Give an example of Bingham plastic fluid.
The correct answer and explanation is :
A classic example of a Bingham plastic fluid is toothpaste.
Explanation:
A Bingham plastic fluid is a type of non-Newtonian fluid that behaves as a solid at low shear stress but flows like a fluid once a certain threshold (called the yield stress) is exceeded. The distinguishing feature of Bingham plastics is their requirement of an initial stress to begin flowing. Below this yield stress, they do not flow or deform, behaving as if they are rigid solids. Once the yield stress is surpassed, the fluid flows and exhibits characteristics of a viscous fluid, with its flow rate increasing as the shear stress increases.
Toothpaste is a great everyday example of a Bingham plastic fluid. When you apply a small force to the toothpaste tube, it doesn’t immediately flow out; this is because the toothpaste behaves like a solid until a certain stress (the yield stress) is applied. Once the yield stress is overcome, the toothpaste begins to flow out of the tube in a controlled manner. This property makes it easier to control the amount of toothpaste dispensed.
The behavior of Bingham plastics is typically described by the Bingham plastic model, which is represented by the equation:
$$
\tau = \tau_y + \eta \left( \frac{du}{dy} \right)
$$
Where:
- $\tau$ is the shear stress,
- $\tau_y$ is the yield stress (the minimum stress required to initiate flow),
- $\eta$ is the plastic viscosity (a measure of how much resistance the fluid offers once flowing),
- $\frac{du}{dy}$ is the shear rate (rate at which the fluid layers are moving relative to each other).
Toothpaste typically requires a moderate amount of force to flow out of the tube but does not flow excessively, offering controlled dispensing. This behavior makes Bingham plastics like toothpaste useful in various applications where controlling the flow is crucial, such as in coatings, lubricants, and other household products.