Non-Newtonian Viscosity Models

Several models have been proposed to describe the dependence of viscosity on shear rate. One of the most used in engineering applications is the two-parameter Ostwald-De Waele model given by (45) 

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 model predicts a zero shear rate viscosity at low values of the shear rate at higher values of k, the model predicts shear-thinning behavior, while r is underpredicted at very high shear rates. 

The Carreau model is a function of r Q, a characteristic time ti, and a dimensionless parameter n. It can be written as 

Though the model predicts very well the variation of viscosity with shear rate for polymer solutions, it slightly underestimates the zero shear rate viscosity. 

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Table 17.1 Material properties of the aqueous solutions of polyvinylpyrrolidone (PVP) and Praestol with parameters for the non-Newtonian viscosity models and properties for air...

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