Temporal linear instability analysis of an electrified coaxial jet with inner driving liquid inside a coaxial electrode

In this paper, a temporal linear stability analysis is performed of a coaxial jet composed of two immiscible liquids inside a coaxial electrode. This analysis is carried out to investigate the case of an inner driving coaxial electrospray system. The assumption is made that the inner liquid has high electric conductivity, and the outer liquid is an insulating dielectric. The dimensionless dispersion equation for both the axisymmetric and non-axisymmetric modes is derived and solved numerically for the axisymmetric case. The effects of the relevant dimensionless parameters on the instability of the jet are discussed in detail. These parameters include the dimensionless electrostatic force E, the dielectric constant ratio ε, the diameter ratios a and b, the velocity ratio Λ, the density ratio S, the Weber number, and the interface tension ratio ζ. Two independent unstable modes, modes 1 and 2, are found and analyzed. Among the various parameters, the dimensionless electrostatic force and the dielectric constant have a similar and remarkable influence on modes 1 and 2, altering drastically the regime of the jet as they vary. The interface tension on the outer interface promotes the instability of both modes 1 and 2 in the region of long wavelengths while suppressing the growth rate in the region characterized by short wavelengths. The interface tension on the inner interface, however, promotes instability of only mode 2 in the same way. The diameter ratio a has a great effect on mode 2 while a negligible influence on mode 1. And the diameter ratio b has a slight effect on both the unstable modes.