Spatial gradients and evolving density profiles in Stokesian sedimentation

We report spatially-resolved measurements of spatial density gradients in sedimenting suspensions of spheres and discs using x-ray absorption methods. We prepare the suspension with a homogeneously distributed global volume fraction Φ_o, and then measure the time-resolved evolution of the local volume fraction Φ during sedimentation, revealing that the suspension develops a density gradient along the height of the container. The density profile evolves with time: every band of fixed local volume fraction (Φ) settles at a steady velocity that depends both on its local volume fraction and the global volume fraction Φ_o. As is well known, the typical sedimentation speed decreases as the global volume fraction is increased, but for a given global volume fraction, we find surprisingly, that higher local densities correspond to faster settling velocities. This suggests that the dynamics of hindered settling are not local: settling dynamics are determined by the global and local value of the volume fraction, as well as its gradient.