Everyone learns about the hydrologic cycle in school. The following image will refresh you, if it's been awhile (or click on the wiki page link).
In the Earth's ecosphere, there is little emphasis on the transport of minerals carried by liquid water flow, because it's literally considered "a drop in the ocean". But in a CELSS, soil minerals leach out and end up in the water reservoir sumps, building up as water is evaporated back into the atmosphere. Not only does this brine sink have to be planned for, the "sea" might be a useful part of the ecosystem for growing algae and shrimp, as a staple food for aquaponics fish.
Soil bed reactors do act as quite sustainable filters to limit both erosion (loss of particulate minerals) and leaching (loss of soluble minerals), with the soil microbiotics and plants doing most of the the biological reintroduction of minerals, but ultimately water flows downhill, carrying some amount of its mineral load with it. At some point you'll need to collect these mineral deposits back out of the sump to reintroduce them into the various biological organisms in the ecosystem. Hence the common membrane filter (as opposed to the Great Filter, which I for one would like to avoid; more on this in a future post).
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In my aquaponics set up (as I imagine it is in most), one of the few manual tasks I have is cleaning pump filters (fish feeding is mostly automated except for occasional table scraps, or entertaining my 5 yr old daughter). I have tried vortex filters, but they are not that effective for the flow rates and space considerations for my small scale operation. So every month or so I have to consecutively turn off each pump, reach down into the turbid water of my sump, pull out the pump, open it up, remove the filter, clean the filter, reassemble, return to sump, switch on, and repeat for the next pump. It's not that frequent, and really not that onerous. With a better setup it might only need to be done twice a year. The filters are foam and normally outlast the pumps, usually because I'm not staying on top of my most frequent manual tasks of topping off the water, which in Denver's dry climate evaporates out of my system at a rate of about 1/3 gal/day. I've not gotten around to automating the refill process yet, mostly because overflow contingency is not existent (no drains), and the system is in my basement.
Anyhow, the filters are essential to my aquaponics system; and were I better at maintaining water level and pump integrity, the filters would eventually need replacing. Hence the common particulate filter.
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So that's two kinds of common filter, but how do you make such a filter? Glad you asked.
Yesterday I ran across this article about filters made of wood. This is a form of membrane filter. Pore size and hydrophylia are what control the size of contaminants excluded. Looking at the method of making these wood filters, I think there are oportunities to make a simplified version without the hydrophobic silane coating that would work as a particulate filter, without necessarily barring solutes. Either way, there is a vacuum freeze drying step. Very much doable if you've been growing some trees in your hab and happen to have an airlock with vacuum outside.
To accomplish the silane coatings you'd need a CVD setup. Which you also might have if you read my last post.