A Brief Guide to Newtonian and Non-Newtonian Fluids

We usually use the terms liquid and fluid interchangeably in general to refer to something that is in a liquid state, such as water. However, there is a stark difference in both terms. 

In physics, the term fluid refers to any liquid, gas or other material that continuously changes its shape and form under the influence of any force or stress. The shear modulus of fluid is zero, which means such substances cannot resist any force. Although fluid refers to everything that flows generally, including both gas and liquid phases, the definition of fluid often varies depending upon the branch of science. 

Important concepts

Before diving into the concept of Newtonian and non-Newtonian fluids, we must have a basic understanding of some terms. These are as follows:

• • Stress: Stress can be defined as force per unit area, with the force being applied externally due to various reasons.
  • Strain: Strain can be defined as the amount of deformation experienced by the body in the direction in which the force is applied, divided by the original or initial dimensions of the body. Strain can be a result of stress itself. 

• Viscosity: Viscosity is the measure of a fluid’s resistance to deformation at a particular rate.

Classification of fluids

Fluids are classified into two major types depending on the relationship between shear stress and the rate of the strain. These two types of fluids are:

• Newtonian fluids – those fluids for which viscosity does not depend on the  stress rate. An example is water.
• Non-Newtonian fluids – those fluids for which viscosity is independent of the stress rate. Some examples are blood and paint.

Newtonian law of viscosity

The Newtonian law of viscosity states that the shear stress must be directly proportional to the velocity gradient, also called the rate of shear strain.

Given below is the relation between the force applied, viscosity and rate of shear strain:

F= μAdudy

Where:

• F represents force
• μ represents viscosity
• A represents the area
• du/dy represents the rate of shear strain

Therefore, the fluid is a Newtonian fluid if the viscosity remains constant.

Newtonian fluids

Newtonian fluids are named after Sir Isaac Newton, who used a differential equation for the first time to find out the relation between the shear stress rate and strain rate for fluids. Newton, among his many well-known accomplishments, discovered the basic principles of viscosity. According to Newton’s observations, a fluid’s viscosity is a function of shear stress and temperature.

According to Newton no stirring or such actions will change the viscosity of a fluid. However, this does not always happen. You may have noticed that if curd is beaten for a long time, its consistency becomes thinner. However, in case of water, there is no change in the viscosity even if it is stirred for long. Therefore it can be said that Newton understood only half of the picture of the whole scenario. 

Hence, a Newtonian fluid is a fluid in which the stress arising due to its flow is linearly correlated to the local strain rate. As discussed earlier, the strain rate is the rate of change of deformation over a period of time. Newtonian fluids are mathematical models of fluids that are the simplest and  viscous . Examples of Newtonian fluids include water and gasoline.

Non-Newtonian fluids

Non-Newtonian fluids are fluids that do not follow Newton’s law of viscosity. As discussed earlier, Newton’s law of viscosity means the viscosity must be constant and independent of the stress. 

In non-Newtonian fluids, the viscosity does not remain constant. In non-Newtonian fluids, the viscosity changes due to any external force. Here the viscosity of the fluid can change under force to either become more liquidy or more solid. 

Examples of non-Newtonian fluids include common food items such as custard, starch suspensions, and other fluids like salt solutions, blood, paint, and shampoo.

Conclusion

Fluids are substances that can flow and do not show any resistance toward permanent deformation. Fluids can be divided into two major types: Newtonian and non-Newtonian. 

Newtonian fluids are the ones that obey Newton’s law of constant viscosity. These fluids have a constant viscosity and zero shear rate and shear stress. Non-Newtonian fluids are those that do not have a constant viscosity and have a variable relationship with shear stress. Examples of Newtonian fluids include water and air. Examples of non-Newtonian fluids include salt solutions, blood, paint, toothpaste, and starch solutions.