Brownian motion in shear flow: direct observation of anomalous diffusion.

Brownian motion in a simple shear flow has been experimentally investigated by using a different method for observation and analysis. A number of polystyrene spheres dispersed in sheared water were tracked with a confocal scanning laser microscope, and the time dependences of their coordinates were obtained. Since in the usual mean-square displacement in the flow direction the contribution from the Brownian motion is overwhelmed by that due to the convection, we considered an alternative displacement for which the convection effect could be removed. We found that the new mean-square displacement consists of the normal Einstein diffusion term, which is linear in t, and an anomalous t(3) term arising from the coupling between the diffusion along the velocity gradient and the convection.