An electrostatic generator can be made by collecting charge from water droplets. To explain the operation of this device it is worthwhile considering the how charge can be collected using the more simple arrangement of a positively charged object brought close the tip dripping water tap as shown in Figure 3.
Figure 3. Induction Charging Water Drops
Overall water is electrically netural but there are a small fractions of the molecules, (the number comes from the pH of the liquid) which form ions and carry either a positive or negative charge. In the presence of a positively charged object, the negative ions in the water are attacted to the positive charge which the positive ions in the water are repelled. When a drop falls, the negative charge is isolated and the drop becomes negatively charged. The charge can be collected by catching the water in a metal container. The inside of the container becomes netural and the negative charge accumulates on the outside of the container.
An initial imbalance in charge caused through the ions in the water causes the first initial drop to become very slightly positively or negatively charged. The small charge difference is enough to start the charging process. Let us say for the sake of argument, that the first drop falling into the bucket C is positively charged. The positive charge causes the ring B to become slightly positively charged which creates attracts negative ions from the water. This cause drops falling from the second tap to become negative. The negative charge stored in D also causes the metal ring A to become negatively charged which attracts positive ions from the dripping tap.
Thus the water is separated into two streams of positive and negatively charge drops and as water is collected in the buckets the charge on each of the buckets increases and reinforces the charge on the rings. The charge on the buckets builds up until it is great enough to cause a breakdown in the field across the spark gap at E or if the distance is too great between the spark gap, coronal discharge from sharp edges causes the charge to leak into the air.
I have built a Kelvin water dropper from Lego and various bits of junk. It has not been as easy to make work as you might expect.
Where does the energy come from to make the electricity? In order to raise water to the height of the nozzels work must be done and this takes the kinetic energy of the falling drops and slowing them down.