Long-Range Correlations in Sedimentation

Using particle image velocimetry we have measured the sedimentation dynamics of non-Brownian colloidal spheres over a wide range of low concentrations ( φ≤0.05) and sample cell sizes W. Fluctuations in the settling velocity show universal large-scale finite-range correlations, in the form of swirls, which depend simply on volume fraction and particle radius and follow 〈δV_z(0)δV_z(z)〉^1/2≃2.0V_sedφ^1/3exp(-z/2ξ), where ξ≃20aφ^-1/3. In turn, the predicted divergence of the velocity variance with increasing cell size W is cut off in a universal way as W exceeds the swirl size and is well represented by 〈δV_z²(0)〉^1/2 = 2.0V_sedφ^1/3[1-exp(-W/60aφ^-1/3)].