# DBT JRF 2022 — Question 102

Exam: DBT JRF 2022 · Section: B · Topic: Bioprocess Engineering › Gas-Liquid Mass Transfer - Interfacial Area · Difficulty: Medium

## Question

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:

## Options

- **A.** 6000 cm³/l
- **B.** 600 cm³/l
- **C.** 60 cm³/l
- **D.** 6 cm³/l

## Answer

Option A

## Explanation

Interfacial area per unit volume in bubble column: For a bubble column bioreactor: $a = \frac{6\varepsilon}{d_b}$ where $a$ = interfacial area per unit volume (m⁻¹ or cm⁻¹), $\varepsilon$ = gas hold-up (fraction), $d_b$ = bubble diameter. Given: $\varepsilon = 0.1$ (10% gas hold-up), $d_b = 1\,\text{mm} = 0.1\,\text{cm}$ $a = \frac{6 \times 0.1}{0.1\,\text{cm}} = \frac{0.6}{0.1} = 6\,\text{cm}^{-1}$ Converting to cm²/L (multiply by 1000 mL/L... actually per mL to per L): $6\,\text{cm}^{-1} = 6\,\text{cm}^2/\text{cm}^3 = 6000\,\text{cm}^2/\text{L}$ Or in m²/m³: $6\,\text{cm}^{-1} = 600\,\text{m}^{-1} = 600\,\text{m}^2/\text{m}^3$ Answer: Interfacial area $a = 6\,\text{cm}^{-1}$ (or 600 m²/m³).

Source: https://mypyqbuddy.com/questions/if-in-a-bioreactor-the-gas-hold-up-6a104cd5920734408bc0c775