Fiber spinning critical draw ratio

The experimental and theoretical literature on instabilities in fiber spinning has been reviewed in detail by Jung and Hyun (28). The theoretical analysis began with the work of Pearson et al. (29-32), who examined the behavior of inelastic fluids under a variety of conditions using linear stability analysis for the governing equations. For Newtonian fluids, they found a critical draw ratio of 20.2. Shear thinning and shear thickening fluids... 

Draw resonance occurs in processes where the extrudate is exposed to a free surface stretching flow, such as blown film extrusion, fiber spinning, and blow molding. It manifests itself in a regular cyclic variation of the dimensions of the extrudate. An extensive review [169] and an analysis [170] of draw resonance were done by Petrie and Denn. Draw resonance occurs above a certain critical draw ratio while the polymer is still in the molten state when it is taken up and rapidly quenched after take-up. 

The steady-state solution for fiber spinning (Newtonian and isothermal case) was presented in Section 9.1.1, and it consists of Eqs. 9.26 and 9.28. Linearized (small disturbances) stability analysis involves (Fisher and Denn, 1976) the study of finite amplitude disturbances, and we do not present it. Rather, we present the results of such an analysis. The value of Dr = 20.21 is considered to be the critical draw ratio beyond which the flow becomes unstable. Figure 9.13 (Donnelly and Weinberger, 1975) shows experimental data that confirm the theory. More specifically, silicone oil (of viscosity equal to 100 Pa-s), which seems to be Newtonian, was extruded and the ratio of maximum to minimum filament diameters was plotted against the draw ratio. An instability appears at a draw ratio of about 17, or about 22 if we take into consideration about 14% die swell. The value of the critical draw ratio of 22 compares well with the theoretical value of 20.21. Pearson and Shah (1974) extended the analysis to a power-law fluid and included surface tension, gravitational. 

Fig. 7 a, b. Maximum draw ratio for spinning as a function of the PpPTA concentration in sulfuric acid. The critical concentration is near 8%. Temperature of the spinning solution and the coagulation bath are both 30 °C, (A) air-gap spinning, (A) inneret placed in coagulation bath b) Modulus of the fibers spun according to the conditions of Fig. 7a... 

Two series of PBTA/PI block copolymers were synthesized in this study and solution processed into molecular composite fibers via dry-jet wet-spinning. The unique rheological properties of liquid-crystalline PBTA homopolymers and PBTA/PI block copolymers were studied with a cone-and-plate rheometer. For block copolymers, the critical concentration decreased with an increase in PBTA content. The flow curves of isotropic and anisotropic solutions could be described via the power-law model and Carreau model, respectively. Copolymer fibers possess tensile strength and modulus located between those of PBTA fibers and PI fibers. Moreover, the tensile strength and modulus of Col fibers increase with an increase in PBTA content. Besides, increasing the draw ratios would give rise to an increase in the mechanical properties of copolymer fibers... 

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