Stability analysis of conducting jets under ac radial electric fields for arbitrary viscosity

Abstract

A temporal linear modal stability analysis is presented for conducting viscous liquid jets flowing with nonzero velocity relative to an ambient gas and subjected to an ac radial electric field. Parametric resonance between natural dc frequencies and the frequency (or multiple) of the imposed ac field eventually leads to destabilization of the jet for perturbations with wave numbers in the stable domain. In this way, it is possible to obtain drops of smaller size. The main result is the extension of the stability analysis to liquids of arbitrary viscosity using a dynamical approach, instead of previous variational models valid for slightly viscous liquids. The effect of the outer gas in relative motion is taken into account in the framework of currently available semiempirical theories. A brief discussion of the dispersion relation for dc fields is included as the natural starting point for the discussion of the ac case. Use of the 1-D averaged model for axisymmetric perturbations, an alternative to the 3-D approach, allows a complete determination, in this particular case, of the distribution and nature of roots of the dispersion relation in the complex plane. The theoretical study presented here is ready to be compared to future experiments in the Rayleigh and first wind-induced regime, as no relevant instability mechanisms have been excluded; namely, capillary instability, viscous damping, quasi-electrostatic pressure effects, Kelvin–Helmholtz instability corrected to account for the gas viscosity, and finally, parametric resonance.