Ethan Clarke
Fluids are classified as Newtonian or non-Newtonian depending on whether their flow follows Newton's law of viscosity. Non-Newtonian fluids are those whose viscosity is dependent on the instantaneous shear rate of the fluid. A pseudoplastic fluid is a type of non-Newtonian fluid that starts shearing as soon as any force is applied to it and then decreases in viscosity as the shear rate increases. This behaviour is sometimes considered synonymous with shear thinning. The flow behaviour index, n, is used to describe this property, with n being less than 1 for pseudoplastic fluids.
| Characteristics | Values |
|---|---|
| Fluids for which the flow behaviour index n is | Less than unity |
| Viscosity coefficient | Smaller at a greater rate of velocity gradient |
| Curve | Flattens as the shear rate (velocity gradient) increases |
| Also known as | Shear thinning elements |
| Viscosity | Decreases under shear strain |
| Examples | Wall paint, ketchup, whipped cream, blood, paint, nail polish, polymer solutions, cement slurries, coal ashes, slags, etc. |
| Opposite behaviour | Dilatant or shear-thickening |
| Bingham plastics | Fluids which require a finite deformation to initiate flow |
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What You'll Learn
Pseudo-plastic fluids are shear-thinning materials
Pseudo-plastic fluids, or non-Newtonian fluids, exhibit shear-thinning behaviour. This means that their viscosity decreases under shear strain. In other words, they have a larger dynamic viscosity at low shear rates and a lower dynamic viscosity at high shear rates. This is the opposite of shear-thickening fluids, where viscosity increases as the rate of shear strain increases.
The shear-thinning behaviour of pseudo-plastic fluids is caused by the disentanglement of polymer chains during flow. At rest, high molecular weight polymers are entangled and randomly oriented. However, when agitated at a high enough rate, these highly anisotropic polymer chains start to disentangle and align along the direction of the shear force. This leads to less molecular interaction and an increase in free space, resulting in decreased viscosity.
Shear-thinning behaviour is observed in many industrial and everyday applications, including complex fluids and suspensions. For example, ketchup is a shear-thinning material. When at rest, it is viscous and flows slowly under the force of gravity. However, when the ketchup bottle is squeezed, shaken, or struck, the viscosity decreases, and the ketchup flows out more quickly. Similarly, modern wall paint is a pseudo-plastic material. The shear created by a brush or roller allows it to thin and evenly cover the application surface. Once applied, the paint regains its higher viscosity, avoiding drips and runs.
The flow behaviour index 'n' is used to characterise pseudo-plastic fluids. When ''n' is less than unity, the fluid is considered pseudo-plastic, indicating that the apparent viscosity decreases with an increasing shear rate. This relationship between shear rate and viscosity is described by the power-law model, which categorises fluids that do not depend on fluid shear stress rate history.
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Pseudo-plastic fluids are non-Newtonian
The flow behaviour of fluids is often referred to as rheological behaviour. Fluids are classified as either Newtonian or non-Newtonian. Newtonian fluids, such as water, oil, and air, have a constant viscosity coefficient, meaning their viscosity remains the same regardless of the force applied. Non-Newtonian fluids, on the other hand, have a variable viscosity that changes with the rate of deformation or shear rate. This means that non-Newtonian fluids can either be shear-thickening (dilatant) or shear-thinning (pseudoplastic).
The viscosity of a pseudo-plastic fluid is dependent on the instantaneous shear rate of the fluid. This means that the resistance of a pseudo-plastic fluid to deformation depends on the speed at which that deformation is occurring. As a result, pseudo-plastic fluids have a non-linear relationship between shear rate and shear stress, with the flow resistance increasing less-than-linearly with deformation. This is in contrast to Newtonian fluids, which have a linear relationship between shear rate and shear stress.
Examples of pseudo-plastic fluids include polymer solutions, molten polymers, complex fluids, and suspensions such as ketchup, whipped cream, blood, paint, and nail polish. Pseudo-plastic fluids can also include Bingham plastics, which require a finite deformation or yield stress to initiate flow, such as toothpaste or mayonnaise. When the yield stress is exceeded, the behaviour of Bingham fluids becomes pseudo-plastic.
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Pseudo-plastic fluids are the opposite of dilatant fluids
Pseudo-plastic fluids, also known as shear-thinning fluids, are a type of non-Newtonian fluid. Non-Newtonian fluids are fluids whose viscosity changes as the shear rate changes. In the case of pseudo-plastic fluids, their viscosity decreases as the shear rate increases. In other words, they show a decrease in viscosity with an increasing rate of deformation.
The flow behaviour index n for pseudo-plastic fluids is less than unity (n<1). This means that the viscosity coefficient is smaller at a greater rate of velocity gradient, and the curve becomes flatter as the shear rate (velocity gradient) increases.
Some examples of pseudo-plastic fluids include polymer solutions, molten polymers, ketchup, whipped cream, blood, paint, and nail polish. Pseudo-plastic fluids can also be created by adding certain additives to a system, such as carboxymethyl cellulose.
On the other hand, dilatant fluids, also known as shear-thickening fluids, are also non-Newtonian fluids. However, they exhibit the opposite behaviour to pseudo-plastic fluids. The viscosity of dilatant fluids increases as the shear rate increases, which is the opposite of shear thinning. This behaviour is due to the particles in the fluid entering a state of flocculation and behaving more like a solid when high shear forces are applied.
Dilatant fluids are used in some industrial applications, such as in all-wheel-drive systems and for body armour. Examples of dilatant fluids include a mixture of cornstarch and water (oobleck) and wet sand.
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Pseudo-plastic fluids are sometimes called power-law fluids
Pseudo-plastic fluids are fluids that exhibit non-Newtonian behaviour, meaning their viscosity is not constant and is dependent on the instantaneous shear rate. In other words, pseudo-plastic fluids show a decrease in viscosity as the rate of deformation increases, and they are sometimes referred to as shear-thinning materials. This behaviour is often observed in polymer solutions and molten polymers, as well as complex fluids and suspensions like ketchup, whipped cream, blood, paint, and nail polish.
The flow behaviour of pseudo-plastic fluids can be described using the power-law model, which relates the shear stress applied to the fluid to the shear rate using the equation:
\(\tau = k{\left( {\frac{{\partial u}}{{\partial y}}} \right)^n}\)
In this equation, \(\tau\) represents the shear stress, \(\frac{{\partial u}}{{\partial y}}\) represents the velocity gradient or shear rate, k is the flow consistency index, and n is the flow behaviour index. The value of n is less than 1 for pseudo-plastic fluids, indicating that their viscosity decreases with increasing shear rate. This is in contrast to dilatant fluids, where a value of n greater than 1 indicates that viscosity increases with shear rate.
The power-law model is a generalised Newtonian fluid model and is one of the most commonly used models to describe non-Newtonian behaviour, including that of pseudo-plastic fluids. It is sometimes referred to as the Ostwald-de Waele relationship model. The power-law model can also be used to relate the apparent viscosity of the fluid to the shear rate, with Equation 2 using η to denote apparent viscosity.
Due to their unique rheological behaviour, pseudo-plastic fluids have various industrial and everyday applications. For example, modern wall paint is a pseudo-plastic material. When applied to a surface, the shear created by the brush or roller allows the paint to thin and evenly coat the surface. Once applied, the paint regains its higher viscosity, avoiding drips and runs.
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Pseudo-plastic fluids are distinct from Bingham plastics
The key distinction between the two lies in their rheological behaviour. Rheology describes the flow behaviour of fluids. Bingham plastics are time-independent fluids that require a finite deformation or critical shear stress to initiate flow. In simpler terms, they need a certain amount of force or stress to start flowing. Examples of Bingham plastics include toothpaste, drilling mud, and clay suspensions. Pseudo-plastic fluids, also known as shear-thinning materials, exhibit a decrease in viscosity as the rate of deformation or shear rate increases. This means that they become less viscous as they are agitated or stressed. Common examples of pseudo-plastic fluids include ketchup, paint, and polymer solutions.
The mathematical models used to describe these fluids also differ. The Bingham plastic model, or Bingham fluid constitutive equation, represents the relationship between shear stress and shear strain, with the plot of shear stress against shear strain not passing through the origin. The Power Law model, on the other hand, describes the behaviour of pseudo-plastic fluids when n < 1. This model illustrates how viscosity decreases as the shear rate increases.
Furthermore, the applications of these fluids vary due to their distinct properties. Bingham plastics are commonly used in drilling engineering and the handling of slurries, taking advantage of their ability to maintain structure until a certain stress is achieved. Pseudo-plastic fluids, with their shear-thinning behaviour, find applications in everyday products like ketchup and paint, as well as in industrial processes where low viscosity during normal operations and high viscosity during specific conditions are desired.
In summary, pseudo-plastic fluids and Bingham plastics differ in their fundamental definitions, rheological behaviour, mathematical models, and practical applications. While Bingham plastics require a critical stress to initiate flow, pseudo-plastic fluids exhibit shear-thinning behaviour, becoming less viscous as the shear rate increases. These distinctions make each type of fluid suitable for different purposes.
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Frequently asked questions
A pseudo-plastic fluid is a non-Newtonian fluid that starts shearing as soon as any force is applied to it, then decreases in viscosity as the rate of shear increases.
For pseudo-plastic fluids, the flow behaviour index n is less than unity. A value of n smaller than 1 represents a pseudo-plastic fluid.
Examples of pseudo-plastic fluids include ketchup, whipped cream, blood, paint, and nail polish.
In a pseudo-plastic fluid, the viscosity coefficient is smaller at a greater rate of velocity gradient. These fluids are known as shear-thinning fluids, meaning their viscosity decreases under shear strain.
