Linear stability analysis of a non-Newtonian liquid jet under AC electric fields

When AC electric fields are applied to a non-Newtonian liquid jet, the parametric resonance occurs in the interface. In this paper, effects of the fluid viscoelasticity are mainly studied by Floquet stability analysis. The viscoelasticity is modeled using the Oldroyd-B constitutive equation. The fluid elasticity has weak effects on the linear capillary instability as in the DC cases, but strongly affects the parametric instability. When the oscillation period is comparable to the relaxation time, the elasticity increases the maximum growth rate to a great extent. The critical frequency, beyond which the resonance decays, also increases greatly with the increasing fluid elasticity. An increase in the time constant ratio (i.e. the deformation retardation time) leads to a smaller maximum growth rate, but the reduction of the parametric mode is much more distinct. In addition, the dominate wavenumber is insensitive to the fluid elasticity and the time constant ratio. Moreover, the competition between the capillary and the parametric instabilities reveals that strengthening the electric field, improving the fluid elasticity and lowering the frequency are helpful to observe the resonant instability experimentally.