Rheological Models for Polymer Melt Flow

When log (viscosity) is plotted against log (shear rate) or log (shear stress) for the range of shear rates encounterd in many polymer processing operations, the result is a straight line. This suggests a simple power law relation of the type 

It is common practice nowadays to express the apparent viscosity as a function of the shear rate, This may be obtained using the deflnition of apparent viscosity r a as the ratio of shear stress to shear rate, ie 

Equations (5.21), (5.22) and (5.23) are useful for the high strain rates experienced in injection moulding or extrusion but unfortunately they do not predict the low strain rate situation very well where plastic melts tend towards Newtonian behaviour (ie n -) 1). This is illustrated in Fig. 5.7. 

Carreau proposed an alternative equation to overcome this problem. It has the form 

It may be seen that when y 1, this equation reduces to the Power Law (5.23) but as shown in Fig. 5.7, it also predicts the low shear rate situation very well. 

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Fig. 5.6 Flow in an Annular Slot 5.4 Rheological Models for Polymer Melt Flow...

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