Investigation of the stability of a planar Oldroyd-B jet

Abstract

The stability characteristics of incompressible, viscoelastic planar jets are investigated in the present work. The Oldroyd-B constitutive equation represents the viscoelastic fluid behavior. Linear stability theory is used to study the sinuous and varicose stability modes’ growth rates, wave velocity, and neutral curves as a function of the Weissenberg number, Reynolds number, and solvent viscosity coefficient. A canonical velocity profile gives the laminar jet base flow. The polymer stress tensor components are computed considering a parallel flow approximation, verified by comparing profiles with stress tensor profiles obtained by computational fluid dynamic simulations. The modified Orr–Sommerfeld equation with included viscoelastic effects is solved by a shooting method. The results show that viscoelastic effects become significant for low Reynolds numbers, stabilizing the sinuous mode and destabilizing the varicose mode compared to the Newtonian jet stability results. Neutral curves are also presented, showing the viscoelastic effects on the critical Reynolds number and the possible existence of elastic instability in the limit of low Reynolds numbers.