If you push air down, it's going to displace the air below it off to the sides, so I don't think it'll make a big difference. My main concern would be that the

If you push air down, it's going to displace the air below it off to the sides, so I don't think it'll make a big difference. My main concern would be that the filters limit flow, and thus it might be more likely to pull air up, causing a tight vertical loop (air goes down, turns outwards, and then back up while still inside the filter ring). I don't really have a solid mental model of how air flow works, though. Some experimenting with the shape (and some colored smoke, perhaps) could be interesting. What if the filters tilted inwards to be slightly narrower than the fan's reach? Or if they were shorter than the ceiling-to-fan distance and just inside? Or does it help to put them further out? (Seems unlikely, but would be a good thing to test.)