The Kelvin Generator is a classic physics experiment. The machine is a type of induction generator. A charge imbalance in the system is reinforced as it is running, building and building the charge, until it arcs across the spark gap, to balance itself out.
Here is a link to a youtube video of a lecture from MIT, the Kelvin Generator is explained in detail, the demonstration of the machine happens around 47:28. This webpage has pretty good instructions on making your own waterdrop generator, although the graphics are a little too 1978.