Temporal analysis of a non-Newtonian liquid jet in a compressible gas

The temporal instability behavior of a non-Newtonian liquid jet in a compressible gas is investigated theoretically. A corotational Jeffreys model is used for describing the viscoelastic liquid state. The dispersion relation is solved by Chebyshev collocation method. Besides, the effects of compressibility of gas, Reynolds number, elasticity number, and the ratio of deformation retardation time to stress relaxation time on the instability of non-Newtonian liquid jet with the axisymmetric and first asymmetric disturbances are studied in this case. The results show that gas compressibility is an unstable factor on the jet instability for both of the axisymmetric and the first asymmetric disturbances. For the liquid instability with the axisymmetric disturbance, it is noted that the time constant ratio always makes the jet being stable, and the elastic number makes the jet being unstable, but these effects are different on the liquid instability with the first asymmetric disturbance.