Stability loss and sensitivity in hollow fiber drawing

Stability of hollow fiber drawing is studied, based on the quasi-one-dimensional equations of thin film dynamics. It is shown that the model isothermal drawing process is unstable when the draw ratio E (that of output to input velocities) exceeds the critical value E_* = 20.22 when the viscosity force is dominating. Under stable regimes with E < E_*, the response of the as-drawn fiber to external perturbations is studied (the sensitivity problem). In unstable situations with E > E_*, onset of the so-called draw resonance regime with self-sustained oscillations is predicted by using numerical simulation. The effects of the inertia, gravity, surface tension, and gas pressure differential are considered.