Effects of spatially decaying elastic tension on the instability of viscoelastic jets

Abstract

This paper theoretically examines the spatial linear instability of viscoelastic jets subjected to unrelaxed axial stress tension and moving within an inviscid stationary gas medium. Unlike the constant value assumption of previous studies, the effects of spatial decaying of the unrelaxed stress tension are included here. The Oldroyd-B constitutive equation has been adopted to model fluid viscoelasticity. Results indicated that the effects of unrelaxed stress tension were complicated and mainly dependent on stress relaxation time. When stress relaxation time was short, the maximum growth rates along the jet decreased to the constant value of the completely relaxed case; increasing unrelaxed tension slightly decreased the breakup length. When the stress relaxation time increased to exceed the critical value, the maximum growth rates continued to increase along the jet and larger unrelaxed tensions caused longer breakup lengths. This twofold effect can be explained by the competition between the stabilizing effects of the unrelaxed tension itself and the destabilizing effects of the spatial decay. Moreover, the fluid elasticity suppressed instability when the unrelaxed tension was great. Responses to the spatial decaying unrelaxed tension of the axisymmetric and nonaxisymmetric disturbances for high-speed viscoelastic jets were similar to those of the capillary case. Generally, the complex effects of the interplay between fluid elasticity and the spatially decaying unrelaxed tension may qualitatively explain the breakup behaviors of viscoelastic jets in experiments.