Stokes Drag on a Sphere in a Nematic Liquid Crystal

Abstract

The Stokes-Einstein relation relates the diffusion coefficient of a spherical Brownian particle in a viscous fluid to its friction coefficient. For a particle suspended in anisotropic liquid, theory predicts that the drag coefficient should also be anisotropic. Using video microscopy coupled with particle tracking routines, the Brownian fluctuations of micrometer-sized particles were analyzed to yield a quantitative measurement of the diffusion coefficients parallel and perpendicular to the nematic director. The experimental values agree quite well with recent numerical calculations that take into account the distortions of the director field in the vicinity of the particles.