I think I understand it now. Take a droplet of black polymer goop and put it in oil. Turn on an electric field. If the field is strong enough, the droplet will start to spin!
Here's why. Though the oil doesn't conduct electricity well, a few electrons will move through the oil, pushed by the electric field. They'll land on top of the droplet and stick there - because we've chosen a kind of goop that's *very* hard for electrons to move through.
More electrons will land on one side than the other, by chance. The electric field will keep pushing them down, so they will start to turn the droplet. When they reach the bottom of the droplet, some will fall off and continue moving through the oil. And this process will continue, making the droplet turn faster and faster.
This effect is called Quincke rotation. This theory of why it works is called the Taylor-Melcher model.
@nickzoicnick helped me think of a nice analogy. Suppose you have a waterwheel in a torrential rain. If a bit more rain lands on one side than another, it will start to turn the waterwheel. And once the wheel starts turning, the rain can make it turn faster!
Hmm, I'm still confused by why the droplet spins faster and faster. If we imagine electrons coming down from above, we need more electrons to stick to the side of the droplet that's moving down. Why does that happen? I guess I should learn more about the Taylor-Melcher model.
https://www.youtube.com/watch?v=Z6rGIfDujdI