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I don’t know if this is correct, but when I did the same job I silver taped anywhere I thought air may get in. I didn’t seal the whole area with dpm as I was worried about the ceiling below getting damp as it wouldn’t wick. As I say I don’t know if that was right, but it was warmer and the ceiling didn’t go mouldy.
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If you're concerned about airtightness and moisture, use a vapour-permeable airtightness membrane. There are many expensive ones out there; I used a much cheaper one called 'Barri-Air'.
Foil tape will initially work, but the adhesive will fail relatively quickly, after which it'll be doing nothing. Ideally you'd use an airtightness tape; these use adhesives designed to last. Any taping needs to be pressed down whilst applying with a card spatula tool to activate the adhesive.
My first floor office floor is cold, it sits partially above an unheated entrance hall. Haven’t carpeted that room yet so I’m going to lift the boards and insulate underneath.
Should I put some kind of draught proofing membrane in as well? Beneath or above the insulation? Or will rockwool between the joists be sufficient to block the sort of draught I would get anyway? Floor will be carpeted.