Iterated stretching of viscoelastic jets

Abstract

We examine, with asymptotic analysis and numerical simulation, the iterated stretching dynamics of FENE and Oldroyd-B jets of initial radius r0, shear viscosity ν, Weissenberg number We, retardation number S, and capillary number Ca. The usual Rayleigh instability stretches the local uniaxial extensional flow region near a minimum in jet radius into a primary filament of radius [Ca(1−S)/We]1/2r0 between two beads. The strain-rate within the filament remains constant while its radius (elastic stress) decreases (increases) exponentially in time with a long elastic relaxation time 3We(r02/ν). Instabilities convected from the bead relieve the tension at the necks during this slow elastic drainage and trigger a filament recoil. Secondary filaments then form at the necks from the resulting stretching. This iterated stretching is predicted to occur successively to generate high-generation filaments of radius rn, (rn/r0)=√(rn−1/r0)3/2 until finite-extensibility effects set in.