I see no information about AC, thus I assume it is DC only.
--> there is no DC current flow through a capacitor. Zero.
Btw: on an ideal capacitor no (zero) electrons go "through" a capacitor ...in the meaning of "passing the dielectric".
But the same ammount of electrons that go "into one pin" of the capacitor will go out at the other pin of the capacitor.
Thus it looks like the electrons go through the capacitor.
The current source changes its own voltage to whatever amount pulls its spec current through the circuit. Initially it may be low amplitude. However I think eventually it goes to infinite voltage since there only seems to be continual charging of capacitors C1 C3, and no discharge cycle.