Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
Which of the following events occur during the stationary phase of bacterial growth?
P. Rise in cell number stops
Q. Spore formation in some Gram-positive bacteria such as Bacillus subtilis
R. Cell size increases in some Gram-negative bacteria such as Escherichia coli
S. Growth rate of bacterial cells nearly equals their death rate
T. Decrease in peptidoglycan crosslinking
(A) P, Q and S only (B) P, S and T only (C) Q, R and S only (D) P, R and T only
Options:
(A) P, Q and S only
(B) P, S and T only
(C) Q, R and S only
(D) P, R and T only
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.29)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (1 Mark)
- **Topic**: Downstream Processing / Solid-Liquid Separation (Dead-End Filtration & Darcy's Law)
**2. Detailed Step-by-Step Derivation**:
- In downstream processing, dead-end cake filtration is governed by **Darcy's Law** and the Ruth cake filtration equation:
$\frac{dV}{dt} = \frac{A \Delta P}{\mu (R_m + R_c)}$
where:
- $\frac{dV}{dt}$ is the volumetric filtration rate.
- $A$ is the filtration surface area.
- $\Delta P$ is the total pressure drop across the filter medium and cake.
- $\mu$ is the dynamic viscosity of the filtrate/solution.
- $R_m$ is the filter medium resistance.
- $R_c$ is the specific cake resistance ($R_c = \frac{\alpha c V}{A}$).
- Inspecting the mathematical dependence on viscosity $\mu$:
$\text{Rate of filtration} \propto \frac{1}{\mu}$
- The rate of filtration is **inversely proportional to the viscosity of the solution**.
- **Option-by-Option Evaluation**:
- **Option (A) [INCORRECT]**: Rate is directly proportional to $\Delta P$ (first power), not the square root $\sqrt{\Delta P}$.
- **Option (B) [INCORRECT]**: Rate is directly proportional, not inversely proportional, to pressure drop $\Delta P$.
- **Option (C) [CORRECT]**: Rate of filtration is inversely proportional to the first power of solution viscosity ($\propto 1/\mu$).
- **Option (D) [INCORRECT]**: It depends on $\mu^{-1}$, not $\mu^{-2}$.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **C**
- **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).
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