Abstract
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.
Highlights
A conducting droplet immersed in a dielectric medium and set on the lower plate of a condenser acquires an electrical charge when subjected to a uniform electrical field
The charge Q0 acquired by the sphere, namely the Maxwell’s charge, and the electrical force F0 exerted by the electrical field EN on the sphere
A uniform electric field exerts a lifting force on a conductive droplet immersed in a dielectric fluid and in contact with an electrode
Summary
A conducting droplet immersed in a dielectric medium and set on the lower plate of a condenser acquires an electrical charge when subjected to a uniform electrical field. Lebedev and Skal’skaya [4], Felici [5] and Jones [6] have showed that the electrical force must include the interaction force with the droplet image due to the electrode plane They conclude their study by noticing the fact that a complete theoretical model should take into account the electric field distribution around the exact deformed drop. The method used by Lebedev and Skal’skaya [4], for solving the electrostatic problem of a grounded sphere lying on a plane in an electric field, was generalized to the case of a portion of sphere protruding from a plane electrode by Le Ny [9] This latter gave the charge and force evolutions as functions of the protrusion radii.
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