material modeling for process instabilities

For the theoretical description of the fiber spinning process, the laws of hydrodynamics, such as continuity equation or momentum conservation, are linked to a material law, the constitutive equation. The resulting system of partial differential equations represents the center of the mathematical analysis.

Experimental studies show that the spinning process becomes unstable at a certain take-off speed, which means that both the cross-sectional and velocity profiles of the fiber begin to oscillate. This critical extraction ratio is material dependent. For the optimization of the process stability, it is therefore very interesting to theoretically investigate the stability of the differential equations describing the system and to establish a relationship with material parameters that are relevant in practice. In addition to studying various instability prediction methods, material models must be designed that correctly describe the experimental data. For this purpose, in addition to experiments under industrial conditions, knowledge from the molecular and rheological characterization will help.