Question

Suppose, P1 is the milk pressure before the first stage and P2 is the milk pressure before the second stage. Best homogenization will be achieved when:

• A. P2 P1 = 0.2
• B. P2 P1 = 0.6
• C. P2 P1 = 1.0
• D. P2 P1 = 1.4

Hint:

In a two-stage homogenizer, the second-stage pressure should be set to approximately 15--20% of the total pressure (\(P_2 / P_1 = 0.2\)) to break up fat globule clusters without reducing first-stage efficiency.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In high-pressure milk homogenization, a two-stage homogenizer is often used to prevent the re-coalescence of fat globules.
The first stage breaks up the fat globules using high pressure, while the second stage applies a lower backpressure to disperse any clusters that form immediately after the first stage.

Step 2: Detailed Explanation:
In a two-stage homogenizer, the total pressure \(P_1\) is applied across the first stage, where the primary size reduction occurs.
The second-stage pressure \(P_2\) acts as a controlled backpressure.
The second-stage valve provides sufficient shear to disrupt fat globule clusters without causing additional cavitation.
To optimize this process and prevent the re-coalescence of fat globules, the second-stage pressure is typically maintained at 15% to 20% of the total operating pressure.
This relationship can be expressed as:
\[ \frac{P_2}{P_1} \approx 0.15 \text{ to } 0.20 \] For example, if the total pressure \(P_1\) is 200 bar, the second-stage pressure \(P_2\) is set to approximately 40 bar.
This gives a ratio of:
\[ \frac{P_2}{P_1} = \frac{40}{200} = 0.2 \] Setting \(P_2\) too high (such as a ratio of 0.6 or 1.0) reduces the pressure drop across the first stage, which decreases the energy available for primary size reduction.
Setting it too low reduces the effectiveness of cluster dispersion.

Step 3: Final Answer:
Therefore, the best homogenization is achieved when \(P_2 / P_1 = 0.2\).