Periodic time dependent electrogravitational instability of a fluid cylinder

Abstract

The electrogravitational instability of a dielectric fluid cylinder dispersed in a gravitational dielectric medium of negligible motion has been developed on using the macroscopic perturbation technique based on the normal mode analysis. The model is acting upon the pressure gradient, self-gravitating and electrodynamic (with periodic time dependent electric field) forces. For all axisymmetric and non-axisymmetric disturbances the system is governed by the Hill's second-order integro-differential equation in the disturbed surface displacement. The self-gravitating forces are destabilizing only in the axisymmetric disturbances domain 0⩽x⩽1.0668 and stabilizing in all other domains, where x is the dimensionless longitudinal wavenumber. The electric field is always stabilizing not only in the axisymmetric mode m= 0 but also in those of non-axisymmetric m≠ 0. The frequency of the time dependent periodic electric field is only destabilizing in a few axisymmetric states of perturbations while it is strongly stabilizing in the remaining axisymmetric disturbance states and also stable in all states of the non-axisymmetric perturbations. Resonance domains may arise due to the periodicity of the electric field and in some ranges of the wavenumber, the stability conditions depend solely on the frequency of the field. The self-gravitating destabilizing influence could not be suppressed whatever is the greatest value of the magnitude and frequency of the periodic electric field because the gravitational destabilizing influence will persist.