How do capacitors discharge?
Electrons are forced off one of the capacitor’s plates and attracted to the opposite plate through the circuit.
Prior to being discharged the capacitor will have been charged. Electrons will have accumulated on one plate (negative plate) having been forced onto it by the power supply. The other plate (positive) will have a deficiency of electrons as they will have been forced off of it by the supply.
Before discharging the accumulated electrons on the negative plate repel each other but have nowhere to go. The positive plate is unable to exert an influence on the electrons in such a way as to force electrons off of the negative plate because there is a dielectric (insulating) material between the plates.
Discharging will begin once a circuit is connected between the terminals of the capacitor. During discharge electrons on the negative plate will be forced off of the plate by the repulsion of the other electrons on the plate. The positively charged plate will attract electrons from the circuit toward itself. These influences will result in a current flowing between the plates.
Further to the general method of discharge one can also appreciate the exponential decay nature of the current that flows during discharge. Immediately after the circuit is connected there is a maximum amount of accumulated negative charge on the negative plate and max. deficiency of negative charge on positive plate. There are therefore maximum attractive / repulsive electrostatic resultant forces on the electrons in the plates and circuit.
As time progresses the accumulated charge will decrease and the electron deficiency decreases also. Those attractive and repulsive resultant forces decrease. There is also less charge available to move around the circuit. So the current decreases and it does so with an exponential decay.