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_sed φ^1/3 exp(−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 ⟨δV²_z(0)⟩^1/2 = 2.0V_sedφ^1/3 [1 − exp(−W/60aφ^−1/3)].