Shear thinning materials cross model

Mathematical models, which can predict the shape of a flow curve of a shear thinning material including lower and upper Newtonian regions, require at least four parameters. The Cross model is one such model ... 

Under conditions of steady fully developed flow, molten polymers are shear thinning over many orders of magnitude of the shear rate. Like many other materials, they exhibit Newtonian behaviour at very low shear rates however, they also have Newtonian behaviour at very high shear rates as shown in Figure 1.20. The term pseudoplastic is used to describe this type of behaviour. Unfortunately, the same term is frequently used for shear thinning behaviour, that is the falling viscosity part of the full curve for a pseudoplastic material. The whole flow curve can be represented by the Cross model [Cross (1965)] ... 

Because the plastic material shows a shear thinning behavior we use the cross model (eq.l) to characterize... 

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