Akzo Nobel – Instability in the Spinning of Fibers #SWI1998

A well-known problem in the spinning of fibers by drawing a liquid through a spin hole is that when the speed is increased, there appears an instability in the sense that the cross-section of the filament is no longer independent of time. In fact, oscillations arise at a large speed of spinning.

In 1969 Matovich and Pierson found through a linear stability analysis, a criterion for this instability for the case of a Newtonian fluid with constant viscosity. When the cross-section of the fiber is denoted by A, the vertical speed by v, then the dimensionless model is given by

A_t + (Av)_x = 0 ,        (Av_x)_x = 0 ,

A(0,t) = 1 ,        v(0,t) = 1 ,        v(1,t) = s.

Recently (1998) Van der Hout at Akzo Nobel was able to show that the heuristic method of Matovich and Pierson is justifiable.

It is still unclear however whether a (Hopf) bifurcation occurs at the change of stability.

The Study Group is asked to investigate whether such a stability analysis can be performed for the cases of:

1. Non-constant viscosity (e.g. for a given temperature profile)
2. Power-law liquid
3. Memory liquid (e.g. Maxwell model)

Also here the question is relevant whether a bifurcation can be shown.

Literature:
Stability of stationary velocity profiles in airgap wetspinning of Newtonian fluids, R. van der Hout, 1998.
Spinning a molten thread line, J.R.A. Pearson & M.A. Matovich, 1969.
Spinning a molten thread line, M.A. Matovich & J.R.A. Pearson, 1969.