Nonlinear dynamics of hollow, compound jets at low Reynolds numbers

Abstract

The leading-order fluid dynamics equations of isothermal, axisymmetric, Newtonian, hollow, compound fibers at low Reynolds numbers are derived by means of asymptotic methods based on the slenderness ratio. These fibers consist of an inner material which is an annular jet surrounded by another annular jet in contact with ambient air. The leading-order equations are one-dimensional, and analytical solutions are obtained for steady flows at zero Reynolds numbers, zero gravitational pull, and inertialess jets. A linear stability analysis of the viscous flow regime indicates that the stability of hollow, compound jets is governed by the same eigenvalue equation as that for the spinning of round fibers. Numerical studies of the time-dependent equations subject to axial velocity perturbations at the nozzle exit and/or the take-up point indicate that the fiber dynamics evolves from periodic to chaotic motions as the extension or draw ratio is increased. The power spectrum of the interface radius at the take-up point broadens and the phase diagrams exhibit holes at large draw ratios. The number of holes increases as the draw ratio is increased, thus indicating the presence of strange attractors and chaotic motions.