Grey dust all over Apt.

Persistent dust like this (if there are no issues like Muffler asks about) is usually down to problems with airflow I would have thought.

There is dust present in the air, keeping it moving on is what you need to ensure.

OP I assume you don't have any form of solid fuel heating or a system recirculating air?

Wow that is a lot of dust. Nothing compared to our house which has cats, massive dogs, people that wear wellies around the house and soild fuel fires. That said our dust is composed of pet hair, dirt from outside and fine dust from burning coal and wood. All of which is very identifiable. The dirt you have makes me think you exfoliate a lot and have a plague of dust mites both of which I very much doubt. So wtf is that you are brushing up?

Are the walls painted? If so with what? Its almost like you have dusty plaster walls that are creating that or chalk paint that is going back to chalk dust?

First thing I'd do next time you get a sample is to put it on a non combustible surface and put a flame to it. Does it burn and is there a smell from the burning? If it is due to dust mites then I suspect it will burn. Dust from say plasterboard won't do anything.

I'd also take a look at it under a microscope - even a kids one if available.

Also put some vinegar on a sample if its lime based like plasterboard dust it should fizz and bubble a bit.

What I am saying is if you can determine what it is you have a better idea of where to look where it is coming from.

I'd also want an analysis because you are breathing that all the time and I'd want to know it wasn't detrimental to my health.

Do you tumble dry clothes in the apartment? It almost looks like some of the fine dust I get out of the bottom of our dryer/in our utility room.

This dust; it's light, fluffy and forms peaks. It's not trailing like ash would, it's not a dense product of gypsum and isn't a clothing residue/dust.

It's floculating like a celulose would. Celulose is wood/paper and cellulose is often a grey/white material, especially if derived from paper mulch. Celulose burns readily, but treated celulose (with bauxite as a flame suppressant) does not.

Collect a sample and burn a small amount, let it smoulder. Does it have a 'paper-like' acrid aroma?

Yep, thinking the same. Wonder if its coming from the ceiling where the light fittings are. That stuff can blow around if the attic space is overly open or being disturbed.

I'd be intrigued to know what insulation was used in the house when it was refurbed ,

Sealing around light fittings, and possibly around switches / plugs could be a good start ,

I bet you'll find the more you look the More you'll find covered up ,

Do your neighbours have the same problem

I don't think we're fully confident that it's cellulose yet though.

OP, Do you have downlighters in the ceiling? Where does the accumulate the most and in what parts of the app does it not accumulate? Does it collect high-up or only low down? Do you see dust in the air at all?

Try contacting the State Laboratory and explain your situation. They might be willing to help. If they are unwilling ask them if they would just run an IR spectrum. If you post a scan of the result I’ll tell you if it’s cellulose.

Another option is to contact the chemistry department of Trinity or UCC. If you ask them to ID the material they might not be too willing but they might be willing to support a specific request.

I could give you names of commercial labs but a simple one off analysis would cost hundreds and a complete analysis thousands and at the end of it all they still might not be able to tell you what it is.

is it happening in the same places every time/

would a blow door test help find the cause. it would help find other draughts as well so wouldnt be wasted money

Another suggestion OP. Hope you like incense sticks 😀. Have you tried seeing how the air moves in the house. If you light an incense stick and very slowly walk around with it then you will get an idea of any drafts and how the air is moving around the house. Tracing the air movements back to their source my reveal something? Also pick the worst room for this dust and light half a dozen incense sticks and put them all over, then site down relax and watch how the smoke moves around.