So for the normal folks who checked out with the math I just showed that porosity is not a function of grain size for cubic packing. It can be shown that this is also true for the other ordered packing lattices. However, it is not true for the random arrangement of spheres. Grains making up substrates in the bonsai pot are not arranged in ordered packings because they are energetically unstable, and the grains are randomly distributed.

For RANDOMLY packed grain, the porosity is controlled by the frictional and cohesive forces operating between the grains. For these kind of systems, porosity is a function of the grain surface area.

But here's the wierd thing - relative to the grain size, surface area is large for small grains and small for large grains.

So, all other factors are equal, a given weight of coarse grains will be stabilized at a lower porosity than the same weight of finer grains.

Say what? That's right - randomly packed coarse grains will have a lower porosity than randomly packed small grains. Here is the data for randomly packed angular vs rounded grains. See the porosity decreases as grain size increases toward some theoretical limit.

Now the effect gets smaller and smaller as the grain size grows - and these are pretty fine grains. An 1/8th of an inch is about 3000 microns. So this is a little theoretical. But interesting nonetheless.

Scott