Carreau fluid

The Cross and the temperature-dependent Cross-WLF model (42) is an often used GNF-type model accounting for, like the Ellis and Carreau fluids for the viscosity at both low and high shear rates,... 

The viscosity is given by the Carreau fluid equation, which for melts is... 

When the fluid is non-Newtonian, it may not be possible to solve the problem analytically. For example, for the Brrd-Carreau fluid (Bird et al., 1987, p. 171) the viscosity is... 

Solve for the start-up flow of the Carreau fluid and problem described in Problem 10.3. How long does it take to reach steady state ... 

Plot these data in the form of t — / and yu, — / on logarithmic coordinates. Evaluate the power-law parameters for this fluid. Does the use of the Ellis fluid (equation 1.15) or of the truncated Carreau fluid (equation 1.14) model offer any improvement over the power-law model in representing these data What are the mean and maximum % deviations from the data for these three models ... 

Using the concept of a shear thinning fluid, Shuler and Advani [8] investigated the use of a Carreau fluid model to fit the squeeze flow data for a clay/nylon and an APC-2 composite material. Their results were calculated numerically assuming a full-stick flow condition and seem to match their experimental data quite well. In particular, they studied the... 

Keywords squeeze flow, Plytron , full-slip condition, full-stick condition, unidirectional continuous-fiber reinforced composites, shear thinning fluid, Carreau fluid, APC-2, composite laminate, UD laminate. 

Rodrigue et al. (1994) Cylinders, bars, and irregular-shaped rock particles Carreau fluid model Extensive results on drag in pseudoplastic, viscoelastic, and Boger fluids, Re< 50... 

Incorporation of viscosity variations in non-elastic generalized Newtonian flow models is based on using empirical rheological relationships such as the power law or Carreau equation, described in Chapter 1. In these relationships fluid viscosity is given as a function of shear rate and material parameters. Therefore in the application of finite element schemes to non-Newtonian flow, shear rate at the elemental level should be calculated and used to update the fluid viscosity. The shear rale is defined as the second invariant of the rate of deformation tensor as (Bird et at.., 1977)... 

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

For non-Newtonian fluids, any model parameter with the dimensions or physical significance of viscosity (e.g., the power law consistency, m, or the Carreau parameters r,]co and j/0) will depend on temperature in a manner similar to the viscosity of a Newtonian fluid [e.g., Eq. (3-34)]. 

The complete expression for tVDe is given by Darby and Pivsa-Art (1991) as a function of the viscoelastic fluid properties of the fluid (i.e., the Carreau parameters /y0, X, and p). This expression is... 

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). 

Cheng J, Carreau PJ, Chhabra RP. On the effect of wall and bottom clearance on mixing of viscoelastic fluids. In Tatterson GB, Calabrese RV, Penny WR, eds. Industrial Mixing Fundamentals with Applications. New York Amer Inst Chem Eng, 1995 115-122. 

Basic Protocol 2 is for time-dependent non-Newtonian fluids. This type of test is typically only compatible with rheometers that have steady-state conditions built into the control software. This test is known as an equilibrium flow test and may be performed as a function of shear rate or shear stress. If controlled shear stress is used, the zero-shear viscosity may be seen as a clear plateau in the data. If controlled shear rate is used, this zone may not be clearly delineated. Logarithmic plots of viscosity versus shear rate are typically presented, and the Cross or Carreau-Yasuda models are used to fit the data. If a partial flow curve is generated, then subset models such as the Williamson, Sisko, or Power Law models are used (unithi.i). 

Estrogens are synthesized not only in females but also in males. The synthesis of this hormone by cytochrome P450 aromatase in Leydig and Sertoli cells of the testis is well known (Carreau et al., 1999). This cytochrome is also found in the brain, where estrogen is important for imprinting male behavior (Beyer, 1999). There is clear evidence that the role of ER in males is associated with the maintenance of fluid reabsorption in the head of the epididymis (Hess et al., 1997). The loss of ER function in males interferes with the resorp-tive function of efferent ductules, a function that is essential for fertility (Hess, 2000). 

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. 

In addition to the Newtonian fluid, Valsamis and Canedo (70) also used the Carreau constitutive equation to solve the continuity equation (Eq. 10.2-37) together with the following form of the equation of motion... 

We can generalize to include fluids for non-constant viscosity to obtain further dimensionless characteristic values. Two examples are given in Fig. 6.12, and a numerical example for an extruder with a product whose viscosity can be described by the Carreau model is given in Chapter 6. 

Carreau P., Charest G., Corneille J.L., Wdrmeubergartg on nicht-Newtonsche Fluide in Riihrkesseln beim Hazen und Kiihlen, Can. ). Chem. Engng. 44 (1966) 1, p. 3-8... 

Carreau P., Patterson I., Yap C.Y., Mixing of ciscolelastic fluids with helical-ribbon agitators. Can. J. Chem. Engng. 54 (1976) 3, p. 135-142... 

Compare the Carreau viscosity as a function of shear rate (Fig. 10.8 and Problem 10.3) with that of the power-law fluid in Problem 10.2. 

A typical viscosity characteristic of many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels, etc.) is illustrated by the curves labeled structural viscosity in Figures 5.2 and 5.3. These flnids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. This can often be attributed to a reversible structure or network that forms in the rest or eqnilibrinm state. When the material is sheared, the structure breaks down, resnlting in a shear-dependent (shear thinning) behavior. This type of behavior is exhibited by flnids as diverse as polymer solutions, blood, latex emulsions, paint, mud (sediment), etc. An example of a useful model that represents this type of behavior is the Carreau model ... 

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