If you simply tape up the plastic it will fall down. It will not matter whether you use painters plastic or heavier weight stuff. Dust walls are important, more important than that is they stay up. A leak or rip in the wrong place will still let the room get clouded with dust.
I build my dust wall with 4 mil poly and 2X4s. In areas of finished floors I use poly on the floor for spills and 1/4" plywood seamed with duct tape for durability, from dropping framing material and such. If I am using plywood protection, I build the 2X wall on the edge of the plywood. To save a lot of explanation, here is a sketch.
I have added a few pics of my last job where I built this type of dust wall, the pics were to highlight details behind the drywall after it was covered, not to highlight the dust wall, although the details show a little of the idea I am trying to get across.
To evacuate the dust I plan ahead where I can set up a box fan that runs full time while demo is going on.
This fan went in where a new window was going in, it stayed after the window was set to get the drywall dust out while sanding.
For the entrance, I do not like the zippered openings that cut into the plastic, at points in time the traffic will be heavy in and out of this space, I have tripped many times going through the zippered opening. In time I have ripped it and had dust coming out, dusting the floor, Try taping over this area again, or any area once a seal has failed. If the though is being more careful, it is easy to say, but try being careful with a large heavy item in your hands walking backwards bring in a load of materials, it only takes one time. To get past this I use a double flap of poly 4' wide at the other end of the room from the fan so the air is always drawn in through the flap door into the work space. There is a walk area outside to protect when a person steps out to keep the trash coming off the shoes. This must be strictly maintained or a trail will end up going through the house.
Concrete dust becomes air-bourn when it is pulverized (due to tool use: drilling, sawing, hammering, etc.). The fine silt concrete dust is thrown into the surrounding air by electric tool motor fans or other air currents. The particulate is so small and light-weight any slight breeze will distribute it until it finally sinks and lands on a surface.
Where, when, and how long will depend on too many extenuating circumstances to even guess at. The best way to deal with any dust becoming air-born is to stop it before it happens. I've found a shop-vac held just above the concrete surface that is being worked on does a smashing right good job at eliminating dust.
Best Answer
Cover entire top of wardrobe with king sized bed sheet. Lay it down gently across the top, right on the dust. Don't stir it up.
Scoot edges in along the top of wardrobe, pushing dust in front of them. Dust pushed into the air will remain trapped under the sheet.
When you have pushed edges in to center, dust will be inside sheet. Gather edges in the middle of the wardrobe and take sheet (now bag) outside to shake dust out.
Bring sheet back in and use it to wipe off residual dust. Take back outside to shake.
Bring sheet back in and use furniture polish and sheet to clean wardrobe top.
would it be too much to ask that you post a picture of the dust? Prurient interest, perhaps, but I want to see dust that thick.