On the stability of a rotating electrified liquid jet. Effect of an axial electric field

The electrohydrodynamic stability of a liquid cylinder subject to surface tension and subjected to periodic rotation has been elaborated for all axisymmetric perturbations. The dielectric fluids are assumed to be stressed by a uniform axial electric field. The analysis is based on the method of multiple time scales. The zeroth-order perturbation yields a transcendental dispersion relation. The axial electric field plays a stabilizing role and can be used to suppress the instability of the constant rotation. It is observed in the case of constant rotation that if the outer surrounding medium is rotating faster than the inner liquid jet it makes the system more stable. The problem to first order in the perturbation is solved analytically. The solvability condition is obtained. The transition curves are examined. The frequency of the rotation can be used to control the position of the resonance regions. The analytical results show that the increase of the amplitude of the angular velocity has a destabilizing effect. The axial electric field plays a dual role in the stability criterion, a stabilizing influence in the nonresonance case and a destabilizing role at the resonance case.