What is the efficient way to get the grime out of a rim brake track?

For the caked-on stuff that the cloth will not shift, the escalation ladder that works:

• Warm soapy water and a stiff brush first. A lot of what looks permanent is just wet-weather road film and comes off with detergent.
• A green scouring pad, dry, for the black glaze. This is safe on an aluminium braking surface and is what most shops reach for. It takes seconds and leaves the track visibly bright.
• Fine abrasive only if there is a real ridge of built-up material. Rare, and if you are doing this often something else is wrong.

Never use a scouring pad or any abrasive on a carbon rim — the braking surface there is a resin layer and you will destroy it. That is the one hard rule in this whole job.

The trick that makes it fast is to use the brake pads as the tool.

Fold a rag or a piece of kitchen paper, dampen it lightly, slide it between the pad and the rim, squeeze the lever gently and spin the wheel. The pad presses the cloth into the braking surface with even pressure all the way round, including into the grooves, and the wheel does the work.

A few rotations, turn the cloth to a clean part, repeat. Both sides at once because there are two pads. This takes under a minute per wheel and gets most of the deposit.

It also solves your solvent constraint neatly. The liquid is on the cloth rather than on the wheel, so nothing runs down into the hub or onto the tyre sidewall.

Worth checking the pads at the same time, because half of the "dirty rim" complaints I see are actually contaminated pads.

Pads pick up grit and small metal fragments that then embed in the rubber. Once that happens the pad becomes an abrasive tool and every stop drags those particles down the braking surface — you get a squeal, a groove worn into the rim, and a track that gets dirty again immediately.

So: pick the pads out with a sharp point, then dress the surface flat with sandpaper on a hard block. Doing that at the same time as the rim is the difference between a clean rim next week and a dirty one by Tuesday.

And check rim wear while you are there. Most rims have a wear indicator — a groove or a dimple — and a rim worn thin enough can fail suddenly under braking.

One preventative that costs nothing: fit mudguards if your bike will take them.

Most of what ends up on a brake track is road spray thrown up by your own front wheel. A front mudguard with a decent flap cuts that dramatically, and the difference in how often you need to do any of the above is large enough to notice within a fortnight of wet riding.