I'm doing research into portable power generators for a university class and need help understanding how charging a device works. From my research, I've found certain methods of harvesting energy can yield an output of about .5mW of electricity. If you were to try to charge a device with this output, what would happen? For examples sake, lets say we were trying to charge my phone's battery. The battery is a 3200mAh, 3.8 V Li-Ion battery, and the default charger is a 5.3V, 2A charger.
On such a device, how does the amount of wattage being inputted affect charging? Is there a minimum amount of watts needed before the device will charge at all? What do the battery and charger voltage requirements mean?