Blending Correlations for Laminar and Turbulent Flow

The results for blending for motionless mixers can be correlated by plotting coefficient of variation reduction CoVr versus L/D. In laminar flow there is no effect of viscosity, flow rate or initial CoV on these correlations. CoVr is usually found to correlate with the L/D in an exponential form. 

1 Laminar Flow Effective Shear Rate. In laminar flow, the fluids are often shear thinning (i.e., the viscosity decreases with increasing shear rate). The apparent or effective shear rate in an empty pipe with Newtonian fluids is 

For motionless mixers in laminar flow, the shear rate is higher. This and the extra surface area are what contribute to the higher pressure drop. Table 7-7 gives some 

Mixing Performance for a 12HEV3 Static Mixer 3D, 0.1% Centerline Injection 

With this apparent or effective shear rate a rheogram relating effective viscosity to shear rate can be used to calculate an effective viscosity for pressure drop calculations. For another experimental approach, see Jaffer and Wood (1998). 

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