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I am working on an outdoor LED lighting project where I'm making my own rope lights to hold up to the elements. I am using waterproof LED strips which are surrounded in a plastic "jelly-like" material and I am enclosing them in clear, plastic tubing. This means that I intend to slide the LED strips inside the plastic tubing and it's a slow go because I'm getting plastic-on-plastic rubbing. To put this in context, the strips are 6 feet long and about 3/8" wide and I'm putting them in tubing with a 1/2" inner diameter.

So, I think I need some sort of lubricant to make sliding them in easier but I also need it to not leave a residue so that it won't interfere with the clarity of the tubing and wont affect the electronics of the LED strips. Any suggestions?

Polydimethylsiloxane meets almost all your requirements. PDMS is non-conductive, optically clear, inert, non toxic, non flammable, and extremely slippery. It's typically an ingredient in silicone oil, but you can probably buy it separately somewhere too.

Other than PDMS, mineral oil would also work. Much easier to get too.

There will definitely be reside, if you want to call it that though. Neither substance will evaporate, so it's going to be there forever. On the other hand, that property will help you disassemble them if you need to repair it in the future.

Maybe just use as little as possible? Probably just on the contact surfaces.

Perhaps: Wrap them in paper or cloth, insert, pull paper or cloth out while holding the lights in place. Cloth might be less prone to rip and leave a chunk inside the tube, but you have a fair amount of clearance so paper might work if you are careful and use sturdy paper. Perhaps drywall tape, thinking about fairly sturdy paper in long strips?

Or, since the lights are waterproof, use some distilled water - not the greatest lubricant, but no residue once you dry it out, and not incompatible with the materials.

Might try a vacuum cleaner to "suck" the strips into place - the air passing though the tube might help move things along, wiggling the strip to break the plastic-to-plastic contact as it rushes through.

Try doing it horizontally, with the LEDs facing up. Generally in that type, the waterproofing is a "half-dome" arrangement. The flat bottom has no or little plastic. This seems almost silly, as the troublesome plastic is waterproofing.

The other option is to use non-waterproofed LED strips where the LEDs are directly exposed to the elements. Then, do a super good job of sealing the tubes, and call it "done". For bonus points, inject inert nitrogen or other canned gas into the tube before the final seal, to displace (humid) air and prevent condensation.

I've used ordinary laundry detergent, the liquid form, to pull wiring through small diameter plastic conduit. You can easily test the viability of this answer by applying a dilute solution to the tubing and to the LED strip. You should notice a reduction in friction while pushing the strip into the tubing, first without soapy solution, then with the solution applied.

Having a pull line will make things easier, especially if you have four or more hands. All four hands need not be on one body, of course. One person pulls, the other pushes (always helps!) while yet another applies continuous soap solution at the entry point.

The soap will not leave much residue and should not affect the illumination overmuch. If it is critical to remove the soap, a hose will slosh through the tubing once the LEDs are in place.