Model Ellis

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 ... 

The Ellis model (41), is a three-parameter model, in which the non-Newtonian viscosity is a function of the absolute value of the shear stress tensor, x,... 

The three parameters are a, which is the slope of the curve log(/y/— 1) vs. log(r/Tj /2 ) ii/2, which is the shear stress value, where r = t 0/2 and t]0, which is the zero shear viscosity. Thus the Ellis model matches the low shear Newtonian plateau and the shearthinning region. 

The Ellis model is in general given as a shear stress dependent viscosity r/([Pg.547]

Electrophorus, 329 Electrostatic interaction, 275 Elliptic anisotropy, 289 Ellis model, 547 Elongation/Elongational, 459 at break, 454, 475 flow, 532,585 rate, 459 viscosity, 585 at yield, 457 Emeraldine, 344 End-to-end distances, 246, 248 End groups, 7, 8 End of pyrolysis, 765... 

The Ellis (46), Carreau (47), and Cross-Williamson (48) models are three-parameter models. The Ellis model gives the viscosity as a function of T o, the shear rate cr, the parameter ai/2, which is the shear rate for which the viscosity is rio/2, and a dimensionless parameter a. The equation is... 

The power law does not describe the regions of the viscosity curve near y = 0 and y —> oo. To this end, the Ellis model at low shear rates and the Sisko model at high shear rates can be used (2). The models are given by... 

A plot of viscosity vs. shear rate (Figure 5.5) shows that the fluid approaches Newtonian behavior at low shear rates and is shear thinning at higher shear rates, with power law-type behavior. As shown in Figure 5.5, the Ellis model gives a good representation of these data. 

In many cases, it is useful to have a simple mathematical model of the shear stress-shear rate relationship. Equation (4.3) defines Newtonian fluids. For non-Newtonian fluids, with data over a wide range of shear, a good fit gives the Ellis model (Middleman, 1975) ... 

Ellis model See viscosity, non-Newtonian flow Ellis model. 

When the deviations from the power-law model are significant only at low shear rates, it is perhaps more appropriate to nse the Ellis model. 

The two viscosity equations presented so far are examples of the form of equation (1.11). The three-constant Ellis model is an illustration of the inverse form, namely, equation (1.10). In simple shear, the apparent viscosity of an Ellis model fluid is given by ... 

The fitting of the data to the Ellis model, equation (1.15), however, needs a nonlinear regression approach to minimise the sum of squares. The best values are... 

Since dV /dy is positive here, the shear stress for an Ellis model fluid is given by ... 

Zero shear viscosity represents a function of The following Figure 32 relates the Ellis model coefficient to the viscoelastic data. 

Ellis model n. A three-constant model of pseudoplastic flow that merges Newton s law of flow, applicable at very low shear rates, with the power law at high rates and provides a smooth transition between the two. For onedimensional flow the equation is... 

The approximate parameters for other solid materials are collected together in table 2. The data has been read off graphs in Frost and Ashby s book [5] and has been fitted to the Ellis model. 

Table 2 Approximate values of the Ellis model parameters that describe the creep of some solid materials.

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