What can I use to get rid of rust patches on a bike frame? Can I just use model paint over the rust to hide it?

It depends on how obsessive you want to get and also the type of rust.

Red rust (Fe2O3) is relatively easy to remove either with chemical or mechanical means, or reverse electrolysis (Electrolytic Rust Removal aka Magic). The electrolysis method works like magic especially on heavy rust.

Black rust (Fe3O4) is harder and also more difficult to remove. Rust also tends to cause pitting of the metal (formation of small pits on the surface) which can be difficult to get into. I use a special stainless steel Dremel brush which is soft enough not to harm the base metal but hard enough to remove the Fe3O4. This works well but you need a lot of patience.

Here is the brush in question:


... along with a low temperature silver brazing rod.

The worst case of rust I had to deal with was a bottom bracket on an old Hobbs of Barbican frame (tip: if a frame is this rusty it's best to avoid it!). I used reverse electrolysis with a sodium hydroxide solution, then the Dremel. Finally I filled the pits in with low temperature silver braze. It took a full month of weekends.

The result:



The yellow patches are the silver. I also had to braze in a new chainstay bridge (stainless steel tube). Altogether a lot of work and it still has to be electroplated.

Buy Evaporust from auto store. Soak some paper towels in it. Wrap the paper towels around the frame and make sure it is touching the frame(no air bubbles) where the rust is. Cover the frame with a trashbag to keep the paper towel from drying out.
Let it sit there for 2-10 hours depending on the rust. Rinse with water and dry. It should remove rust, grease, dirt, etc. If its really deep rust, you can unwrap it and rub the spot with a towel after 5ish hours to remove some of it and let the rest come off easier then.

Use nail polish or an auto paint pen(auto store) to match the color and to get small spots. Paint pens work great for small chips. You need to remove the rust before painting. If you paint over rust, the paint wont adhere permanantly and the problem will just continue.

The evaporust can be reused over and over.

For rust removal in spots, I use Naval Jelly. Just don't leave on too long! It'll stay on spots so it's easy to apply. Also easy to remove and clean afterwards.

oxalic acid (Barkeepers friend, wood bleach), vinegar, lemon juice, molasses, phosphoric acid (Naval jelly), evaporust are all chelating agents and all work.

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Google, rust treatment and removal has been covered in depth at least 500 to 600 times.

Very clever idea! *I've soaked parts in Evaporust & it works great, but never thought of your technique to remove rust from a spot on the frame. *In my experience, Evaporust does lose it's effectiveness after multiple reuses.*

Yeah, you can actually wrap a whole frame and fork and use only 6 or 7 ounces of evaporust. Just wrap that paper towels in a spiral fashion and cut a handful up into thinner strips to attach where tubes meet in the corners. Throw the frame into a couple trash bags and leave it.
I did this for a frame that was really scratched- just dozens of chips and whatnot that were bare metal deep and had been left out in the elements. The rust wasn't deep, but it was all over the frame.