Linear spatial instability of unrelaxed viscoelastic jets

The spatial linear instability of viscoelastic jets subjected to unrelaxed axial stress and moving in a gas medium is examined theoretically. Different from previous studies, in which the unrelaxed elastic tension is assumed to remains at the exit value, the effects of spatial decaying of the unrelaxed stress for the cases of moderate stress relaxation time are included in the present work. The surrounding gas is inviscid, incompressible and stationary. The Oldroyd-B model are applied to describe the rheology properties of the viscoelastic fluids. Results show that the effects of unrelaxed stress tension are complicated for different stress relaxation time. When the stress relaxation time is small, the stabilizing effect of the unrelaxed stress tension is enhanced with the unrelaxed tension decaying along the flow direction; when the stress relaxation time exceeds the critical value, the stabilizing effect of the unrelaxed stress tension is weakened. This twofold effect can be explained by the competition between the viscoelastic dissipation and the work done by the unrelaxed tension for different physical parameters. This may provide a qualitative explanation for the complex influences of elasticity observed in experiments.