The instability characteristics of a liquid jet discharging from a nozzle into a stagnant gas are investigated using the linear stability theory. Starting with the equations of motion for incompressible, inviscid, axisymmetric flows in cylindrical coordinates, a dispersion relation is obtained, where the amplification factor of the disturbance is related to its wave number. The parameters of the problem are the laminar velocity profile shape parameter, surface tension, fluid densities, and electrical charge of the liquid jet. The dispersion relation is numerically solved as a function of the wave number. The growth of instabilities occurs in two modes, the Rayleigh and atomization modes. For $rWe<1$ (where $We$ represents the Weber number and $r$ represents the gas-to-liquid density ratio) corresponds to a Rayleigh or long wave instability, where atomization does not occur. On the contrary, for $rWe>>1$ the waves at the liquid-gas interface are shorter and when they reach a threshold amplitude the jet breaks down or atomizes. The surface tension stabilizes the flow in the atomization regime, while the density stratification and electric charges destabilize it. Additionally, a fully developed flow is more stable compared to an underdeveloped one. For the Rayleigh regime, both the surface tension and electric charges destabilize the flow.

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