Question

In power law model for fluid rheology, if the flow behavior index (n) is $<$1, then with increase in shear stress, the apparent viscosity:

• A. remains unchanged.
• B. increases.
• C. decreases.
• D. increases initially followed by a decrease.

Hint:

$n < 1$: Shear-thinning (Pseudoplastic). $n > 1$: Shear-thickening (Dilatant). $n = 1$: Newtonian.

Answer 1

The Correct Option is C

Step 1: Concept
Fluid rheology describes how fluids flow under stress. The Power Law model is $\tau = K (\gamma)^n$.

Step 2: Meaning
Apparent viscosity ($\eta$) is the ratio of shear stress to shear rate: $\eta = K (\gamma)^{n-1}$.

Step 3: Analysis
If $n < 1$, then $(n-1)$ is negative. This means as the shear rate (or shear stress) increases, the viscosity $\eta$ decreases. This behavior is known as shear-thinning or pseudoplastic behavior.

Step 4: Conclusion
For $n < 1$, the fluid becomes "thinner" as it is stressed. Final Answer: (C)