Question

Among the shear stress versus shear strain rate curves shown in the figure, which one corresponds to a shear thinning fluid?

• A. P
• B. Q
• C. R
• D. S

Hint:

Remember the shapes: - Newtonian $\Rightarrow$ straight line. - Shear-thinning $\Rightarrow$ slope decreases with shear rate (concave down). - Shear-thickening $\Rightarrow$ slope increases (concave up). - Bingham plastic $\Rightarrow$ offset straight line with yield stress.

Answer 1

The Correct Option is B

Step 1: Recall rheology definitions.
- A Newtonian fluid has a linear relation between shear stress $\tau$ and shear strain rate $\dot\gamma$: \[ \tau = \mu \dot\gamma, \] where $\mu$ is constant viscosity. Graphically, this is a straight line through the origin. - A shear-thinning (pseudoplastic) fluid has {apparent viscosity decreasing} with strain rate. That means at low $\dot\gamma$, the slope $\tau/\dot\gamma$ is high, but it {flattens} (slope reduces) as $\dot\gamma$ increases. The curve is concave downward. - A shear-thickening (dilatant) fluid has apparent viscosity increasing with shear rate: slope steepens with $\dot\gamma$ (concave upward). - A Bingham plastic behaves as a rigid solid until a yield stress $\tau_y$ is reached, then flows linearly with slope $\mu$ (offset straight line).
Step 2: Identify curves in the figure.
- Curve P: concave upward (shear-thickening). - Curve Q: concave downward (shear-thinning). - Curve R: straight line through origin (Newtonian). - Curve S: line with intercept (yield stress) before flow (Bingham plastic).
Step 3: Pick the correct one.
Shear-thinning corresponds to curve Q. Final Answer: \[ \boxed{\text{(B) Q}} \]