A unifying theory for velocity fluctuations in sedimentation

This paper presents a theory for the velocity fluctuations in sedimentation that unifies all previous experimental results and numerical simulations. The central idea is that velocity fluctuations in experiments decrease below those of an independently-distributed uniform density sediment between side walls because of the development of a vertical stratification in the cell, owing to the broadening of the sediment front. We show through numerical simulations, scaling arguments, theoretical calculations, and experimental observations that a very small stratification changes the characteristics of the density and velocity fluctuations. If the initial velocity fluctuations are large enough (the cell is thick enough) the fluctuations decay continuously in time, throughout the experiment. For intermediate values of the initial velocity fluctuations (cell thicknesses) the fluctuations decrease below that of an independently-distributed uniform sediment, and appear to stay at roughly constant levels throughout the experiment. For small enough initial fluctuations (cell thicknesses) the fluctuations quantitatively agree with those predicted by independent Poisson distribution estimates. Theoretical calculations quantitatively agree with the simulations and all previous experiments. The velocity fluctuations in sedimentation are therefore not universal as often suggested, but instead depend on both the cell shape and developing stratification.