Finite conductivity effects on electrostatically sprayed liquid jets

Electrostatic spraying of drops is often characterized by the formation of a thin jet. Experimentally, this jet appears to be stable over a portion of its length. In this paper the capillary instability of a jet of a conducting liquid is examined theoretically. The formation of such a jet requires both an axial electric field and a surface charge. A finite conductivity jet allows the charge and axial field to coexist. The result is an electrical surface force with both normal and shearing components. For some values of field and charge, the capillary instability of the jet is stabilized by the electrical forces. A charge density 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. Calculations of the growth rate of instabilities for different values of the electrical parameters are presented.