Difference Between Newtonian and Non Newtonian Fluids

When studying fluids, it’s crucial to understand the difference between Newtonian and Non Newtonian fluids. This classification primarily revolves around how these fluids respond to applied stress and how their viscosity behaves under varying shear rates. 

Understanding the difference between Newtonian and non-Newtonian fluids is essential in fluid mechanics. This article breaks down their behavior, key characteristics, and real-life examples. It makes it simple to see how they are classified. It also explains how they are used in various applications. Before moving to Newtonian and non-Newtonian fluids let’s understand some basic concepts.

What is viscosity?

Viscosity refers to a fluid’s resistance to flow. In simpler terms, it measures how easily a liquid or gas can move through space. High-viscosity fluids are thick and flow slowly, while low-viscosity fluids are thin and flow quickly. The concept of viscosity plays a crucial role in everyday life. It includes instances ranging from the oil in your car engine to the syrup on your pancakes.

Newton’s Law of Viscosity

Sir Isaac Newton was a pioneer in mathematics and the study of physics and fluid mechanics. In the 17^th century, he formulated Newton’s Law of Viscosity, which states that

“The force required to move one layer of fluid past another is directly proportional to the velocity gradient. It is also directly proportional to the area of contact. Conversely, it is inversely proportional to the distance between the layers.“

The Mathematical Expression of Newton’s Law of Viscosity

Where:

‘τ’ is the Shear Stress = F/A
‘F’ is the force applied to the fluid layers.
‘A' is the area of contact between the fluid layers.
‘μ‘ is the dynamic viscosity of the fluid.
‘du/dy' shows the velocity gradient or the change in velocity with respect to distance.

What Are Newtonian Fluids? 

Newtonian fluids are defined by their consistent viscosity, which remains constant regardless of the applied shear rate. This means that the flow behavior and resistance to deformation do not change with the force applied. Common examples of Newtonian fluids include: 

• Water
• Air
• Mineral oils
• Gasoline

Newtonian fluids, named after Sir Isaac Newton, exhibit a linear relationship between shear stress and shear rate. Their viscosity remains constant under steady temperature and pressure conditions, ensuring predictable flow behavior regardless of applied shear stress or deformation rate.

Characteristics of Newtonian Fluids

1. Constant Viscosity: The viscosity of Newtonian fluids remains unchanged regardless of the shear rate. This leads to a linear relationship between shear stress and shear rate. 

2. Predictable Behavior: The flow behavior can be easily predicted using simple equations, such as Newton’s law of viscosity, where shear stress is directly proportional to shear rate. 

3. Temperature Dependency: Viscosity can change with temperature for Newtonian fluids. For example, heating water will decrease its viscosity, making it flow more easily. 

The relationships between the shear stress and shear rate

The figure below shows curves of shear stress against the rate of shear at constant temperature and pressure.

The simplest behavior is shown by a curve. This curve is a straight line passing through the origin. It demonstrates Newtonian fluids behavior.

The other curves shown in Figure represent the rheological behavior of liquids.

What Are Non-Newtonian Fluids?

Non-Newtonian fluids, on the other hand, exhibit varying viscosity based on the applied shear rate. Their behavior is much more complex and can change depending on external forces or time. Common examples include: 

• Ketchup
• Paint
• Blood
• Silly Putty

A Non-Newtonian fluid deviates from Newton’s law of viscosity, exhibiting a non-linear relationship between shear stress and shear rate. Unlike Newtonian fluids, their flow characteristics can depend on external forces, time, or other conditions, leading to variable and often unpredictable behavior.

Characteristics of Non Newtonian Fluids 

1. Variable Viscosity: The viscosity of Non-Newtonian fluids increase or decrease with an increase in shear rate. This can be categorized into several types:   

• Shear-thinning (Pseudoplastic):

Viscosity decreases with an increase in shear rate (e.g., ketchup). Pseudoplastic Fluids’ viscosity decreases with an increase in velocity gradient (shear rate). The curve passes through the origin, is concave downward at low shears, and becomes nearly linear at high shears.

• Shear-thickening (Dilatant):

Viscosity increases with an increase in shear rate (e.g., cornstarch in water). The curve is concave upward at low and almost linear at high.

The experimental curves for pseudoplastic and dilatant fluids can be represented by a Power Law. This law is also called the Ostwald-de-Waele equation.

Where, k and n are arbitrary constants.

Newtonian fluids : n = 1, k = μ

Pseudoplastic fluids : n < 1

Dilatent fluids : n > 1

• Bingham Plastic:

Requires a certain yield stress before flowing (e.g., toothpaste).  These fluids resist small shear stress but flow linearly under the action of larger shear stress. Unless the threshold shear stress τ₀ is exceeded, Bingham fluids do not deform or flow. Representation of these fluids is as follows

Where, τ₀ is the yield stress (threshold shear stress) and η is commonly called the coefficient of rigidity.

2. Time-Dependent Behavior: Some Non-Newtonian fluids exhibit thixotropic or rheopectic properties, meaning their viscosity changes over time under constant shear stress. 

None of the curves in the Figure above (shear stress vs. shear rate) depends on the history of the fluid. A given material sample shows the same behavior no matter how long the shearing stress has been applied.

Such is not the case for some non-Newtonian liquids, whose stress-vs.-rate-of-shear curves depend on how long the shear has been active.

Thixotropic fluids break down under continued shear. On mixing, they give lower shear stress for a given shear rate. In other words, their apparent viscosity decreases with time.

Rheopectic substances behave in a reverse manner, and the shear stress increases with time, as does the apparent viscosity. The original structures and apparent viscosities are usually recovered on standing.

3. Complex Flow Patterns: The flow behavior of Non-Newtonian fluids can be unpredictable, often requiring specialized models for accurate analysis. 

The rheological characteristics of fluids are summarized in the Table below

Designation	Effect of increasing shear rate	Time dependent?
Pseudoplastic	Thins	No
Thixotropic	Thins	Yes
Newtonian	None	No
Dilatant	Thickens	No
Rheopectic	Thickens	Yes

Key Difference between Newtonian and non Newtonian Fluids

Viscosity Variation

The key difference between Newtonian and non-Newtonian fluid is how its viscosity behaves. While Newtonian fluids maintain a constant viscosity, non-Newtonian fluids can exhibit varying viscosity levels.

Shear Rate (Shear Strain) Sensitivity

Non-Newtonian fluids are sensitive to changes in shear rate. This sensitivity can lead to intriguing phenomena, such as the Oobleck effect. In this effect, a mixture of cornstarch and water behaves as a solid or a liquid. This behavior depends on the applied force.

Applications of Newtonian and Non Newtonian Fluids

Understanding the differences between these two types of fluids is essential in various fields, including: 

• Engineering: Knowledge of fluid behavior is crucial in designing systems involving fluid transport and processing.
• Medicine: Understanding blood flow and other biological fluids helps in diagnosing and treating medical conditions.
• Food Industry: The behavior of food products like sauces and dressings can impact processing and consumer acceptance.

Conclusion

In summary, the main difference between Newtonian and Non Newtonian fluids lies in their viscosity behavior under applied shear. While Newtonian fluids maintain a constant viscosity and predictable flow behavior, Non Newtonian fluids exhibit complexities with their viscosity depending on the shear rate and time. This fundamental understanding is important across various scientific and industrial applications, influencing how materials are processed and used.

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