GATE BT 2018 • Q46 MCQ • 2 Marks

Section 4: Bioprocess Engineering and Process Biotechnology

Mass transfer in bioprocesses (kLa)

Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)

Question Statement:

Shear stress versus shear rate behavior of four different types of fluids (I, II, III and IV) are shown in the figure below. Which one of the following options is correct?

Options:

  • (A) I-Newtonian, II-Bingham plastic, III-Dilatant, IV-Pseudoplastic
  • (B) I-Pseudoplastic, II-Dilatant, III-Newtonian, IV-Bingham plastic
  • (C) I-Newtonian, II-Pseudoplastic, III-Bingham plastic, IV-Dilatant
  • (D) I-Newtonian, II-Bingham plastic, III-Pseudoplastic, IV-Dilatant GATE 2018 Biotechnology

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.46)** **1. Governing Concept & Question Classification**: - **Section**: BT - **Question Type**: **MCQ** (2 Marks) - **Topic**: Bioprocess Engineering / Fluid Mechanics (Rheological Classification of Fluids) **2. Detailed Step-by-Step Analysis**: - In fluid mechanics, fluids are classified based on their shear stress ($ au$) versus shear rate ($\dot{\gamma}$) behavior: 1. **Curve I (Linear through origin)**: $ au = \mu \dot{\gamma}$, where dynamic viscosity $\mu$ is constant regardless of shear rate. This represents a **Newtonian fluid** (e.g., water, dilute broth). 2. **Curve II (Linear with a non-zero yield stress $ au_0$)**: $ au = au_0 + \mu_p \dot{\gamma}$. The fluid resists flow until a critical yield stress $ au_0$ is exceeded, after which it flows linearly. This represents a **Bingham plastic** (e.g., sewage sludge, toothpaste). 3. **Curve III (Curving downward, convex to shear stress axis)**: Flow index $n < 1$, where apparent viscosity decreases with increasing shear rate (shear-thinning). This represents a **Pseudoplastic fluid** (e.g., polymer solutions, mycelial broths like *Penicillium*). 4. **Curve IV (Curving upward, concave to shear stress axis)**: Flow index $n > 1$, where apparent viscosity increases with increasing shear rate (shear-thickening). This represents a **Dilatant fluid** (e.g., concentrated cornstarch suspension). - Matching summary: **I-Newtonian, II-Bingham plastic, III-Pseudoplastic, IV-Dilatant**. - **Option-by-Option Evaluation**: - **Option (A) [INCORRECT]**: Swaps dilatant and pseudoplastic. - **Option (B) [INCORRECT]**: Assigns pseudoplastic to curve I. - **Option (C) [INCORRECT]**: Assigns pseudoplastic to curve II. - **Option (D) [CORRECT]**: Precisely assigns I-Newtonian, II-Bingham plastic, III-Pseudoplastic, IV-Dilatant. **3. Final Answer / Verification Summary**: - **Official GATE Answer Key**: **D** - **Scoring Criteria**: +2.0 Marks (Negative marking: -0.67 marks).

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