We apply a hybrid Molecular Dynamics and mesoscopic simulation technique to study the steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.08 to 12. Hydrodynamic back-flow causes a reduction of the average sedimentation velocity relative to the Stokes velocity. We find that this effect is independent of Pe number. Velocity fluctuations show the expected effects of thermal fluctuations at short correlation times. At longer times, non-equilibrium hydrodynamic fluctuations are visible, and their character appears to be independent of the thermal fluctuations. The hydrodynamic fluctuations dominate the diffusive behavior even for modest Pe number, while conversely the short-time fluctuations are dominated by thermal effects for a surprisingly large Pe numbers. Inspired by recent experiments, we also study finite sedimentation in a horizontal planar slit. In our simulations distinct lateral patterns emerge, in agreement with observations in the experiments.
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