Apologies if I am posting in the wrong place. The classic article “Why don’t the raisins in Raisin Bran all wind up at the bottom of the box?” http://www.straightdope.com/classics/a3_090.html was in the email newsletter, and the link there “[Comment on this answer]” brought me here.
I don’t buy the logic of: "First, while a crumb weighs less than a big piece, the crumbs and chunks in aggregate weigh more per unit of volume. That’s because the big pieces have lots of space between them and the crumbs don’t. "
The bulk of crumbs may be more or less dense, but that is because of relative particle shape, not because of relative particle size.
The aggregate weigh per unit of volume or bulk density depends on the packing geometry, which depends primarily on the particle shape, so if the crumbs are somehow fluffy, spiky or hollow in shape when compared to the big pieces, they will have a lower bulk density. If they are solid and more spherical, they will have a higher bulk density. They do, however, seem to wind up at the bottom of the jar, regardless.
Imagine two similar containers each part-filled with same-size polished steel bearing balls, the balls in one container being many times the diameter of those in the other, and the containers having been vibrated to cause the balls to pack down as far as possible. If the balls are small compared to the containers, boundary effects can be ignored. The balls in both containers will settle to the same close pack http://en.wikipedia.org/wiki/Sphere_packing#Sphere_packing with a bulk density of about 74% of the density of the balls, despite there being much bigger spaces between the larger balls. It is about shape, not size.
Concerning “the mechanics of sifting”, one can visualise taking a handful of the tiny balls and dropping them into the container of much larger balls where they would run down through the large gaps to the bottom of the container.
What happens in the opposite case, i.e. taking a large ball and putting it into a vibrated small-ball container is not obvious to me. I think that if the vibration causes behaviour to approximate frictionlessness, the large ball should submerge and sink to the bottom, but that is just by analogy with a solid ball in a less dense fluid. So I am not sure that “big pieces don’t make much headway sinking into the densely packed small stuff”. Comments?
As to the flip reply to the initial question, observation of Raisin Bran in milk shows that the raisins sink whereas the alleged “bran” shows some floating, some neutral buoyancy and some sinking. Having no real evidence at all, I would guess the non-migration of raisins is due more to friction effects than density differences.
, that’s why I said it was not obvious to me.