4-mode Giesekus model

To help understand and quantitatively evaluate the secondary movement shown above, Debbaut et al. [75, 77] augmented this experimental work with a three-dimensional flow simulation that incorporated viscoelastic effects. The finite element method, using a 4-mode Giesekus model as the viscoelastic constitutive equation, was used for the simulation. The polymer used for the experiment and simulation was a low-density polyethylene. Figures 12.20 and 12.21 show the experimental observations and the numerical predictions of the deformations of the interface for the rectangular straight channel [78], and for the teardrop channel [75], respectively. 

Figure 9.8 Normalized first normal stress coefficient, V /2 (o°,x) as a function of normalized shear rate %, compared to the theoretical predictions of the one-mode Giesekus model (lines) (T = 20°C, 15%-MDMAO-HNO3, pH = 3.5).204,205...

There are numerous other constitutive equations of both differential and integral type for polymer melts, and some do a better job of matching data from a variety of experiments than does the PTT equation. The overall structure of the differential equations is usually of the form employed here The total stress is a sum of individual stress modes, each associated with one term in the linear viscoelastic spectrum, and there is an invariant derivative similar in structure to the one in the PTT equation, but with different quadratic nonlinearities in t and Vv. The Giesekus model, for example, which is also widely used, has the following form ... 

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.

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