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 (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 〈Vₙ (0) Vₙ (z) 〉^1/22. 0Vₒ₄₃^1/3exp (-z/2), where 20a^-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 〈Vₙ^2 (0) 〉^1/2{0ex{0ex}=0ex{0ex}2. 0V}ₒ₄₃^1/31-exp (-W/60a^-1/3).