Problems with non-Linear Material Properties

Most dimensional analyses deal with problems with linear material properties. However, in polymer processing, the viscosity is temperature as well as rate of deformation dependent. In addition, other properties are temperature and pressure dependent. In Example 4.4, one such non-linearity was introduced, namely the temperature dependance of the viscosity. In a similar way the rate of deformation dependence of the viscosity may also be introduced. Choosing the power-law model for the viscosity 

In extrusion problems, the rate of deformation is directly proportional to the rotational speed of the screw. Hence, a characteristic viscosity can be defined as 

In addition, the length of the extruder is directly proportional to the amount of pressure build-up in the pumping section of the extruder. Hence, to fully account for shear thinning as well as L/D of the extruder the operating curves data for an extruder can be significantly reduced. This is done by plotting n4 (throughput) as a function of n3/nio (pressure). 

For the screw characteristic curves presented in Fig. 4.12 and in Fig. 4.13 for a conventional and grooved fed extruder, respectively, the reduced graphs are shown in Fig. 4.14. As can be seen here, each type of extruder can be represented with a single curve for a whole range of rotational speeds. It is to be noted that in this representation the effect of viscous dissipation was not included, which may explain why some of the points fall somewhat outside the fitted lines. 

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