It also appears that there are quite a number of off the shelf versions of similar premise.
Search for "portable shower", "shower in a box" type things and quite few come up. The appear to be fully self contained, but many/most don't use hot water.
What a rabbit hole.
Searching for "portable shower" yielded many results that are just a pump and a heater – no filtering. When I added “recycle” to the search, I got some results listing specific devices. Then I went on to search for the device name and “with soap” and found:
For the EverShower, when asked if you can use soap the reply was: “Yes, although rinsing the pump with fresh water afterwards is recommended. For water-scarce situations, consider skipping soap.”
For the Hotaru, I found this: “The Japanese are really big into LED UV light sterilization of air and water. My guess is that they are filtering the water and then running it through a UV light sterilizer. This could be adequate for rinsing off, but in most cases, will fail if you use soap. In a camping situation, this is still better than no ability to clean yourself at all.”
For the Showerloop, they say: “With Showerloop but it’s still better to let soapy water go down the drain for the longevity of the filter. Our goal is to find or invent a way to filter out all kinds of soap with 100% reliability but that will require way more time and funding than what is currently available.”
Searching for "shower in a box" did not yield much besides many shower enclosures and one bucket-sized tank with a pump and hose. I then searched for "shower in a box" "recycle" "soap" and nothing came up.
None of these are relevant to the OP’s posting.
Looking into the ARV system, I eventually found this link:
https://www.classbforum.com/forums/f5/shower-water-recycling-12274.html
So this has been discussed here before.
As the video goes on they describe the system as three particulate filters with activated carbon and UV. I do not believe that this system will filter soap out of water. Even if the media in the filters could adsorb and remove soap with adequate efficiency, they would quickly clog up or fail in some other way, with the only potential way to restore them being backflushing with a solution that can remove whatever deposits the soap and everything else causes. But backwashing, even if one could find a solution that worked well, would negate the whole concept the OP proposed. I did not see anything that suggested backwashing on the ARV schematic. I suspect that the ARV people are offering a water-only, no-soap solution to rinsing off and that they just replace the filters periodically rather than backflushing. Putting the following search into google yielded no results: advanced rv "recycle" shower water system "soap"
It seems obvious to me that filtering dirty/soapy water into something that I’d want to reuse would, in the context of a B not hooked up to water, take some combination of too much equipment (weight/volume/cost), too much water to backflush/rinse, and probably too much energy if the other two constraints could be satisfied. If you don't have a shower in your rig, you should probably just use some combination of sponge baths in your rig or finding a campsite/gym/truck stop/hotel room shower, or even a gas station bathroom sponge bath, to get clean.
Maybe the OP should just get a class B with a working shower and then refill/dump like everyone else.
Some people in this thread have written that they have seen other people doing this, or that you can find links to other people doing this. Please provide us with links to actual systems that allow one to recycle (really recycle) soapy water in the way the OP described.
