Lattice-Boltzmann simulations have been used to investigate low-Reynolds-number settling of monodisperse and polydisperse suspensions. We confirm the discovery that particle velocity fluctuations are strongly suppressed by no-slip walls at the top and bottom of the system, even in regions distant from the boundaries. We also show that a monodisperse suspension develops a strongly anisotropic long-range microstructure during the settling process, with vanishing density fluctuations in the horizontal plane. We find no numerical evidence that the particle concentration in the bulk is stratified; diffusive spreading of the suspension–supernatant interface is suppressed by hindered settling, as would be expected in moderately concentrated suspensions.

Long-range correlations in particle density fluctuations are destroyed by polydispersity in particle size, and in this case density fluctuations are finite at all length scales and in all directions. However, in polydisperse suspensions there is significant stratification, due to differential settling rather than interface diffusion, which provides an alternative mechanism for screening the hydrodynamic interactions. It is possible that this is the dominant mechanism for hydrodynamic screening in several laboratory experiments.