Instability analysis of a coaxial jet under a radial electric field in the nonequipotential case

Abstract

The linear temporal stability analysis of a coaxial jet model under the radial electric field is carried out on the assumption that all free charges are “frozen” on the outer interface of the conducting liquid (i.e., the nonequipotential case) in the present paper. The analytical dimensionless dispersion relation is derived and solved numerically. Three unstable modes, namely the paravaricose, parasinuous, and transitional modes, are found in the Rayleigh regime and they change into the other two unstable modes, namely mode 1 and mode 2, in the wind induced and atomization regimes if the dimensionless electrostatic force or Weber number is sufficiently amplified. The numerical results show that the dimensionless electrostatic force as well as the Weber number inhibits the jet instability in the long wavelength region while enhances it in the short wavelength region. The relative dielectric constant of the outer liquid alters the behaviors of the nonequipotential case significantly, whereas the electrical permittivity of the inner liquid does not affect the jet instability much. Besides, the relatively small diameter ratio may make the inner and outer interfaces decouple from each other. And the critical diameter ratio is calculated crudely. The differences between the equipotential and nonequipotential cases are clarified step by step.