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 axisymmetri cal disturbances. The corresponding dispersion relation between the wave gr owth 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 Ohn esorge number, indicating that non-Newtonian liquid jets are more unstable than their Newtonian counterparts. This is a well-known effect for small pe rturbations of the jet surface. For non-Newtonian liquid jets the instabili ty behavior is influenced by the interaction of the liquid Viscosity and el asticity effects, in which the liquid viscosity tends to dampen the instabi lity, whereas the elasticity results in an enhancement of instability for s mall perturbations. The validity of the theoretical results for the growth rate spectra and breakup lengths of viscoelastic liquid jets is tested agai nst 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 gro wth rate of disturbances in a regime of low jet Weber numbers and small def ormations. The limits of validity of linear theories for viscoelastic jet i nstability are quantified, taking also into account the onset of non-axisym metric deformations due to bending. (C) 2000 Elsevier Science Ltd. All righ ts reserved.