Question

Fluids that exhibit a yield stress and a flow behaviour index of 1 are referred to as

• A. Newtonian fluids
• B. Shear thinning fluids
• C. Dilatant fluids
• D. Bingham plastic

Hint:

Bingham plastic: $\tau = \tau_0 + \mu_p \dot{\gamma}$ (Yield stress present + linear flow with $n=1$, e.g., toothpaste, tomato paste, chocolate melt).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Rheological flow curves are mathematically modeled using generalized constitutive equations like the Herschel-Bulkley model.

Step 2: Key Formula or Approach:
The Herschel-Bulkley equation is expressed as:
\[\tau = \tau_0 + K \dot{\gamma}^n\] where $\tau$ is shear stress, $\tau_0$ is yield stress, $K$ is consistency index, $\dot{\gamma}$ is shear rate, and $n$ is the flow behavior index.
When yield stress is present ($\tau_0 > 0$) and the flow behavior index is exactly $n = 1$, the model simplifies to the Bingham plastic model:
\[\tau = \tau_0 + \mu_p \dot{\gamma}\] where $\mu_p$ is plastic viscosity.

Step 3: Detailed Explanation:
Newtonian fluids have $\tau_0 = 0, n = 1$; shear thinning fluids have $n < 1$; dilatant fluids have $n > 1$.

Step 4: Final Answer:
Hence, fluids with a yield stress and $n = 1$ are Bingham plastic fluids.