Chloe Zhang
In materials science, a Bingham plastic is a viscoplastic material that behaves like a solid at low stresses but flows as a fluid at high stress. It is named after Eugene C. Bingham, who first proposed the model in 1916. The Bingham plastic model is used to describe the flow behaviour of non-Newtonian fluids, which do not follow Newton's laws due to the presence of particles or large molecules that create a weak solid structure. This model is commonly used in hydraulic analysis and drilling engineering to calculate pressure drops and predict flow behaviour in piping networks. The model has also been applied to the handling of slurries and the treatment of drilling fluids, where it helps identify contamination.
| Characteristics | Values |
|---|---|
| Definition | A viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress |
| Use | Used as a common mathematical model of mud flow in drilling engineering, and in the handling of slurries |
| Examples | Toothpaste, drilling fluids, cement slurries |
| Mathematical Form | Proposed by Eugene C. Bingham in 1916 |
| Flow | Does not flow until a certain value, the yield stress, is reached |
| Shear Stress | Defined in the Bingham Plastic Model as (PV)SR + YP |
| Plastic Viscosity | A measure of how the velocity changes with distance |
| Non-Newtonian Fluids | The Bingham Plastic model is one of the most common viscosity models used in hydraulic analysis |
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The Bingham Plastic Model
> Shear stress = (PV)SR + YP
Where PV represents the viscosity at a very high shear rate, SR is the shear rate, and YP is the yield point or yield stress, which is the minimum stress required for the fluid to flow. This equation illustrates that the shear stress increases linearly with the shear rate, but the fluid will not flow until the yield stress is reached.
The model is useful for treating drilling fluids and understanding the nature of contamination in the fluid. For instance, an increase in plastic viscosity may indicate solid contamination, while an increase in the yield point could suggest chemical contamination. However, the model is not suitable for calculating pressure losses or matching viscosities over a large range of shear rates.
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Yield Point
The yield point (YP) is a crucial characteristic of Bingham plastic fluids, representing the minimum stress required for the fluid to transition from a rigid state to a flowing state. This threshold stress, also known as the yield stress, is a defining feature of Bingham plastics. Below the yield point, the fluid behaves as a solid, exhibiting no flow or deformation. Once the yield stress is exceeded, the fluid begins to flow, and its behaviour transitions from rigid to viscous.
Mathematically, the yield point is expressed as the intercept on the shear stress axis in a plot of shear stress against shear rate. In other words, it is the value of shear stress when the shear rate is zero, denoted as τy or YP. This non-zero shear stress at zero shear rate is referred to as gel strength, signifying that an initial force is necessary to deform and mobilise the fluid.
The yield point is not merely a theoretical concept but has practical implications in various applications. For instance, in drilling engineering, an increase in the yield point may indicate chemical contamination or degradation of the chemicals used to maintain the yield point. This information is valuable for optimising drilling processes and maintaining the integrity of drilling fluids.
The yield point is calculated using specific equations, such as τy = θ300 − μp, where τy represents the yield point, and the variables θ300 and μp are obtained from measurements at a specific rotary speed of a Fann VG meter. This equation is particularly applicable when the rotary speed is set at 300 rpm.
It is important to recognise that the Bingham plastic model, while useful, has limitations. It tends to overestimate the gel strength of the fluid and does not accurately describe the flow behaviour of Bingham plastic fluids in the low-shear rate region. This limitation has prompted ongoing research to develop more accurate models that capture the complex behaviour of these fluids at low shear rates.
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Shear Stress
In the case of Bingham plastic fluids, shear stress plays a crucial role in their unique behaviour. Bingham plastics are a type of viscoplastic material that exhibits both solid and fluid-like properties, depending on the stress applied. At low stresses, they behave as rigid solids, but when the stress reaches a certain threshold, they start to flow as viscous fluids. This threshold stress is known as the yield stress or yield point (YP).
The Bingham plastic model describes the relationship between shear stress and the flow behaviour of these fluids. It is a linear model that illustrates how the shear rate (the change in velocity with distance) increases as shear stress increases. In other words, once the yield stress is exceeded, the fluid begins to flow, and the faster the shear stress increases, the faster the fluid flows.
However, it's important to note that the Bingham plastic model has limitations. It does not accurately describe the flow behaviour of Bingham plastic fluids in the low-shear rate region. In this region, the model overestimates the gel strength of the fluid, which refers to the initial force required to deform and mobilise the fluid. This limitation has led to the development of other models, such as the Herschel-Bulkley model, to better describe the complex behaviour of viscoplastic fluids.
In practical applications, such as drilling engineering, the Bingham plastic model is valuable for understanding and treating drilling fluids. It helps engineers predict how the fluid will behave under different shear stress conditions, ensuring the fluid can effectively suspend and transport cuttings and solids during the drilling process. By considering the shear stress and yield point, engineers can optimise the drilling fluid's composition and viscosity to prevent issues like excessive pressure surges or solids settling.
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Non-Newtonian Fluids
One type of non-Newtonian fluid is a Bingham plastic fluid. These fluids behave as a solid when under low stress and only start to flow (act like a liquid) when the applied stress exceeds a certain threshold value, known as the yield stress. This behaviour is often described as a 'yield value' or 'yield strength', and it is a key characteristic that distinguishes Bingham plastics from other fluid types. Once the yield stress is overcome, Bingham plastic fluids exhibit fluid-like behaviour, with their viscosity decreasing as the applied shear rate increases.
Everyday examples of Bingham plastic fluids include toothpaste, certain types of ketchup, and some types of drilling muds used in oil drilling operations. These substances remain in place or move slowly when under low stress, but flow more easily when squeezed or stirred with sufficient force. The yield stress in these examples prevents the fluid from flowing or deforming too easily, allowing it to maintain its shape or position until sufficient force is applied.
The mathematical representation of the flow behaviour of a Bingham plastic fluid is given by the Bingham plastic model, which combines a linear relationship between shear stress and shear rate (similar to Newtonian fluids) with the concept of a yield stress. This model is often used to describe and predict the behaviour of these complex fluids in engineering and scientific applications, helping to design systems and processes that involve their handling, transport, or use.
The behaviour of Bingham plastic fluids has important implications in various industries. For example, in the food industry, understanding the flow behaviour of products like ketchup or mayonnaise can inform packaging design and dispensing systems. In oil drilling, the yield stress of drilling muds is crucial for maintaining the stability of the borehole and suspending cuttings. In manufacturing processes, knowledge of non-Newtonian fluid behaviour is essential for effective mixing, pumping, and processing of materials with complex flow characteristics.
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Viscosity
Bingham plastic fluids are a type of non-Newtonian fluid, meaning they do not follow Newton's laws of viscosity. These fluids exhibit unique flow characteristics and are used in various industrial applications. The Bingham plastic model describes the flow behaviour of these fluids and is particularly useful for treating drilling fluids.
The viscosity of a Bingham plastic fluid is not constant and depends on the shear rate. At low shear rates, the fluid behaves as a rigid body, and an external force or stress is required to initiate flow. This critical stress, beyond which the fluid starts to flow, is called the yield stress or yield point. The yield point can be calculated using equations such as the one provided by the Fann VG meter.
Once the yield stress is exceeded, the fluid starts to flow, and its viscosity decreases as the shear rate increases. This behaviour is described by the Herschel-Bulkley viscosity model, which requires values for τo and μ∞, or rheological test data. The Swamee-Aggarwal and Darby-Melson equations can also be used to determine the friction factor, which is related to viscosity, for Bingham plastic fluids.
The Bingham plastic model is widely used because it is simple and accurate for estimating pressure loss in turbulent conditions. It is also useful for diagnosing problems with drilling fluids, as changes in viscosity can indicate the nature of contamination, such as solid or chemical contamination.
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Frequently asked questions
A Bingham plastic fluid is a viscoplastic material that behaves like a rigid body at low stress but flows as a viscous fluid when the stress is high.
The Bingham plastic model is a mathematical model that describes the flow behaviour of Bingham plastic fluids. It is used to study the effect of a high shear rate range and the lower shear rate range.
The yield point (YP) is a measure of the shear stress extrapolated to a zero shear rate. It is one of the two parameters required to describe the flow of a Bingham plastic fluid, the other being the slope of the line, or plastic viscosity.
Bingham plastic fluids require a finite stress to be applied to initiate flow. This is because the liquid contains particles or large molecules that interact to create a weak solid structure. Once the structure is broken, the particles move with the liquid under viscous forces.
Many drilling fluids, completion fluids, and some dilute cement slurries are Bingham plastic fluids. A common example is toothpaste, which requires pressure to be applied to the tube before it is extruded.
