Instability of the elliptic liquid jets

The instability of a viscoelastic liquid jet ejecting from an elliptical orifice is researched. For the rheological property of the liquid jet, Jeffreys constitutive model is applied and the free boundary conditions are considered. The dispersion relation between the dimensionless growth rate and disturbance wave number is obtained by adopting the temporal linear analysis to the non-circular jet. Meanwhile, the axis-switching wavelength which is mainly dependent on the surface tension are predicted. Also, the effect of physical factors are discussed in detail especial for the function of the liquid viscoelasticity. The temporal growth increases when elasticity is increased slightly. Different form the effect of the elasticity number El, the influence of the time constant ratio λ is markedly for the reason that the deformation retardation dissipates dramatically the perturbation energy. Besides, the viscous force stabilizes the jet while surface tension and aerodynamic force destabilize it. The more oval the liquid jet is, the more unstable for it.