Electrical Discharge in Capillary Breakup: Controlling the Charge of a Droplet

We studied the detachment of sessile droplets of conductive liquids from an immersed wire by reducing the contact angle using ac electrowetting. Upon detachment, the droplets acquire a certain amount of charge, which is shown to be controlled by a dimensionless parameter $\alpha$. $\alpha$ describes the interplay between the diverging Ohmic resistance of the breaking capillary neck and the ac frequency. In the specific configuration of the present experiment, discharging at high frequency leads to self-excited oscillations in which the droplets periodically detach from and reattach to the wire.