Effect of terminal velocities on macroscopic and microscopic hydrodynamic mixing of stratified suspensions.

We performed numerical experiments to investigate the mixing of stratified suspensions composed of different particle types by gravitational sedimentation. The mixing process is controlled by a dimensionless group Y_{m}∼U_{f}/U_{St1}, where U_{f} is a typical velocity of a macroscopic sedimenting finger and U_{St1} is the Stokes settling velocity of a single spherical particle in the upper suspension. The effects of components of Y_{m}, in particular, terminal velocities of particles, were investigated. For Y_{m}=100, no large difference was observed for the difference of components of Y_{m}, and it was confirmed that the mixing rate is determined by Y_{m}, because macroscopic (vessel-scale) mixing is dominant for large Y_{m}. For Y_{m}=5, macroscopic mixing and microscopic (individual particle-level) mixing due to the particle terminal velocity difference are of the same order, while completely different mixing patterns were observed for positive, zero, and negative terminal velocity differences: macroscopic mixing is promoted by the increase in apparent density due to microscopic mixing, small macroscopic mixing is suppressed by the individual particle settling, and jetting mixing occurs owing to pure liquid layer formation.