@ Olisny I wish I could tell you exactly how this self enclosed sink is made, but my dad made it for me. I can tell you this is a basic sink basin we got at ikea. The drain goes directly into one five gallon bucket. About a quarter from the way down from that bucket there is a tube that goes into a second bucket. By dad made the tube between the two buckets removable so that I could clean the buckets. In the second bucket is a pump which brings the water back to the faucet. I used an old tupperware and cut some holes in it to rest the pump on so that it did not rest on the bottom. My dad was able to make it so that I could turn on and off the water using the knob on the faucet. He also put an additional knob on the side that I could hit with my hip to turn on and off the faucet. I’m not sure how he did that. Obviously the point is for most heavy sludge so settle to the bottom of the first bucket, for any remaining particles to rest in the bottom of the second bucket, and clean water to be filtered through the faucet.
This is the extent of my knowledge on the construction of this sink. If you have specific questions I can ask my dad maybe. I know that to purchase this manufactured (The “Cink” by Creative Industries) is about $1500. My dad said he put this together with $200-300 worth of parts.