I've been thinking about and discussing some details of battery charging and I've realized I've never heard one thing addressed: is there some minimum voltage by which the device supplying the power to charge the battery must exceed the voltage of the battery in order for it to charge?

Looking at this from a slightly different viewpoint, if you connect two batteries plus to plus and minus to minus, with one more charged than the other, will the two batteries come to be of identical voltage?

I'm guessing not. To charge a battery you have to push or pull electrons. Voltage is the electrical analog of a pushing force. That tells me one battery would have to have a slightly higher voltage than the other, and it would quit charging the second battery when the voltage differential falls below the level at which it could push electrons into the other battery.

Just wondering. Ever hear of this detail at all?