Sedimentation and Fluidization

The sedimentation of particles in a fluid due to gravity and the fluidization of particles due to forced counterflow are long-standing fundamental fluid dynamics problems that have technological applications ranging from fluid catalytic cracking to mineral classification to protein recovery. While the one and two particle sedimentation problems are simple and well understood, long-range hydrodynamic interactions render the many-particle problem much more complicated. In particular, the magnitude of velocity fluctuations of sedimenting monodisperse particles has been predicted to diverge with system size. This has been the subject of intense debate for the past fifteen years but recent experiments and simulations may have helped to clarify the behavior in the creeping limit. Much less is known about sedimenting bidisperse or polydisperse suspensions, yet it is essential to understand the velocity fluctuations of these particles since this is the critical step to understand the mixing of polydisperse particles, especially in technological applications.

Gedanken Experiment. If we fixed our pump speed, then a system with perfectly monodisperse spheres will be fluidized as shown on the left. If however, we have a polydisperse spread of particle sizes, the fluid flow cannot possibly cancel gravitational force; the bigger particles will all settle to the bottom whereas the smaller particles will all be blown off the top.

In real experiments, we observed very strong stratification in our fluidized bed!

We postulate that the particles arrange themselves according with Richardson-Zaki relation in order to match pump speed.

We checked that stratification of particles sizes is real by measuring them from various heights of the bed.

Stratification model quantitatively predicts the stratification profile of various experiments