Indeed sand will grind itself down if it is in motion, but not if stationary. Having used sand only a few times, I have found if you clean it properly the water will be crystal clear from the start. This includes black blasting sand, which is very dirty. When you wash sand, as you swirl it, fines will be stirred back into the grains and held there. That is how a sand filter works. Sharp sand traps small particles in the gaps between the grains. If the sand is dirty going in, it will stay dirty and every time it is stirred up it will release trapped fines. I have one tank of panda corys, with brick sand on the bottom. Brick sand is very fine and you can stir it up and the particles are so fine it takes a while for them to settle, but the water stays clear. Same thing with the coarser blasting sand. Stirring it up does not cause the water to get cloudy, because the fines were removed prior to it being placed into the tank. So, while a filter may remove any suspended particles left by an incomplete cleaning, it will not remove what is trapped in the sand.
In my experience, the only way to get sand really clean is to wash it in small quantities, so you aren't reintroducing the dust back into the grains.
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