Question

Increasing the agitation rate in a reactor breaks larger bubbles into smaller bubbles. If gas hold-up does not change and the average bubble diameter reduces to half, then the gas-liquid interfacial area:

• A. reduces by 50%
• B. remains unchanged
• C. increases by 100%
• D. increases by 300%

Hint:

Area is inversely proportional to bubble diameter ($a \propto 1/d_{b}$).

Answer 1

The Correct Option is C

Step 1: Concept
Interfacial area ($a$) in a bioreactor is defined as the total surface area of bubbles per unit volume of liquid.

Step 2: Meaning
The relationship is $a = \frac{6 \cdot \epsilon}{d_{b}}$, where $\epsilon$ is gas hold-up and $d_{b}$ is the bubble diameter.

Step 3: Analysis
If gas hold-up ($\epsilon$) is constant and $d_{b}$ becomes $d_{b}/2$:
New area $a' = \frac{6 \cdot \epsilon}{d_{b}/2} = 2 \cdot (\frac{6 \cdot \epsilon}{d_{b}}) = 2a$.
An increase from $a$ to $2a$ represents a 100% increase.

Step 4: Conclusion
Reducing the bubble diameter by half doubles the surface area available for gas transfer. Final Answer: (C)