If I understand the requirement correctly the kids have come up with the design and you are not asking for advice on how to separate the materials, this kids have done that. You want to implement their idea. And again if I understand correctly the rotating part is like a valve (vane) in the middle of the cylinder, you set the vane vertically pour the mixed materials into the water, the floats float and the sinks sink. You then close the vane and drop the contents, taking out the sinks and leaving the floats. you then open the valve dropping the floats?

What size do you envisage the cylinder being? What size are the particles?.

Right. The kids have designed something that I believe can work. I just don't know how to help them with the automated parts of it. People are giving me other ideas (which I appreciate and will share with the kids). The particles are 10 marbles and 10 golf tees. I actually figure they can drain the whole cylinder before removing either set of particles. I figure the cylinder needs to be 5-7" high and 2-3" wide at least. The smaller the footprint, the better. The kids, however, are still going to need room for the center disk. The kids were thinking maybe part of a pringles can, and I figure that could work.

 

The problem I see with things of the size of marbles/golf tees is going to be sealing and operating a large enough valve in the base of the cylinder. I also suspect you will struggle to seal the axle of the vane into the walls of a pringles can.

With a much more rigid can (e.g. a steel food can) you might be able to use electromagnets to hold a steel plate against the bottom of the can which drops off when the electricity is turned off. You can turn the power on/off to the magnets with MOSFETs driven by your Arduino, It may be worth looking at the kind of servo that is used in remote control aeroplanes to turn the vane. Google will find you an example Arduino sketch for driving this type of servo.