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In granulometry, say I have a tube with an heterogeneous mix of particles of different sizes (sand and stones, by instance). The tube is vertical in the usual gravity field and is placed in the air. If I randomly shake the tube, the smallest particles will eventually be at the bottom, and the largest ones at the top. So the particles are now sorted by size. Why?

A friend of mine considers a volume of the bottom part of the tube has a greater density (or mass) than of the top's. And denser things go downward.

I consider however, by shaking the particles, small ones can fall through the space left between larger ones.

What is the correct explanation?


marked as duplicate by John Rennie, Kyle Kanos, user36790, Hritik Narayan, HDE 226868 Dec 19 '15 at 15:04

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There is a number of effects in play here. I will assume a closed tube, because, if it is open or porous, the effects will change. In general the following things occur:

  1. If you shake it extremely vigorously, you get most of the material moving from end to end, and typically a complete mixing will occur.
  2. If you shake it moderately vigorously, a convection-like current develops across the container, with particles rising in the centre and falling (relatively) at the walls. This is called vibrofluidization, and is a mix of aerodynamic forces and granular collisions. (If you do this in a vacuum, the aerodynamic forces disappear, and the broad convection currents also disappear.) Smaller and lighter (less dense) particles are more affected by the this current, so, while the net result is primarily mixing, denser particles and larger particles tend to drop towards the bottom and resist being entrained in the flow.
  3. If you shake it less vigorously, (i.e. insufficiently for a convection-like current to be set up), vibro-compaction dominates. (This is probably the region of the experiment you are wanting to look at.) Here smaller particles do tend to fall into gaps when they emerge below the particles, or more likely, progressively wedge themselves lower. Larger particles tend to allow gaps to form beside them, which are readily filled by smaller particles, and effectively float to the top when smaller particles fill gaps formed below them - buoyancy through a thousand wedges. At the surface when the large particle is slightly above the level of the sand, this effect is stronger, because there are fewer collisions from above pushing the large particle back down (which would normally limit the size of the gaps that form below the particle). Overall, at this shaking level, particle-size effects dominate, and density plays a minor (though not negligible) role (so your answer is more correct than your friends).
  4. If you shake even less vigorously, the shaking is insufficient to break (particularly Van Der Waals forces) that bind particles together, and the entire powder body moves as a single solid body. Interestingly, the amplitude of vibration required to break these bonds increases as the particle size goes down. Most sands are typically around 80 to 150 microns in size and flow quite well, but if they get below 40, they become very difficult to break apart.

Check out such other terms as vibro-fluidization, vibro-compaction, rheology, entrainment, acoustically enhanced fluidization, and Geldart types of particles.


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