Andrew R Stewart 

Sounds like a good way to clean the outsides of the chain. But it's the insides that are what wear and what benefit if clean. Strong agitation and a flowing/flushing action of the solvent is what works best IMO. Without added heat or compressed air it likely takes far more then 10 minutes to dry a chain. So when then relubing after the "cleaning" the oil is mixing with still wet inside stuff. No wonder this emulsion weeps out and carries the grime not removed.

One time tested method is to remove the chain, place it in a 20 oz soda bottle half filled with mineral spirits or kerosene, cap and shake, snake out chain with a wire/spoke. Place chain in second bottle with solvent and repeat. Do this two to four times. Let chain drip dry overnight and lube when back on the bike. The grime suspended in the MS/kerosene will settle out and the clean can be largely poured off and reused.

Don't forget the power of transfer. All the teeth and pulley surfaces will also want cleaning (and these are FAR easier done with no chain in the way) or they will dirty the "clean" chain lickity split.

I'll use a cloth rag for when I need a strong wipe. Paper towels otherwise. Paper towels for the initial and dirtiest cleaning at the minimum.

The more often you do clean the chain (and that other stuff) the less grime each time will be trying to flush away.

BTW I never allow water to see my chains (excepting when I'm caught in the rain on a ride). Andy