Particle Size Variation...Less Is Better

I was thinking about how particle size variation will affect the "distribution" property of particles in the panel.  If you look at the video right at the end you will see that some of the particles become bunched up at the top of the panel.  From the bottom to the top there is a distribution in the density of the particles in the channel.  At the bottom the density is very high and this drops off near the top.  Why is this?

To answer this, let me first explain why the particles spread out in the first place and don't all bunch up at the top.  When water enters the bottom of the panel it can take a multitude of paths corresponding to the vertical channels.  Lets assume that one channel has particles blocking the top filter, while another channel does not.  In this case, the resistance to flow for the blocked channel will be higher, and consequently more flow will go to the unblocked channel.  This will cause the particles to rise in the unblocked channel (the flow is strong) and fall in the blocked channel (the flow is weak).  After some time the flow will slow to a point where it exactly matches the sink rate of the particles.  Why?  Because if the flow was strong the particles would block the filter, causing the flow to decrease and the particles would fall.  If the particles sank they would unblock the filter causing the flow to increase and the particles to rise.  As you can see, the only stable flow rate is one that matches the sink rate of the particles, and the particles will find this flow rate if there is a sufficient number of them.

This is the story for a mixture of particles with no variance in size.  However, it is not practical nor possible to obtain a collection of particles with zero variance in size.  The result is that the distribution of particles will be higher in the bottom of the panel and lower at the top, as you can see in the video.

The small particles feel a greater flow-force (relative to gravity) and are pushed to the top of the panel, where they stop against the panel and restrict the flow of the channel.  The larger particles feel less of a flow (again, relative to gravity), and remain closer the bottom.

To achieve a perfectly uniform mixture of particles throughout the panel we would then need all the particles to be exactly the same size.  This is obviously not going to happen.  However, it does point to an area of optimization: the smaller the variance in the particle sizes the better. 

The interested reader is encouraged to read about drag force on Wikipedia.