I also have an unfinished basement that I'm working on sealing. Generally the dust comes from the unsealed concrete. Assuming your unfinished basement actually has concrete walls and floor, you can do the same to prevent the dust in the first place. They sell concrete sealer at hardware stores and you can have them color it to your liking as well. Just need to wash the floor and walls first, then paint it with a couple coats depending on the brand of paint. Aside from that, if you don't want to seal the basement, you'll just want to create a walled off area using sheets or plastic or similar that will prevent dust from getting into the area and then using an air purifier like you mentioned. This is really only good as a temporary solution, but it could work fine for a quick fix while you figure out your basement situation.
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Yes, I do have bare concrete walls and floor. That's crazy, I never would've thought they "shed" dust or anything.
For a haunted house a few years ago we put painters tarp on the unfinished walls so they're somewhat partitioned, but not air tight or anything (or I guess "dust tight") but depending on how it works I could easily seal off one of the rooms since it is already pretty sealed. Would I need to cover the floor and walls as well?
I would wash the floors and walls to get rid of any dust that is present. Then I would make a room out of plastic sheets. Finally, I would put use a 20" box fan with a 20" furnace filter taped to it to clear the air of dust.
Thanks for the advice!
I have a pretty powerful 'exhaust fan' that I repurposed exactly this way and.it works way better than my previous box fan did. As in, after kicking up dust with my table saw the airborne dust is clered in less than 10 minutes. Of course, there's still dust on the surfaces.
I built a box around the fan, and I have it suck air through a coconut choir filter, then a allergy ac filter. I put a removable frame around the filter to block air from going around and let me change it, but other than vacuuming the front I've not had to do anything to the filter. It is kind of loud, but I put a dimmer on the power cord and I can turn it down. I generally use it while/after I make a lot of dust, and I have a timer turn it on at night when no one is around to hear the noise.
If your floorboards are visible in the ceiling you'll want to put up some drywall or something on the ceiling, every time someone walks on the floor above, some dust will get knocked loose and fall from the ceiling. You could put up some drop cloths as well for a quicker, less permanent solution.