Nonlinear dynamics of hollow, compound jets at low Reynolds numbers

The leading-order fluid dynamics equations of isothermal, axisymmetric, New tonian, hollow, compound fibers at low Reynolds numbers are derived by mean s of asymptotic methods based on the slenderness ratio. These fibers consis t of an inner material which is an annular jet surrounded by another annula r jet in contact with ambient air. The leading-order equations are one-dime nsional, and analytical solutions are obtained for steady flows at zero Rey nolds numbers, zero gravitational pull, and inertialess jets. A linear stab ility analysis of the viscous flow regime indicates that the stability of h ollow, compound jets is governed by the same eigenvalue equation as that fo r the spinning of round fibers. Numerical studies of the time-dependent equ ations subject to axial velocity perturbations at the nozzle exit and/or th e take-up point indicate that the fiber dynamics evolves from periodic to c haotic motions as the extension or draw ratio is increased. The power spect rum of the interface radius at the take-up point broadens and the phase dia grams exhibit holes at large draw ratios. The number of holes increases as the draw ratio is increased, thus indicating the presence of strange attrac tors and chaotic motions. (C) 2001 Elsevier Science Ltd. All rights reserve d.