Model Carreau

Step 4 - update the value of viscosity (r/) using an appropriate rheological equation (e.g. temperature-dependent form of the Carreau model given as Equation (5.4)). 

Example 5.1 Applying the Carreau model to polypropylene, the following constants are known at 190°C. 

The Carreau model (Carreau, 1972) is very useful for describing the viscosity of structural fluids ... 

Figure 3-8 Viscosity data and Carreau model fit of polyacrylamide solutions. (From Darby and Pivsa-Art, 1991.)...

If r]oo <3C ( /. j/o), the Carreau model reduces to a three-parameter model ( 0,k, and p) that is equivalent to a power law model with a low shear limiting viscosity, also known as the Ellis model ... 

A stress-dependent viscosity model, which has the same general characteristics as the Carreau model, is the Meter model (Meter, 1964) ... 

The Yasuda model (Yasuda et al., 1981) is a modification of the Carreau model with one additional parameter a (a total of five parameters) ... 

ARe>s is the Reynolds number based on the solvent properties, /zs is the solvent viscosity, D is the pipe diameter, F is the velocity in the pipe, and A is the fluid time constant (from the Carreau model fit of the viscosity curve). 

Performing numerical simulations of the extrusion process requires that the shear viscosity be available as a function of shear rate and temperature over the operating conditions of the process. Many models have been developed, and the best model for a particular application will depend on the rheological response of the resin and the operating conditions of the process. In other words, the model must provide an acceptable viscosity for the shear rates and temperatures of the process. The simple models presented here include the power law. Cross, and Carreau models. An excellent description of a broad range of models was presented previously by Tadmor and Gogos [4]. 

Fitting a Bird-Carreau model to viscosity data. Table 7.5 shows the measurements of Ballenger et. al [5] of the viscosity as a function of shear rate for polystyrene at 453 K. 

For this particular data we can assume that Voo = 0, which reduces the Bird-Carreau model to,... 

Fit a Bird-Carreau model to the viscosity curve given in Fig. 7.24. To solve this problem, download a non-linear fitting program from the world wide web. 

The viscosity was modeled using a Carreau model with an Arrhenius temperature... 

Evaluation of GNF Fluid Constants from Viscometric Data Using the flow curve of Chevron/Philips 1409 MI = 50 LDPE in Appendix A, calculate the parameters of the Power Law, Cross and Carreau models. 

A low density polyethylene was used with Carreau model parameters t]0 = 19,500Pa s X = 5.5 s n 0.52. The screw speed was 100 rpm and the pertinent geometric parameters appear in Fig. 10.18 with their numerical values are listed in Table 10.1... 

Fig. 10.47 The effect of the Power Law index in the Carreau model, and the melt-pool size for a characteristic model wedge with e/h — 3 and ot= 15° on the non-Newtonian qp/qd parameters. [Reprinted hy permission from L. N. Valsamis and E. L. Canedo, Mixing in the Farrel Continuous Mixer in Mixing and Compounding of Polymers, I. Manas-Zloczower and Z. Tadmor, Eds., Hanser, Munich, 1994.]...

Carreau model parameter Carreau model parameter Zero shear rate viscosity Arrhenius law parameter Reference temperature Density Specific heat Thermal conductivity... 

Fig. 13.27 Deformation of PS at different displacements 0, 22, 33, 44, and 55 mm. (a) Experimental, (b) Calculated using the Carreau model (T — 230°C). [Reprinted by permission from E. Vos, H. E. H. Meijer, and G. W. M. Peters, Multilayer Injection Molding, Int. Polym. Process., 6, 42 (1991).]...

We acknowledge Dr. Dongyun Ren, who, with the help of Mr. B. J. Jeong and Drs. J. Guo and Linjie Zhu, evaluated, via mathematical regression, the Power Law model, Carreau model, and Cross model parameters. 

Data appeared in Appendix A of First Edition. Power Law model Carreau model ... 

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