Iterated stretching of viscoelastic jets

We examine, with asymptotic analysis and numerical simulation, the iterated stretching dynamics of FENE and Oldroyd-B jets of initial radius r(0), shear viscosity nu, 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](1/2)r(0) between two beads. The strain-fate within the filament remains constant while its radius (elastic stress) decreases (increases) exponentially in time with a long elastic relaxation time 3We(r(0)(2)/nu). 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 r(n), (r(n)/r(0)) = root 2(r(n-1) / r(0))(3/2) until finite-extensibility effects set in. (C) 1999 American Institute of Physics. [S1070-6631(99)01307-0].