Carreau model modified

Both the Carreau and the Cross models can be modified to include a term due to yield stress. For example, the Carreau model with a yield term given in Equation (2.16) was employed in the study of the rheological behavior of glass-filled polymers (Poslinski et al., 1988) ... 

The modified Carreau model and the modified Ellis model are limited to relatively low values of shear rates and shear stresses, reflectively, whereas the modified Ostwald-de Waele power-law model is applicable to the higher-shear-rate region where the data points fall in a straight line on the log-log plot of -q X MFI versus y/MFL... 

Table 6.5 Rheological Parameters of the Modified Carreau Model [Eq. (6.1)] for Different Generic-Type Thermoplastics...

Tables 6.S-6.8 list the model constants and the range of applicability based on the modified Carreau model, the modified Ellis model, the modified Ostwald-de Waele power-law model, and the General Rheological [11] model, respectively, for the master rheograms of most of the polymers discussed in Chapter 4.

It can be seen from Table 6.10 that the damping constant m lies between 0.13 and 0.2, in line with the findings of Wagner [15] for polymer melts. This fact can then be used to generate the unified normal stress difference curves for other polymers [16-18] whose parameter values for the modified Carreau model fit of unified viscosity data are given in Table 6.1. Figures 6.2-6.13 show die predicted normal stress difference curves for different polymer types. The solid line shows the plot generated for a median value of m = 0.16 and the band... 

The rheological models for unified conq>lex viscosity versus frequency curves can be ea y written based on the modified Cox-Mertz rule discussed in Quarter 5. Thus, using Eq. (5.5), the modified Carreau model for complex viscosity can be written from Eq. (6.1) as... 

In order to illustrate the method for determining the shear-rate conditions for blending, we choose LLDPE A and LDPE C. Instead of the power-law model used in Eq. (8.77), we choose the modified Carreau model as given in Ref. 61 whose parametric values are tabulated in Thble 8.8b. Thus, comparing the shear... 

Normal stress difference data are generally collected on viscometers which have an effective upper limit of shear rate not greater than 10/s. Thus, the relationship between the viscosity function and the normal stress difference function is sought in the low-shear-rate region [16]. The modified Carreau model as given by Eq. (6.1) is the obvious choice for selecting this relationship through its use in Eq. (6.10). 

Apparent viscosity-shear rate data of food polymer dispersions have been reviewed by Launay et al. (1986), Lopes da Silva and Rao (1992) and others. The general log versus log y curve, discussed in Chapter 2, has been used to characterize food polymer dispersions. For example, Lopes da Silva et al. (1992) found that both the modified Carreau and the Cross models, wherein the infinite shear viscosity was considered to be negligible, described the apparent viscosity-shear rate data of locustbean (LB)... 

It should be noted that the effects of fillers may be incorporated into the cure and shear-rate effects. The main forms of combined-effects model consist of WLF, power-law or Carreau shear effects, Arrhenius or WLF thermal effects and molecular, conversion or empirical cure effects. Nguyen (1993) and Peters et al. (1993) used a modified Cox-Merz relationship to propose a modified power-law model for highly filled epoxy-resin systems. Nguyen (1993) also questions the validity of the separability of thermal and cure effects in the derivation of combined models. 

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