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In this article, deflections of a viscous filament in a classical fiber spinning set-up are analyzed. The deflections are considered in a direction perpendicular to the vertical equilibrium state of the spin line. The result is a traveling wave equation with non-uniform coefficients representing the non-uniform filament velocity and non-uniform tension in the spin line. Under neglect of air drag, the system is conservative with respect to an energy functional, so that its eigenmodes have purely imaginary characteristic values. A numerical analysis of the eigenmodes of the system reveals that deflections propagate from take-up wheel to spinneret, with frequencies being multiples of a basic frequency and amplitudes sinus shaped with the maximum being shifted toward the spinneret. From the numerical results, a formula is derived, which approximates the basic frequency and traveling wave velocity directly in terms of the spinning process parameters.

This paper presents a method to determine the parameters in a polymer constitutive model using data obtained from a Rheotens experiment. The novelty of the suggested approach is the simultaneous fitting of model parameters to different types of data given by Rheotens, i.e., force-velocity curve, onset of draw resonance and frequency of oscillations. To determine the onset and frequency of oscillations, a stability analysis is exploited and the spectrum of a quasi-hyperbolic differential operator is calculated. The proposed approach is efficient and accurate. To demonstrate its applicability and consistency, a modified Giesekus constitutive model is chosen and model parameters are fitted to the Rheotens data for three different types of polymer (LLDPE, PP, PS).

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