Axisymmetric and non-axisymmetric instability of an electrified viscous coaxial jet

Abstract

A linear study is carried out for the axisymmetric and non-axisymmetric instability of a viscous coaxial jet in a radial electric field. The outer liquid is considered to be a leaky dielectric and the inner a perfect dielectric. The generalized eigenvalue problem is solved and the growth rate of disturbance is obtained by using Chebyshev spectral collocation method. The effects of the radial electric field, liquid viscosity, surface tension as well as other parameters on the instability of the jet are investigated. The radial electric field is found to have a strong destabilizing effect on non-axisymmetric modes, especially those having smaller azimuthal wavenumbers. The helical mode becomes prevalent over other modes when the electric field is sufficiently large. Non-axisymmetric modes with high azimuthal wavenumbers may be the most unstable at zero wavenumber. Liquid viscosity has a strong stabilizing effect on both the axisymmetric and non-axisymmetric instability. Relatively, the helical instability is less suppressed and therefore becomes predominant at high liquid viscosity. Surface tension promotes the instability of the para-sinuous mode and meanwhile suppresses the helical and the other non-axisymmetric modes in long wavelength region.