Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
Which one of the following statements is correct about Reynolds Number (NRe) in
a stirred tank bioreactor?
Options:
(A) NRe is independent of the viscosity of the medium
(B) In laminar flow, mixing time increases with an increase in NRe
(C) NRe is inversely proportional to the impeller speed
(D) In turbulent flow, mixing time is independent of NRe
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2024 Q.14)**
**1. Governing Concept**:
- **Topic**: Bioreactor Fluid Mechanics & Mixing Time
- The impeller Reynolds number is defined as:
$N_{\text{Re}} = \frac{\rho N D_i^2}{\mu}$
- In the fully turbulent regime ($N_{\text{Re}} > 10^4$), the dimensionless mixing time $N \cdot t_m$ is constant for a given geometric configuration.
- Consequently, at a fixed impeller rotational speed $N$, the mixing time $t_m$ becomes independent of the Reynolds number $N_{\text{Re}}$.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: $N_{\text{Re}}$ is inversely proportional to dynamic viscosity $\mu$.
- **Option (B) is INCORRECT**: In laminar flow, mixing time decreases as $N_{\text{Re}}$ increases.
- **Option (C) is INCORRECT**: $N_{\text{Re}}$ is directly proportional to impeller speed $N$, not inversely.
- **Option (D) is CORRECT**: In fully developed turbulent flow, inertial forces dominate viscous forces, making the dimensionless mixing product and $t_m$ (at constant $N$) independent of $N_{\text{Re}}$.
**3. Final Answer**:
- **Correct Choice**: **D**
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