- Shalmali

# Newtonian and Non- Newtonian Fluids

What are viscosity and its types?

*Table of Contents*

Viscosity is one of the properties of the fluid. And yes! Newton has to say something about it too!

Let's see what he stated and how the viscosity of fluids works!

## Viscosity

Viscosity can be simply defined asthe measure of a fluid's resistance to flow.

When fluid is in motion or force is applied against the fluid to flow, there is resistance to the flow. The fluid molecules resist the motion due to cohesive (intermolecular) forces between themselves. The fluid molecules near the plate or pipe do not move due to inertia, in turn, take energy from the adjacent molecules and slow them down too! Sounds like a crab right? Click __here__ to understand it in detail.

### Dynamic / Absolute Viscosity: Newtonian Fluids

**Newton’s law of viscosity** defines the relationship between the __shear stress__ and shear rate of a fluid subjected to mechanical stress.

The ratio of shear stress to shear rate is a constant, for a given temperature and pressure, and is defined as the viscosity or coefficient of viscosity. [1]

The best example for this type of fluid is **water and**** air**, other examples being alcohol, glycerol, etc. Dynamic Viscosity, coefficient of viscosity, or viscosity is the same with SI units, **Pa-s** (Pascal second), and **Poise** and denoted by **μ** (mu).

1 poise = 100 centipoise = 1 g/cm.s = 0.1 Pa s

1 centipoise = 1 mPa.s

As you can see in the graph above, the curve for Newtonian fluids is **linear** which passes through the center of the graph. **The viscosity is independent of the shear rate**.

Newton’s observations led him to believe that a fluid’s viscosity was simply a function of shear stress and temperature — and that it would remain unchanged no matter the shear rate. But... obviously science never fails to surprise us!

### Kinematic Viscosity: Non-Newtonian Fluids

Non-Newtonian fluids do not follow Newton’s law but follow **Power-Law Fluids**.

Kinematic viscosity is the dynamic viscosity divided by density.

SI unit of kinematic viscosity is **m^2/s **and is denoted by ** v** (new).

Here, **viscosity** (ratio of shear stress to shear rate) is **not constant** and is **dependent on the shear rate**.

The curve of the fluid in the graph depends on the **flow behavior index (n).**

## Types of fluids

Newtonian Fluids

Non-Newtonian Fluids

### Dilatant or Shear Thickening fluids

It is a type of material whose viscosity increases as the rate of __shear strain__ increases. In simple words, **viscosity increases as stress increases**.

**Examples: Corn starch and water (oobleck), sand in water, etc.**

As more force is applied to the oobleck, stress increases, and in turn, the viscosity also increases.

Just imagine diving into a pool of dilatant! It hurts!

*Watch this video of placing oobleck on speakers!!!*

**Application: Body Armour**

Military applications like body armor for flexible body movements and sudden attacks, like bullets or knives.

### Pseudoplastic or Shear Thinning fluids

This is a more common type of fluid than dilatant, which occurs naturally. It is a type of material that is opposite of dilatant, which means **the viscosity decreases as the shear rate increases. **

**Examples: Quicksand, blood, milk, paints, nail polish, ketchup, etc.**

Ketchup is an easy example to visualize, the more force you apply, the faster it moves. Or imagine running on a quicksand!

### Rheopectic Fluids

It is a type of material, whose **viscosity increases as stress with respect to time increases.** It is a time-dependent fluid. Rheopectic fluids should not be confused by dilatant fluid. A lot of research is going on, on these fluids for military purposes.

**Examples: Printer Ink, whipped cream, etc**

The longer you whip the cream, the thicker it gets. (But of course, it gets thick up to a certain point!)

### Thixotropic Fluids

It is a type of fluid whose **viscosity decreases as stress with respect to time increases**. Similar to Rheopectic Fluid, Thixotropic Fluids too are time-dependent fluids. It is a more naturally occurring fluid than Rheopctic Fluid.

**Examples: Honey, yogurt, etc**

The more you stir honey, its viscosity decreases and starts to flow easily.

*Watch this video "Rheopectic v. Thixotropic" to get a clear idea.*

### Bingham plastic Fluids

It is a type of material **that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress**. As you can see in the graph above, Bingham plastic's equation line does not pass through the center of the graph.

**Examples: Toothpaste, mayonnaise, chocolate, etc.**

The more force you apply to the toothpaste tube, the more paste flows like a fluid.

## Summary

Newtonian fluids follow Newton's law of viscosity with

**constant**viscosity. The viscosity is**independent**of the shear rate.Non-Newtonian fluids follow the Power-Law of fluids with

**changing**viscosity. The viscosity is**dependent**on the shear rate.Dilatant or Shear Thickening fluids:

**viscosity increases as stress increases.**Pseudoplastic or Shear Thinning fluids:

**viscosity decreases as the stress increases.**Rheopectic Fluids:

**viscosity increases as stress with respect to time increases.**Thixotropic Fluids:

**viscosity decreases as stress with respect to time increases.**Bingham plastic Fluids:

**behaves as a rigid body at low stresses but flows as a viscous fluid at high stress.**

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References:

[1] George H.F., Qureshi F. (2013) Newton’s Law of Viscosity, Newtonian and Non-Newtonian Fluids. In: Wang Q.J., Chung YW. (eds) Encyclopedia of Tribology. Springer, Boston, MA. __https://doi.org/10.1007/978-0-387-92897-5_143__