Statistical Analysis of Droplet Charge Acquired during Contact with Electrodes in Strong Electric Fields

Aqueous droplets acquire charge when they contact electrodes in high-voltage electric fields. Although many researchers have investigated droplet charging under various conditions, the droplet charges are typically reported simply in terms of a mean and standard deviation. Here, we show that droplets often acquire significantly less charge for a single contact compared to the previous and subsequent contacts. These "low-charge events," which are not observed with charging of metal balls, yield up to a 60% decrease in charge acquired by the droplet and occur regardless of the applied field strength, droplet conductivity, or droplet volume. In all cases examined here, the occurrence of low-charge events to good approximation follows a negative binomial distribution (i.e., a Pascal distribution) with a mean probability of 13%. We further demonstrate that approximately 16% of charging events are characterized by "irregular" Taylor cone dynamics, suggesting that instabilities in the electrically driven deformation of the approaching liquid interface may be responsible for the low-charge events. The results indicate that workers using systems involving droplet charging should take into account the high likelihood of droplets randomly acquiring less charge than expected.