Linear analysis of the temporal instability of axisymmetrical non-Newtonian liquid jets

The temporal instability behavior of non-Newtonian liquid jets moving in an inviscid gaseous environment is investigated theoretically for axisymmetrical disturbances. The corresponding dispersion relation between the wave growth rate and the wave number is derived. The linearized stability analysis shows that a jet of a viscoelastic fluid exhibits a larger growth rate of axisymmetric disturbances than a jet of a Newtonian fluid with the same Ohnesorge number, indicating that non-Newtonian liquid jets are more unstable than their Newtonian counterparts. This is a well-known effect for small perturbations of the jet surface. For non-Newtonian liquid jets the instability behavior is influenced by the interaction of the liquid viscosity and elasticity effects, in which the liquid viscosity tends to dampen the instability, whereas the elasticity results in an enhancement of instability for small perturbations. The validity of the theoretical results for the growth rate spectra and breakup lengths of viscoelastic liquid jets is tested against experimental results from the literature. The comparisons confirm that the linearized theory fails to describe the nonlinear phenomena involved in viscoelastic jet breakup correctly, but it yields good results for the growth rate of disturbances in a regime of low jet Weber numbers and small deformations. The limits of validity of linear theories for viscoelastic jet instability are quantified, taking also into account the onset of non-axisymmetric deformations due to bending.