Self-acceleration of a charged jet

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Abstract
When insulators are sprayed electrostatically, charges are injected into the liquid, resulting in the formation of a charged jet. Mutual repulsion between these charges, which reside on the jet surface, causes the jet to accelerate. This acceleration is opposed by surface tension and inertial forces. As the jet accelerates, its radius decreases until it reaches a minimum radius. When the minimum jet size is achieved, the rate of acceleration decreases to zero. Equations are derived which allow this minimum radius to be calculated. In addition to the accelerating jet, the equations have another solution with the jet decelerating. In the experiments the acceleration is observed but not the deceleration. Rather, drops form on the end of the jet, indicating that it becomes unstable before it can decelerate. The values for minimum jet radius calculated from the equations are compared with experimental measurements of the minimum jet size in electrostatic spraying of insulators, and good correlation is obtained.

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