- APSEd

# Newtonian and Non-Newtonian Fluids | Newton's Law of Viscosity

A substance that is capable of flowing is called fluid. It includes both liquids and gases. Fluids that obey Newton's law of viscosity are called Newtonian fluids. These fluids have a linear relationship between viscosity and shear stress. On the opposite is the non-Newtonian fluids that don't obey Newton's law of viscosity. More details on Newtonian and non-newtonian fluids and other related concepts are covered in this blog.

## Viscosity of Fluids

Before getting into Newtonian and non-newtonian fluids it is important to understand the concept of viscosity. Viscosity is the property of fluid by virtue of which it develops a resistance to movement of one fluid layer over an adjacent fluid layer. It takes place due to cohesion in case of liquids and momentum transfer in case of gases.

Viscosity of fluid develops shear stress. Because of this, an external force is required to maintain the flow of fluid.

Viscosity of fluids is independent of pressure but is totally dependent on temperature. It is related as follows.

An increase in temperature leads to a decrease in the cohesion of liquids and a decrease in viscosity for liquids

An increase in temperature leads to an increase in momentum transfer of gases and an increase in viscosity for gases

## Newton's Law of Viscosity

Newton's law of viscosity states that the shear stress developed between two fluid layers is directly proportional to the velocity gradient or the rate of shear strain or the rate of angular deformation.

**𝜏 ∝ (dv/dy)**

*𝜏 = μ * (dv/dy)*

where,

𝜏 - shear stress

μ - coefficient of dynamic viscosity or dynamic viscosity or viscosity

dv/dy - velocity gradient

### Dynamic Viscosity

Dynamic viscosity or the coefficient of viscosity or viscosity is defined as the shear stress required to produce a unit velocity gradient or a unit rate of shear strain or a unit rate of angular deformation. Its unit in the S.I. system is Ns/m^2 i.e., Newton second per meter square, (Pa.s.).

### Kinematic Viscosity

Kinematic viscosity is defined as the ratio of dynamic viscosity to the mass density of the fluid. Its unit in the S.I. system is m^2/s i.e., meter square per second.

## Newtonian Fluids

As said earlier, fluids that obey Newton's law of viscosity are called Newtonian fluids. These fluids have a linear relationship between the rate of angular deformation and shear stress. The viscosity of such fluids remains constant irrespective of the shear rate. Examples of such fluids are water, air, glycerine, gasoline, alcohol etc.

## Non-Newtonian Fluids

On the opposite is the non-Newtonian fluids that don't obey Newton's law of viscosity. When shear is applied, the viscosity of non-Newtonian fluids decreases or increases, depending on the fluid. The behaviour of a non-newtonian fluid can be described in one of the five ways.

**Dilatant -**An increase in shear stress leads to an increase in the viscosity of the fluid. Examples include quicksand and mud slurry.**Pseudoplastic -**It is the opposite of dilatant i.e., an increase in shear decreases the viscosity of the fluid. Examples include blood and ketchup.**Bingham plastic -**It is similar to Newtonian fluids i.e., have a linear relationship between the rate of angular deformation and shear stress. The difference is that they have internal yield stress making them a time-dependent relation. Examples include oil paint.**Rheopectic -**It is very similar to dilatant in that when shear is applied, viscosity increases. The difference here is that viscosity increase is time-dependent. Examples include gypsum paste.**Thixotropic -**Fluids with thixotropic properties experience a decrease in viscosity when shear is applied. This too is time-dependent. Examples include paint and glue.

All the five behaviours along with the behaviour of Newtonian fluids are depicted in a graphical manner below.

With these, we hope all aspects related to Newtonian and Non-Newtonian fluids have been covered. Stay tuned to APSEd blogs by subscribing to the email list by filling out the form below.