Stability of Capillary Waves of an Arbitrary Symmetry on a Jet in a Uniform Electrostatic Field

Abstract

The dispersion relation for capillary waves of an arbitrary azimuthal symmetry on an elliptic cross-section jet in a uniform electrostatic field which is perpendicular to the axis of symmetry of the jet is derived. The stability of the first three azimuthal modes is investigated. It is shown that the stability of capillary waves on the jet reduces with increase in the external electrostatic field strength and the related eccentricity of transverse jet cross-section, as well as with increase in the polarization charge on the jet surface. Comparison with a jet in a radial electrostatic field is carried out. In the case of the transverse electrostatic field the instability growth rates of the capillary waves of any symmetry on the jet surface are turned out to be significantly higher than those in the case of the radial electrostatic field.