Long-range hydrodynamic correlations in quasi-one-dimensional circular and straight geometries.

We report the results of studies of the collective and pair diffusion coefficients of particles in two quasi-one-dimensional geometries: straight 2-mm-long channels and rings with radii between 3 and 35 μm. We find a contribution to the packing fraction dependence of the collective diffusion coefficient that confirms the behavior predicted by Frydel and Diamant [D. Frydel and H. Diamant, Phys. Rev. Lett. 104, 248302 (2010)], indicative of long-range hydrodynamic coupling resulting from collective motion of particles in periodic quasi-one-dimensional geometries. Specifically, we find a proportionality constant of 0.19 ± 0.01 μm(2)/s between the residual collective diffusion coefficient (defined as the collective diffusion coefficient less the mean self-diffusion coefficient of colloids) and the packing fraction for the ring geometries, independent of ring curvature, and a proportionality constant of 0.14 ± 0.01 μm(2)/s for 2-mm straight channels. Both of these values, for circular geometries in particular, are significantly larger than predicted when only ensemble averaging over particle positions is accounted for, which strongly suggests the presence of additional hydrodynamic coupling. These findings are signficant because they imply that the global geometry of the confined suspension influences collective colloidal diffusion even when single file motion of colloids is maintained.