That's a good point.Otherwise I'm looking at installing a vaccum cleaner. .
Would you expect the vacuum to clear the dust if you just left it in one position?
Fans are not magic.
You have now said the tiles are so cold.
This would (obviously) indicate that there is not enough heating in the room and so any 'new' warmer air being sucked into the room from warmer rooms may also cause more condensation.