The Puzzle of the Beads in a Box

Years ago it was shown that if one puts a collection of different sized beads into a container, and the container is shaken or rotated, something unexpected happens.

Most of people (myself included) would think that beads would mix themselves up and the longer they remained in the agitated box, the more completely they’d be mixed. (The second law of thermodynamics – that entropy or disorder always increases – would seem to be in effect here.)

But that’s not what happens. The smaller beads effectively flow underneath the larger beads and you end up with big beads on top and little beads underneath. If you run the simulation in your head, you can sort of see why that happens – the little beads slip into the gaps created by the agitation of the container. Gravity causes this motion to tend downwards.

The reason you apparently violate the “Law of Entropy” is that gravity combined with the agitation is doing work (and putting energy) into the system. It’s always been known to be possible to violate the second law if you pour enough energy into a system so that it becomes ordered.

Beads in a box

But now researchers have found that the simple system of beads in a rotating container can get even more complicated if you put lots of beads in a flat box. Two researchers in Germany have just published their findings:

“Instead of a rotating drum, they confine their mixture of small and large beads to a flat box which they then set rotating at slow speed so inertial effects are minimised. And instead of half filling the box, they almost totally fill it with beads.

You might imagine that the beads would jam, preventing any separation but what actually happens is quite extraordinary. Above some filling threshold, the bead separation flow begins to show a rich pattern of convection.

All this is beautifully filmed and explained in a fluid dynamics video which is well worth looking at (if only to see how scientific publication is changing.)

Rietz and Stannarius say they have been unable to explain these patterns using the known mechanisms of granular convection. So they’re left with a puzzle: how do these patterns emerge?”

Read the full article here.

This is what I love so much about physics. Just when you think you have a handle on what’s going on, someone looks a bit more closely at the system and things get wildly confusing.

Here you have a simple system that is apparently giving rise to highly organized behavior – with less work being done on it than the previously investigated. How does this happen?

When someone tells you that science can explain the world you see around you, don’t just accept their words on faith. Because it doesn’t. It explains relatively simple systems that are mathematically easily solved. Then it extends that simplistic solution to reality.

But as this report above demonstrates – simple systems don’t always scale to more complicated systems – much less to the chaotic, non-linear experience that we call “Reality”.

Author: Nick Knisely

Episcopal bishop, dad, astronomer, erstwhile dancer...

3 thoughts on “The Puzzle of the Beads in a Box”

  1. I remember when I taught high school physics, the looks I got from teenagers when that they had to envision an ideal situation. (no friction, no wind, no outside forces.) Didn’t seem like reality at all to them. Makes our idea of what is a hard science seem a little fuzzy around the edges…

  2. There is one case in which this occurs in nature: farmers fields in New England yield a new crop of rocks every spring. Apparetly the freeze/thaw cycles create enough motion to move the large rocks to the surface. This is where the New England stone wall comes from. The farmers have to clear their fields every spring before they can plant, and the wall provides a convenient place to put them.
    Regarding your final comment, there is a quote I heard a long time ago for which I have never been able to find an attribution: A scientific theory is a set of simplifying assumptions which make the problem solvable.

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