Electro-viscous instability of a swirling compound jet

The aim of this work is to study the effects of a combination of axial and swirl velocity on the instability of an annular liquid jet. A linear instability analysis yields an analytical dispersion relation, which governs the temporal growth of perturbations to an electrified streaming annular viscous liquid jet coated by two cylindrical shells of streaming swirling inviscid gases. The three-layer system is subjected to an electric field normal to the interfaces. In our study, the electric body force vanishes, and the electric field and fluid dynamics are coupled only at the interfaces through the tangential and normal interfacial stress balance equations. The governing electrohydrodynamic equations, along with the hydrodynamic and electrical boundary conditions, are solved, and then the corresponding dispersion relation is obtained. The instability analysis of a inviscid jet is discussed as a special case. Numerical results on the effect of the various problem parameters on the instability and breakup of a liquid jet are presented. It is observed, for instance, that the swirling ratio of the outer gas layer always enhances the stability of flow in the case of axisymmetric disturbances, whereas it has a dual effect (destabilizing effect) corresponding to the case of asymmetric disturbances. It has been found that the higher electrical potential, the larger the maximum growth rate and critical wave number of the disturbances and, consequently, the initial applied electric potential tends the instability and breakup of the liquid jet.