57. You wish to reduce the maximum shear rate in your reactor (given by impeller tip speed),
without changing the power consumption (agitator power). For this, you will:
A. Increase the diameter of impeller and reduce the RPM
B. Reduce the diameter of impeller and increase the RPM
C. Reduce RPM only
D. Reduce diameter of impeller only

Introduction:

In reactor systems, controlling the shear rate is crucial for maintaining efficient mixing and avoiding damage to sensitive materials. The maximum shear rate is influenced by the impeller tip speed, which is determined by both the impeller diameter and the rotational speed (RPM). Reducing this shear rate while keeping the power consumption constant can be tricky, but with the right adjustments to the impeller configuration, it’s possible. This article explores the optimal way to reduce shear rate without changing the power consumption of the reactor.

Shear Rate and Power Consumption in a Reactor

The shear rate in a reactor refers to the rate at which the material is deformed due to the applied forces from the impeller. It is proportional to the tip speed of the impeller, which depends on the impeller’s diameter and rotational speed.

• Impeller Tip Speed (StS_tSt​): St=πDNS_t = \pi D NSt​=πDN, where:

  • $D$ is the diameter of the impeller

  • $N$ is the rotational speed (RPM)

The power consumption of the agitator (P) is given by the formula:

                                         P∝N3D5P

Where:

• P is the power consumed by the agitator

• N is the rotational speed (RPM)

• D is the diameter of the impeller

How to Reduce Shear Rate Without Changing Power Consumption

To reduce the maximum shear rate, we need to decrease the impeller tip speed. However, we must do this while maintaining the same power consumption. The key here is to adjust both the impeller diameter and RPM in a balanced way. Let’s break down the options:

A. Increase the Diameter of Impeller and Reduce the RPM

• Increasing the impeller diameter increases the shear rate because it directly increases the tip speed. However, reducing the RPM compensates for this by decreasing the tip speed.

• The key here is balancing the increase in diameter with a decrease in speed, so the power consumption remains constant. This can indeed reduce the shear rate without changing power consumption.

B. Reduce the Diameter of Impeller and Increase the RPM

• Reducing the impeller diameter decreases the shear rate but requires an increase in RPM to maintain the same tip speed. However, increasing RPM increases power consumption due to the N3N^3N3 dependency in the power equation.

• This adjustment would lead to increased power consumption rather than maintaining it.

C. Reduce RPM Only

• Reducing RPM alone will decrease the tip speed and shear rate, but it will also reduce the power consumption because the power is proportional to N3N^3N3. This does not keep the power consumption constant, which is one of the requirements.

D. Reduce Diameter of Impeller Only

• Reducing the diameter of the impeller decreases the shear rate but also decreases the tip speed. To keep the power consumption constant, this adjustment would typically require an increase in RPM, which leads to an increased shear rate due to the faster impeller motion.

Conclusion:

The best approach to reducing the maximum shear rate in the reactor, while maintaining constant power consumption, is to increase the diameter of the impeller and reduce the RPM. This allows you to balance the tip speed and shear rate without altering the power requirements.

Answer:

A. Increase the diameter of impeller and reduce the RPM