I've been a big proponent of box fan air purifier cubes, but they are bulky and fragile. If your ceiling is 8ft+, elevating them is an attractive option:

I made two of these for my dad's house this afternoon. The goal is for them to be out-of-the-way, and easy to turn on any time he has visitors.

The only heavy part is the box fan, since the rest of the cube is filters and tape, so the goal is to make sure the fan is well supported and not going to tip over. I used an angle bracket and a short length of wood to make a shelf under each fan, and then taped the fan to the shelf and wall. The filters are also taped to the wall. When taking them down I'll probably need to use a small amount of spackle for the holes, and touch up the paint if the tape takes some paint off, which it probably will. If I wanted to avoid having to tape anything to the wall I could have used two angle-bracket shelves each.

With an 8' ceiling you would want to have the cube flush against the ceiling, which gets you a tight-but-probably-ok 6'3" of clearance and three sides for filters. If your ceiling is taller, like these ones were, you can have a fourth filter on top while still maintaining reasonable clearance.

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This design looks like it puts a heavy thing over a place where people might pass with a single point of failure. It reminds me of Damocles sword.

Where do you see the single point of failure?

It looks to me like it's connected to the wall only by the white thing below it.

The white thing below it is not the only thing holding it up, since the filters are also taped to the wall, but I agree that if it failed, the whole thing would fall since it's carrying almost all of the weight.

But it's a metal angle bracket good for about 10x what it's carrying, and attached to the wall via multiple screws. It's not going anywhere.

There's smaller filters of the same (or better!) quality made for different types of air-purifying devices.  If headroom is a problem, I wonder if you could use a smaller, more powerful fan and make a longer tunnel type of box to get the same (or better!) CFM of air filtering.

 

elevating them is an attractive option

I'm not sure attractive is the right word there!  (I'm just kidding, I know what you mean.)

The main downside of small powerful fans is they tend to be quite loud.

Yeah, definitely.

I will note that, at least in the fans-for-computers-and-electronics industry you can pay more money and get the same CFM in a smaller AND quieter size.  Motor type/quality and blade design has some sort of effect on this.  Diminishing returns and all that of course.

I don't know if this really applies to the types of fans a person would be using for something like this.