On the instability of an electrostatically sprayed liquid jet

The stability of a thin jet for electrostatic spraying of insulators using field emission or ionization is examined theoretically. Since the jet is insulating, the charge injected becomes surface charge. This charge can be redistributed through electric mobility and charge convection. In addition, there is an electric field with a component parallel to the jet. This charge and field result in both a normal and a shearing electric force. Calculations show that a charge with no tangential field stabilizes the long wavelengths while it makes the short wavelengths more unstable. On the other hand, a tangential electric field stabilizes the short wavelengths. The effect of both charge and the tangential field is much larger than the sum of the two effects separately. Using fields and charge densities that are easily achievable in an experiment, a stable jet can be produced. Calculations of the growth rate of instabilities for different values of the electrical parameters are presented