Types of fluids and Newton’s law of viscosity

Definition

A fluid is a substance that continuously deforms under the action of shear force, however small, and hence cannot resist shear in the same way as a solid.
Viscosity is the property of a fluid that measures its internal resistance to flow or deformation.
According to Newton’s law of viscosity, the shear stress in a fluid is directly proportional to the velocity gradient normal to the direction of flow.

Mathematically, it is written as:

$$\tau = \mu \frac{du}{dy}$$

where:

• $\tau$ = shear stress
• $\mu$ = dynamic viscosity
• $\frac{du}{dy}$ = velocity gradient

Main Content

1. Types of Fluids

Ideal fluid, real fluid, Newtonian fluid, and non-Newtonian fluid

• are the main categories used to describe fluid behavior.

Ideal fluids

• are hypothetical fluids with zero viscosity and zero compressibility. They do not exist in practice but are useful in simplified theoretical analysis. Real fluids have viscosity and may also be compressible to some extent, so they represent actual liquids and gases such as water, oil, air, and blood.

Newtonian fluids

• obey Newton’s law of viscosity, meaning the shear stress is directly proportional to the rate of shear strain. Examples include water, air, kerosene, and many light oils.

Non-Newtonian fluids

• do not obey a linear relation between shear stress and velocity gradient. Their viscosity changes with stress, time, or flow conditions. Examples include toothpaste, paint, ketchup, mud, blood, and polymer solutions.
• In practical engineering, classifying fluids helps in selecting proper models for flow analysis, equipment design, and process control.

2. Newton’s Law of Viscosity

• Newton’s law of viscosity states that the force of friction between adjacent layers of a fluid depends on the area of contact, the velocity difference between the layers, and the distance separating them.

• If two parallel layers of fluid move with different velocities, a tangential force is required to overcome the internal friction. The shear stress is given by: $$\tau = \mu \frac{du}{dy}$$ where a larger velocity gradient means greater resistance to flow.

• The proportionality constant $\mu$ is called the dynamic viscosity or absolute viscosity. It indicates how “thick” or “sticky” a fluid is. Honey has a high viscosity, while water has a low viscosity.

• For a Newtonian fluid at a given temperature and pressure, viscosity remains constant regardless of the magnitude of shear stress applied.
• This law is fundamental in explaining phenomena such as lubrication between moving machine parts, flow of fluids in pipes, boundary layer formation, and drag on moving bodies.

3. Factors Affecting Viscosity and Fluid Behavior

Temperature

• strongly affects viscosity. In liquids, viscosity generally decreases as temperature increases because intermolecular forces become weaker. In gases, viscosity usually increases with temperature because molecular motion becomes more intense.

Pressure

• has comparatively little effect on the viscosity of liquids under normal conditions, but for gases it can influence flow behavior at very high pressures.

Molecular structure

• also affects viscosity. Long-chain molecules and stronger intermolecular attractions lead to higher viscosity. This is why syrup, oil, and glycerin flow more slowly than water.

Flow conditions

• can determine whether a fluid behaves in a Newtonian or non-Newtonian manner. Some materials may show different viscosities under low and high shear rates.
• Understanding these factors is essential for industries such as chemical processing, food engineering, petroleum transport, pharmaceuticals, and biomedical applications.

Working / Process

1. Consider two adjacent layers of fluid

• Imagine a fluid flowing between two parallel layers, where one layer moves faster than the other.
• The difference in velocity creates a tendency for internal friction between the layers.

2. Apply shear force and observe resistance

• When a tangential force is applied to move one layer relative to another, the fluid resists this motion.
• This resistance is due to viscosity, and it acts opposite to the direction of relative motion.

3. Relate shear stress to velocity gradient

• Measure the velocity change from one layer to the next per unit distance between them.
• Use Newton’s law of viscosity, $\tau = \mu \frac{du}{dy}$, to determine the viscosity or shear stress depending on the known values.
• In practical situations, this relation is used to calculate fluid friction losses, design pipes and pumps, and analyze lubrication systems.

Advantages / Applications

• Helps in classifying fluids into Newtonian and non-Newtonian types, which is important for selecting proper engineering models.
• Used in pipe flow analysis, where viscosity determines pressure drop, friction loss, and pumping power required.
• Essential in lubrication design for machines, engines, gears, and bearings, because viscosity controls the formation of protective oil films.
• Useful in chemical, food, and pharmaceutical industries for processing products like paints, creams, syrups, slurries, and suspensions.
• Important in biomedical engineering, especially for understanding blood flow and designing medical devices.
• Applied in aerodynamics and hydrodynamics for analyzing drag, boundary layers, and flow resistance around bodies moving in fluids.

Summary

• Fluids are substances that flow and cannot resist shear like solids.
• Fluids are broadly classified as ideal, real, Newtonian, and non-Newtonian based on their flow behavior.
• Newton’s law of viscosity states that shear stress is directly proportional to the velocity gradient in a fluid.
• Viscosity is a key property that governs flow resistance and varies with temperature, pressure, and molecular nature.
• Important terms to remember: fluid, viscosity, shear stress, velocity gradient, Newtonian fluid, non-Newtonian fluid, dynamic viscosity.