Phenomenology of shear thinning

It has long been known that the dependence of the non-Newtonian viscosity f7(/c) on shear rate k and the dependence of the dynamic viscosity G co)/co on frequency CO are very nearly equal. This near-equality forms the Cox-Merz rule, which asserts(31) 

Graessley, et al. measured shear thinning in polystyrene n-butylbenzene(33). Seven polymer samples had 19.8 kDa 2.4 MDa six samples had 

Ito and Shishido report r (/c) of 350 kDa polystyrene diethylphthalate using capillary viscometers(38). Polymer weight fractions ranged from 0.15 to 0.53. These results are of particular interest because an unusually wide range of shear rates (up to almost 10 s ) were used, because measurements were made at several temperatures over 20-40°C, and most notably because these materials had a wide (M y/M 2) molecular weight distribution, rather than the narrow distribution used in many other studies. 

In no case was 17 (/c) obtained for k sufficiently large that i (/c) r/oo- These observations therefore do not preclude the possibility that (/c) has an unresolved additive high-frequency relaxation (say, an additional exponential form r/ exp(—a/c )), as opposed to a simple additive constant rjoo. 

The measurements do not determine the low-frequency form. Koenderinck, et al. used their measurements to validate the Cox-Merz rule. 

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Figure 3-2 presents a number of t/D and rj/D curves which summarize the various phenomenological descriptions of how dispersion viscosity depends upon shear rate or time. In many cases, one observes shear thinning (viscosity decreases with increasing shear rate) and thixotropic behavior (viscosity falls with time at a constant shear rate). For this reason, the flow curve is recorded (as shown in Fig. 3-1) by measuring the shear stress both as a function of increasing shear rate and as a function of decreasing shear rate. The hysteresis visible in Fig. 3-1 is typical of thixotropic dispersions. 

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