I have a Harbor Breeze 98120 ceiling fan. Is there a variable speed control that will run it very slow? I am doing an experiment and need 6 to 10 rpm. I have some electrical background.

Years ago before we had a lot of fancy ceiling fans to chose from I had an enormous ceiling fan that would almost blow you off your chair as it was so fast. I put a regular light rheostat on it and it would work just fine. The only problem was that the rheostat would make a bunch of noise and it would be hard for me to sleep through it, but it would work just fine and slow the fan down to almost nothing.

6 to 10 rpm will be very difficult. Using the correct value AC capacitor you should be able to drop it down to around 20 rpm. This is much better than using a rheostat/solid state control.

BTW does it have to be this model fan?

I just looked up that model number.. . That's, like, the cheapest ceiling fan you can buy. You'll have MUCH better luck slowing down a fan with a better motor.