188. If in a bioreactor, the gas hold up (𝜀) is 0.1 and the average diameter of the air bubbles is 1
mm; then the interfacial area (of the air bubble – liquid interface), per unit reactor volume is:
A. 6000 𝑐𝑚3/𝐼
B. 600 𝑐𝑚3/𝐼
C. 60 𝑐𝑚3/𝐼
D. 6 𝑐𝑚3/𝐼

Explanation:

To calculate the interfacial area (a) of air bubbles in a bioreactor per unit volume, we use the formula:

a=6⋅εdba = \frac{6 \cdot \varepsilon}{d_b}a=db​6⋅ε​

Where:

• $\epsilon$ is the gas hold-up (dimensionless),

• dbd_bdb​ is the average bubble diameter (in cm),

• $a$ is the interfacial area per unit volume (in cm²/cm³ or cm²/mL or cm²/L).

Given:

• Gas hold-up, $\epsilon =0.1$

• Bubble diameter, db=1 mm=0.1 cmd_b = 1 \text{ mm} = 0.1 \text{ cm}db​=1 mm=0.1 cm

Calculation:

a=6×0.10.1=0.60.1=6 cm2/cm3a = \frac{6 \times 0.1}{0.1} = \frac{0.6}{0.1} = 6 \text{ cm}^2/\text{cm}^3a=0.16×0.1​=0.10.6​=6 cm2/cm3

Since 1 cm³ = 1 mL and 1000 mL = 1 L, convert cm²/cm³ to cm²/L:

6 cm2/cm3×1000=6000 cm2/L6 \text{ cm}^2/\text{cm}^3 \times 1000 = 6000 \text{ cm}^2/\text{L}6 cm2/cm3×1000=6000 cm2/L

Conclusion:

The interfacial area per unit reactor volume is:

6000 cm2/L\boxed{6000 \text{ cm}^2/\text{L}}6000 cm2/L​

Correct Answer: A. 6000 cm²/L