Cleaning Carbon Black off a Bicycle Brake pads for a rim brake are usually treated with Carbon Black (powered carbon) to make them last longer. This is what makes them black.

When I ride a road bike in hilly areas, the carbon black accumulates on the rim and on areas surrounding the brake pads. Later, if I ride the bike in the rain (without fenders), this powder mixes with dirty water kicked up by the wheels, and spreads around on the frame of the bike, and into gaps on the headset and bottom bracket. If allowed to dry, it becomes extremely difficult to remove.

Right now I remove as much as I can with elbow grease, and then make an abrasive paste out of water and baking soda. The paste works pretty well, but leaves a residue. Further, on some of the really bad stains, it seems to spread out the carbon as much as clean it off. It still needs a lot of rubbing.

Is there a standard cleaner in which carbon black is soluble? Is there a better way to remove it?
Since no answers I will post my comment as an answer  

Car wheel cleaner. It is made to deal with brake dust.  

But I would not user car wheel cleaner on paint.
For hard to clean on paint I use a cleaner wax.