I think I need some womanly help here; re: hair problem

I have a little problem here with hair, though it's probably not what you think... my hair is pretty long and a few get pulled out here and there, and they get wrapped and jammed up around the wheels of my desk chair. It's to the point now where the chair scoots instead of rolls. I really love this chair and I can't get the wheels off their axles without breaking them, so I thought there might be a chimical solution. I'm wondering if any of your basic household cleaning supplies, or other chemicles would be able to disolve the hair if the wheels were soaked in it... Any suggestions?

Thanks!