Forces and charges on an undeformable droplet in the DC field of a plate condenser

A single conducting drop resting on the lower plane electrode of a horizontal condenser and surrounded by a dielectric fluid is considered. When a DC field is applied to the electrodes, the drop acquires electric charges and is subjected to an electrostatic force normal to the electrode. This driving force may eventually detach the drop if the applied field strength exceeds a threshold value. For small drops, the gravitational field and the electrical force effect can be neglected with respect to the surface tension. In this case, it may be assumed that drops are undeformable and keep a spherical cap shape. Based on this model, charges and forces are calculated analytically in any wetting conditions. To this end, previous studies concerning solid spheres are conveniently extended. The usefulness of the above model is then considered to determine the lift-off threshold value. For non-wetting conditions, new experimental results are presented: they fit precisely the derived theoretical lift-off conditions. For wetting conditions, the preceding calculations are shown to be unable to provide any testable criterion. The undeformability assumption has to be relaxed.