Bingham Plastic Model

Definition

The Bingham Plastic Model describes a type of non-Newtonian fluid that behaves as a solid until a certain yield stress is exceeded, after which it flows like a viscous fluid. This model helps in understanding how materials like toothpaste or certain slurries require an initial force to start flowing, connecting the concept of yield stress to fluid behavior.

5 Must Know Facts For Your Next Test

1. The Bingham Plastic Model is defined by the equation: $$ au = au_y + u \frac{du}{dy}$$, where $$\tau$$ is the shear stress, $$\tau_y$$ is the yield stress, and $$\nu$$ is the plastic viscosity.
2. In this model, below the yield stress, the fluid does not flow; this is different from Newtonian fluids, which flow regardless of applied stress.
3. Common examples of Bingham plastics include mayonnaise, mud, and certain types of paints, all requiring a specific amount of force before they start to move.
4. Understanding the Bingham Plastic behavior is crucial in industries where precise control over the flow of materials is necessary, such as food processing and construction.
5. The Bingham Plastic Model helps predict how materials will behave under different loading conditions, influencing design and engineering decisions.

Review Questions

• How does the yield stress in the Bingham Plastic Model influence the flow behavior of materials?
  • Yield stress is critical in the Bingham Plastic Model because it defines the threshold at which a material transitions from a solid-like state to a flowing state. When stress applied to the material exceeds this yield stress, it begins to flow with a viscosity that can be determined. Understanding this behavior allows engineers to predict when and how these materials will start to move under varying conditions.
• Compare and contrast the Bingham Plastic Model with Newtonian fluids regarding their response to applied stress.
  • Unlike Newtonian fluids, which have a constant viscosity regardless of shear stress, Bingham plastics require an initial yield stress to be overcome before they begin to flow. Once this yield point is surpassed, Bingham plastics exhibit linear behavior in their shear stress versus shear rate relationship, characterized by constant plastic viscosity. This distinction is essential for designing systems where controlled flow is needed.
• Evaluate the implications of using the Bingham Plastic Model in industrial applications involving non-Newtonian fluids.
  • Using the Bingham Plastic Model in industrial applications allows engineers to accurately forecast how non-Newtonian fluids behave under different conditions. For instance, knowing the yield stress helps in designing equipment like mixers or pumps that handle materials such as slurries or pastes effectively. This model’s predictive capabilities can lead to enhanced efficiency and safety in processes like construction and food production, where material properties play a significant role in overall performance.

Related terms

Yield Stress: The minimum stress required to initiate flow in a Bingham plastic material.

Viscosity:

A measure of a fluid's resistance to deformation or flow, which can change depending on the stress applied for non-Newtonian fluids.

Thixotropic: A property of certain non-Newtonian fluids that become less viscous over time under constant shear stress.