 99%
“…These fluid films are unique among monolayer liquid systems in that they are in a symmetric environment with vapor on both sides. Such substrate-free monolayer fluid molecular films are of fundamental interest in soft matter nanoscience, serving as fluid systems of reduced dimensionality for the study of fluctuation, symmetry, and interface effects (9,10). Here we show that single and few layer smectic films can be used to measure the surface energy of a substrate-free fluid molecular monolayer.…”
mentioning
confidence: 76%
“…The experiment provides a set of reliable data against which further theoretical modeling can be developed. It is also relevant to a class of problems related to the mobility and microrheology of interfacial particles in a monolayer or membrane, such as lipid or proteinassociated domains in cell membranes [24][25][26].…”
Section: Prl 111 168304 (2013) P H Y S I C a L R E V I E W L E T T Ementioning
confidence: 99%
“…When the Saffman length [23,24] S ¼ s = b ) h (large s regime), the effect of the liquid subphase is negligibly small and the HIs are essentially 2D [25,26]. In this case, C rr is expected to depend logarithmically on r [23,27].…”
mentioning
confidence: 99%