Spinline simulations

Some of the material in this chapter is covered in the texts by Middleman, Pearson, and Tadmor and Gogos cited previously. The standard text on the mechanics of fiber spinning, which predates most of the published work on spinline simulation, is... 

The alternate parameters for PET spinline simulation, as well as parameters for polypropylene, are developed in... 

These orientation functions, when plotted against the spinline stress, unify into three curves, respectively independent of the molecular weight of PP and spinning temperature used [5]. The crystallization and orientation during melt spinning are often simulated. 

We know two conditions at the point of solidification, which we denote z = L. The solidification temperature for amorphous and slowly crystallizing polymers will typically be close to the glass transition temperature, which is known. We assume little or no deformation of the solidified fiber, so the spinline velocity at solidification will equal the takeup velocity, which is also known. Hence, for simulation purposes we may assume that we are given v(L) and T(L). The boundary conditions are therefore... 

This is obviously an oversimplified picture. To handle solidification properly, it is necessary to include an equation that describes the growth of a glassy or crystalline phase and a stress equation that accounts for the biphasic nature of the system. Such descriptions are the subject of recent research, and these results should be used in new simulation codes, especially for semicrystalline polymers, but the approximation of an instantaneous transition from a liquid to an undeformable solid at a fixed average temperature T = Tl captures the important features of the spinline and suffices for our purposes here. 

Figure 7.5. Simulation of PET spinline data. Reprinted from Gagon and Denn, Polym. Eng. Sci, 21, 844 (1981).

Figure 10.6. Simulation of George s PET pilot plant spinning experiments using a single-mode Giesekus fluid in a spinline model that incorporates crystallization. Reprinted with permission from Shrinkhande et al., J. Appl. Polym. Sci., 100, 3240 (2006). Copyright John Wiley Sons, Inc.

Kohler and McHugh s calculations for Young s Run 9 indicated that there was substantial crystallization. The Giesekus model for the melt is still inadequate, despite the inclusion of stress-induced crystallization in the spinline model, and the response does not differ greatly from the PTT simulations without crystallization. 

The narrow molecular weight distribution of metallocene homopolypropylene directly translates into narrow stress relaxation time spectra of the molten polymer. In a spinning process, where the polymer melt is stretched and subsequently crystallized, this means a more rapid decay of the stress in the fibers, and as a consequence, allows higher spinning speeds and finer fibers. A fully viscoelastic simulation of the spinning process indicates that metallocene polymers exhibit a more pronounced spinline profile, allowing the production of thinner filaments than can be achieved using conventional polypropylene (Fig. 43). 

FIG. 43 Spinline profile simulations of metallocene and Ziegler-Natta catalyzed pol5 propylene. (From Ref 64.)... 

Doufas, A.K., McHugh, A,J, Miller, C., and Immaneni, A, (2000) Simulation of melt spinning including flow-induced crystallization. Part II. Quantitative comparisons with industrial spinline data. J. Non-Newtonian Fluid Meek, 92, 81-103. 

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