Not knowing the answer to your question, I decided to do some research. A great number of glues say they will not work on polyethylene. I only found one that said it would; a 3M spray adhesive. But your application doesn't sound right for a spray adhesive.
Some people say they have had success with hot melt glue. I tried it once and it didn't work; but YMMV.
Cori popped their head over the parapet saw what was going on and said
May not be relevant but:- You can find worldwide very expensive LOCTITE glue (Loctite 406,20g), and its primer (Loctite 770,10g) for soft plastics (polyethelyne).
Always wondered is polythene and polyethelyne the same thing.
More like least-worst, as in nothing is really good.
I have experienced the "hot melt" glues including/and the glues used in glue guns to have some (but short of full) ability to stick to polyethylene and the similar polypropylene.
Epoxy sometimes has ability to stick to (and with much less than normal full ability) to polyethylene, and I suspect only that good to some grades of polyethylene - there are different grades of polyethylene.
Please consider similarity of polyethylene to the similar (but even less gluable) polytetrafluoroethylene, AKA PTFE, aka "Teflon" (I believe a trademark of one of the more major manufacturers thereof) - famously "no-stick"!
3M 5200 MIGHT work. Worth a try. Available from any store that carrys marine/boating supplies. If that doesn't do it, I think you will need to find someone who does plastic fabrication and welding.
Yes it can be glued with difficulty. A PHD student I lodged with at Uni had to make chemical preparation apparatus out of polythene due to the strange chemicals he was working with (?). Problem with polythene is it is "oily" and most glues won't stick.
He assembled is apparatus either by friction welding, rotate one piece in fast and force onto other piece
or hot air gun and plastic rod
or finally etching surface with chromic acid (nasty stuff) to produce a "crust" which can then be glued.
It can, but you need to flame flash the surface first by passing the flame from something like a propane torch over it briefly. Flashing is a method of surface preparation for many low surface energy plastics, such as polypropylene or polyethylene.
Surface energy defines the ability of adhesives to wet plastic surfaces and allow adhesion. Surface wetting refers to how well a liquid flows and intimately covers a surface.
Maximum adhesion develops when the adhesive thoroughly wets the surface to be bonded. The better the wetting the better the surface contact and the greater the attractive force between the adhesive and the plastic surface.
Surfaces with low surface energy are more difficult to bond because conventional adhesives cannot wet them resulting in minimal contact with the plastic surface and unsatisfactory bonds.
If you put a drop of water on polyethylene it beads, if you put it on the same surface after flame flashing it will spread. Once flashed even cyanoacrylate (Superglue) will work successfully on polyethylene.
My friend, who is no longer with us, owned a shop in the Long Beach (CA) Marina that installed polyethylene water and gas tanks in boats and RVs. He would buy the PE tanks in all different sizes and the PE spouts also in different sizes. Because of different applications the tanks were manufactured with no holes and the spouts were of all different sizes.
How to "glue" the spout to the tank ??? Well, he would cut a hole in the tank of the appropriate size in the proper location. He would then take the proper spout which had a flat flange on it and place it in his 3/8" drill (with an adapter that he had made). He would then place the flat surface of the spout flange against the tank directly over the previously drilled hole. He would then turn on the drill. The friction of the spout flange against the tank would heat up and melt both the tank and spout ... thus "welding" the spout to the tank. This took quite a bit of skill but he was real good at it.
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