Capillary instability of fluid cylinder under the effect of transverse varying electric field

The electrodynamic instability of a capillary dielectric fluid cylinder (radius a and density p) penetrated by a uniform axial electric field surrounded by a transverse varying electric field is investigated. A general dispersion relation to all possible axisymmetric modes of perturbation for all short wavelengths and long wavelengths is derived and discussed in detail. The model is capillary stable to axisymmetric modes if the longitudinal wave number normalized with respect to the jet radius is equal to or greater than 1.05757 and vice versa. The axial electric fields pervading the interior and the exterior ofthe cylinder are stabilizing or destabilizing for all disturbance modes according to some restrictions. The transverse varying electric field is purely stabilizing in the axisymmetric disturbances for all wavelengths. The electrodynamic force has a strong stabilizing influence in the axisymmetric mode and can suppress the capillary instability above a certain value of the basic electric field.