The box fan's CFM is probably a good order of magnitude higher than most commercial purifiers, meaning in theory it should move more air through the filter, the

The box fan's CFM is probably a good order of magnitude higher than most commercial purifiers, meaning in theory it should move more air through the filter, thereby cleaning the room faster. That said, it probably doesn't provide much vacuum/head, so the air that gets drawn through it probably doesn't change much with tape, although I'm guessing the energy draw goes down... So two comments for DIY air filters, put fiberglass or similar prefilter over the hepa filters, and/or add more filters instead of tape around the fan. Even if they aren't hepa they will catch stuff.