Impeller zone shear rates

Maximum impeller zone shear rate will be higher in the larger tank, but the average impeller zone shear rate will be lower therefore, there will be a mu(m greater variation in shear rates in a full-scale tank than in a pilot unit. 

The final column shows results for a constant Reynolds number, which requires that the total power decrease on scaleup. This is not normally practical, and therefore we must accept an increased Reynolds number on scaleup. To complete this picture refer to Fig. 15, which shows that the maximum impeller zone shear rate increases, while the average impeller zone shear rate decreases during scaleup. 

Some processes are governed by the maximum impeller zone shear rate. For example, the dispersion of a pigment in a paint depends upon the maximum impeller zone shear rate for the ultimate minimum particle size. However, when constant tip speed is used to maintain this, the other geometric variables must be changed to maintain a reasonable blend time, even though process results on full scale will probably take much longer than those on small scale. 

In order to make the pilot unit more like a commercial unit in macroscale characteristics, the pilot unit impeller must be designed to lengthen the blend time and to increase the low maximum impeller zone shear rate. This will result in a greater range of shear rates than is normally found in a pilot unit. 

As a general rule, the operating speed of the mixer tends to go down, while the peripheral speed of the impeller tends to go up. The speed of the mixer is related to the average impeller zone macroscale shear and thus typically goes down in scaleup while the impeller peripheral speed is often related to the maximum impeller zone macroscale shear rate, see Fig. 5. Out in the rest of the tank (away from the impeller) there another spectrum of shear rates which typically is about a factor of 10 lower than the average impeller zone shear rate. These particular impeller zone shear rates tend to decrease on scaleup. 

Figure 5. Effect of scale-up on maximum and average impellers zone shear rates...

Referring to this table, it is seen that if constant power per unit volume is used as a parameter, then maximum impeller zone shear rates go up while the pumping capacity system goes down. Another column shows that a constant impeller tip speed, the power per unit volume goes down drastically and the pumping capacity goes down still further. 

In general, small scale models have too much pumping capacity and too little impeller zone shear rate to be typical of the performance to be expected in a full scale prototype. Thus, it is normally necessary to purposely scale down the pumping capacity, and increase the shear rate on small scale equipment to more closely duplicate the performance which will be expected on full size units. 

There is also a tendency for the maximum impeller shear rate to go up while the average impeller zone shear rate will go down on scaleup. In... 

In duplicating maximum impeller zone shear rates on a small scale, there may be a very severe design problem in the mechanics of the mixer, or the shaft speed, mechanical seals and other things. This means that careful consideration must be given to the type of runs to be made and whether the pilot plant or the semi-work-scale equipment must be available at all times to duplicate the maximum impeller zone shear rates in the plant or whether this sort of data will be obtained on a different type of unit dedicated to that particular variable. 

Maximum impeller zone shear rate (relative) 1.00 1.30 1.30 1.15 1.00... 

MIZSR Maximum impeller zone shear rate... 

---