We confine charged spheres in cells with the smallest dimension along the direction of gravity ĝ. The particles are density mismatched with the surrounding medium and sediment along ĝ with typical Péclet numbers of Pe approximately 10(-3). After a certain time, we find that the number of particles N increases near both upper and lower plates until a characteristic time tau is reached; above this time N plateaus. We attribute the observed phenomenology to collective particle motions driven by gravity and mediated by hydrodynamic interactions; these could yield formation of swirls made of particles with correlated velocities that could eventually drive the particles towards the upper plate. The characteristic time for these migrations scales with plate-to-plate separation Lz as tau approximately Lz1.2, exactly as the characteristic decay time of velocity fluctuations in sedimentation processes [S. Y. Tee, Phys. Rev. Lett. 89, 054501 (2002)], despite that in these experiments the smallest cell dimension is perpendicular to ĝ and 7<Pe<50. In the absence of gravitational field, the observed particle migrations disappear, emphasizing the key role played by gravity in these experiments.