Drawing of annular liquid jets at low Reynolds numbers

Asymptotic methods based on the slenderness ratio are used to obtain the leading-order equations that govern the fluid dynamics of axisymmetric, isothermal, Newtonian, annular liquid jets such as those employed in the manufacture of textile fibres, annular membranes, composite fibres and optical fibres, at low Reynolds numbers. It is shown that 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 annular jets is governed by the same eigenvalue equation as that for the spinning of round fibres. 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 annular jet dynamics evolves from periodic to chaotic motions as the extension or draw ratio is increased. The power spectrum of the annular jet's 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.