I came across a question a while back. It stated that a oil droplet was suspended vertically within an electric field. The man who suspended it had left to eat a very LONG lunch, and came back to see that it was splattered on the top plate (nothing with the setup had changed), and the question asked us to state a physical reason for such an event. I thought it was because of a transfer of momentum from electrons moving from the negative plate on the bottom to the positive plate on top, which just so happened to collide with the oil droplet. Someone else answered saying that the droplet evaporated slightly, which caused it's mass to decrease and so the force acting upon it managed to accelerate it more than that of gravity, causing it to move upwards slowly. That was the correct solution, but I'm just a bit confused, since wouldn't it lose some charge when it evaporates as well? So overall the q/m ratio would still be the same? They said it was unlikely that it evaporated some of its charge, so I'm just wondering how the charge within an object is distributed. Is it distributed evenly throughout, or is it more concentrated in some areas?
You have to consider Gauss's law which says that the electric flux out of any closed surface is proportional to the charge enclosed by the surface regardless of the charge distribution.
Without more information, it sounds like in this case it is implied that volatility of the oil is sufficient to overcome any effect of the electric field or charge. As such, if the oil drop is able to expel molecules of oil, then those molecules would likely carry neutral charge.
Millikan used a similar set up in his oil drop experiment to determine the charge of the electron. His experiment was very sensitive to the mass of the oil which made him choose one with a low vapor pressure in order pass through the vacuum with minimal loss of mass due to evaporation.