Review
https://www.cleanairkits.com/products/luggables is basically one side of a Corsi-Rosenthal box, takes up very little floor space if placed by a wall, and is quiet, affordable, and effective.
That works well enough, but a Vital 200S currently costs $160 at amazon, less than the cheapest variant of the thing you linked, and has a slightly higher max air delivery rate, some granular carbon in the filter, and features like power buttons. The Vital 200S on speed 2 has similar power usage and slightly less noise, but less airflow, but a carbon layer always reduces airflow. It doesn't have a rear intake so it can be placed against a wall. It also has a washable prefilter.
Compared to what you linked, the design in this post has 3 filters instead of 2, some noise blocking, and a single large fan instead of multiple fans. Effective floor area usage should be slightly less, but of course it has to go together with shelving for that.
Let's consider air purifier design a bit.
This post is about a potential new category of air purifier, but existing air purifiers are already worth using. You should probably have at least one at your home. For larger rooms, the Levoit Vital 200S-P is a reasonable option; that's an Amazon affiliate link. See also: /r/AirPurifiers and review sites such as HouseFresh.
Someone once told me that they didn't want an air purifier because it would make their incense and scented candles ineffective. I'm afraid I can't help with that issue.
What do we want from an air purifier?
We want a quiet and efficient fan. For that:
We also want a quiet motor:
You might think that fans meeting those criteria should be easy to find. People buy a lot of fans, and surely some people want quiet ones that aren't too expensive, right? But no. There are lots of floor fans, but compared to computer fans they're almost all poorly-designed, even the expensive ones. Maybe people actually want some noise so it feels like the fan is working?
We want standardized filters that are easy to replace. They should be either cylindrical or (preferably) rectangular.
To get a long time between replacement and low pressure, we want a large filter area.
If we're using carbon filters, granular carbon is more effective than carbon foam.
Washable fabric pre-filters seem worthwhile.
Some goals for the overall configuration:
For these reasons, air purifiers are often circular or box-shaped, sit on the floor, and have upward exhaust. In some cases, people want an exhaust that points directly at them, from the side.
We want the air purifier to not take up much floor space. This is a factor that hasn't been considered very much, but it's important. Consider a "Corsi-Rosenthal Box" using 24" (actual width) furnace filters. It obviously takes up at least 4 square feet of floor space, which in America today is often worth over $600, significantly more than the purchase cost. If you include clearance around it for airflow, in an expensive area that could use over $4000 worth of space.
Obviously, we could minimize wasted space by putting a filter in the bottom of a shelf unit, or on top of a cabinet. But per the above, that would give air recirculation or wouldn't capture dust near the floor well.
Considering the above goals, I had an idea: what if an air filter is integrated with a shelving unit, with a chimney through it for filtered air? That could significantly reduce the effective amount of space used by an air purifier.
Let's consider what that could be like. I guess this can be an example of how much detail my conceptual designs usually have.
I think the design could be broken into 3 parts: a base with filters, shelving, and a tube with a fan.
Make a triangular prism frame, with each rectangular face being 22" by 22". Glue 12 foam strips to it, to act as gaskets.
Get 3x 20"x20" air filters. Put them against the square faces of the frame.
Get a sheet of stretchy fabric, which wraps around the air filters and fastens somehow, maybe with snap fasteners or hooks. This fabric can hold the filters against the foam gaskets.
Put a solid triangular top and bottom on the prism frame. In the top, cut a 12" circular hole.
On 2 sides of the triangular top, add some handles to make the base easier to pull.
Take a normal shelving unit, with:
Cut a 12" hole in the shelves for the tube to go through, in the middle rear.
The top shelf should have a plastic "protrusion holder" assembly that the 3 tube protrusions (see below) can rest on. This acts to hold the tube up during filter replacement, and keeps the tube from hitting the shelves and making noise.
This shelving goes over the base.
Get a cylindrical tube, 12" outer diameter and perhaps 48" long. It might be metal or plastic, but I suppose the cheapest option would probably be cardboard.
Put a single large electric fan at the bottom of the tube. It should have swept blades with good airfoils, inside a duct with minimal clearance to the blades.
Put the tube through the holes in the shelves. The tube fits into the hole in the base, and sticks out a couple inches from the top shelf to prevent stuff from falling in.
A small hole in the tube has a USB port to connect a fan controller. Connect that to a controller on the middle of the bottom shelf. A cable inside the tube connects that port to the fan.
The fan power cord comes out the side of the fan, and normally sits on top of the triangular top of the base. Since we're trying to improve air quality, the cord should use EVA, not PVC.
Above the fan, glue a ridged foam sheet to the inside of part of the tube, to absorb some fan noise.
The top of the tube and the top shelf should have 3 protrusions that can sit on each other to temporarily hold the tube out of the base when the tube is lifted and rotated. One option would be to glue 3 steel plates with threaded holes to the inside of the tube, and use internal hex bolts as the protrusions. (Those protrusions need to be attached to the tube after putting the tube in the shelf, because the power cord is on the other end, and the fan might be wider than the tube. And you don't want to put the power cord through the bottom, because then you'd have to unplug the power cord to pull the base out to replace the filters.)
Lift the tube up, and rotate it so it sits higher on the top shelf protrusion holder.
Remove any items under the bottom shelf.
Pull the filter base out using the 2 handles.
Remove the fabric fasteners.
Clean the fabric prefilter.
Replace the 3 air filters.
Assemble the shelving frame, and put it in place.
Put the tube on the floor inside the shelving frame, and plug it in.
For each shelf: attach 4 brackets to the frame, then slide the shelf over the tube to rest on the brackets. (The brackets might have rods with an interrupted thread for attachment to the frame.)
At the top of the tube, attach the 3 protrusion bolts. Lift the tube up (the protrusions fit through slots in the top shelf) and set it down on the protrusion holder.
Assemble the base frame.
Insert the 3 filters, and wrap them with the fabric prefilter.
Slide the base under the bottom shelf.
Rotate and lower the tube into the base, fitting the protrusion bolts into slots in the protrusion holder.
The advantage of a Corsi-Rosenthal Box is largely its option value. It substitutes labor and tape or hot glue for structures that have to be manufactured beforehand and kept in warehouses. This is important when demand suddenly increases due to, say, a pandemic or wildfire.
A frame with foam gaskets makes filter replacement easier than gluing filters together, but we still have to ask whether that's worthwhile. With thicker filters, eg 20x20x4" ones, the above design should normally need filter replacement less than once a year.
There are also compact commercial air purifiers. Something with a tall cylindrical filter could be as small as just the "tube" - compared to that, we're trading movability and modularity for using standard rectangular filters that are cheaper and last longer and can optionally have a granular carbon layer or just be extra-thick. But someone concerned about the value of space might not care much about filter costs.
Shelving with an integrated air filter might just be too specialized and inflexible a product for people, but it would be quieter, because the tube (and its foam lining) would absorb some sound and direct sound upwards.