Shear-Thinning Effect and the Power Law Equation

Flowability of plastics is largely determined by the dependence of viscosity on shear rate. Viscosity of water, for example, does not change with shear rate. When water moves through a capillary, fast or slow, its viscosity is same. In a forced oscillation rheometer, parallel plates immersed in water can move fast or slow, but the viscosity of water remains still the same. Therefore, a plot of viscosity against shear rate looks as a flat straight line, parallel to the horizontal axis (Fig. 17.1). 

These polymer fluids are typically called non-Newtonian or nonlinear fluids, as they show a decrease of viscosity with increasing fluid velocity (shear rate). This is also known as shear thinning. This behavior results from the fact that the polymer molecules are long and have many contact points interacting with each other, or entanglements. These molecular interactions determine the viscosity of polymers. When one moves them slowly, viscosity is still relatively high. For example, it is 

The linear part of the double logarithmic plot is described by the following equation (the power law equation)  

Here A is a time constant and is often interpreted as the relaxation time of the polymer, particularly in the filled composites. It significantly increases with wood flour content in filled high density polyethylene (HDPE) [4], The authors suggested that it is a result from the increased relaxation time of the reduced amount of polymer in the filled composite. 

The relaxation time in rheology, and particularly in rotational rheometry, is a measure of the rate at which the viscoelastic fluid changes in response to the change in flow due to the oscillatory movements of the fluid. Typically, an apparent relaxation time is defined as the time for the disturbances to decrease by a factor of 1/e, that is, 0.368. 

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The Power-Law Index of Some Neat Plastics As it was explained in the section Shear-thinning Effect and the Power Law Equation, the higher the deviation of a molten plastic from Newtonian behavior, the lower its power-law index and the steeper the dependence of its viscosity on shear rate. The lower the power-law index, the more sensitive the shear viscosity to flow speed. As it will be shown in this chapter later, the lower the quality of a regrind, the lower (often) its power-law index. As can be seen from Tables 17.4 and 17.5, PVC, PS, ABS, and PMMA have particularly low power-law index compared to PET or PE, hence, that lowers the window of processability for the former plastics in terms of speed. Both the... 

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