Viscosity Krieger-Dougherty relation

FIGURE 11.13 Viscosity vs. volume solids loading. Krieger-Dougherty relation. For small loading (<5%) it is linear as predicted by Einstein. 

In Figure 7.7, the plots of r vs. < > calculated from Simha s Eq 7.24, Mooney s Eq 7.28, and Krieger-Dougherty s Eq 7.8 are compared with the empirical curve-htted relation, Eq 7.5. For all the relations, the intrinsic viscosity [t]] = 2.5 was used. However, to optimize the fit, different values for the maximum packing volume fraction, ( ) = 0.78, 0.91, and 0.62 respectively, had to be used. Detailed analysis of Thomas data made it possible to conclude... 

The viscosity data of Figure 5 can be reduced to a single curve by replotting nr as a function of /o indicating that the relative viscosity at zero shear rate is a unique function of /0 A relation between dispersion viscosity and

0, derived by Mooney (5) and modified, by Krieger and Dougherty (6), gives... 

The relative viscosity is related to the volume fraction g> by the Dougherty- Krieger equation [40] for hard spheres,... 

To derive a more general relation for the phase inversion concentration, one may start by computing r](A) = t BT r( A) t (B) = tiArij( B), where rjr is the relative viscosity. The latter dependence can be expressed as (Krieger and Dougherty 1959)... 

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