Fluid Viscosity(Definition and units)

Viscosity:

Resistance to flow is know as viscosity. Denoted using 'µ'. According to Newton's Law shear stress in the fluid is directly proportional to it's viscosity.

This fluid viscosity plays a major role in many engineering applications, like petroleum industries, chemical and fertilizers, coating & printing, food processing etc.

Ƭ = µ  dv/dy

Here

Ƭ = Shear stress

dv/dy = Velocity gradient

µ =   Viscosity of fluid

 

The fluids which follows this linearity between shear stress and velocity gradient (shear rate ) are know as 'Newtonian Fluids'. Most of the gases and liquids are Newtonian fluids. Those fluids don't follow this linear relationship are known as "Non Newtonian Fluids"

Some of the "Non Newtonian Fluids" are Bingham plastics, Pseudo plastics, and Dialatant.

Bingham plastics:

Bingham plastics requires some threshold energy or yield stress (To) to start flowing as a material. The behavior is as shown in figure-1. In figure-1 it is denoted as Curve-4.


The representation of this stress is as shown below,

Τ = To + μ (dV/dY)

Here,

Ƭ       = Shear stress

dv/dy = Velocity gradient

To     = Yield stress.

µ       =   Viscosity of fluid

Example for Bingham plastics are: Sewage sludge, Tooth paste.

The following figure shows the behavior of various types of fluids with it's shear rate.

Inferences from the above diagram

• Incase of Newtonian fluids T varies linearly with shear (Curve - 2)
• Incase of Pseudo plastics viscosity decreases with increase in shear stress (Curve-1). This is called "shear rate thinning" behavior.
• Incase of Dialatants  viscosity increases with increase in shear stress (Curve-3). This is called "shear rate thickening" behavior.
• Incase of bingham plastics after some yield stress (To), shows the  linear behavior between shear stress and shear rate. 

Pseudo plastics: 

The fluids which shows decrease in viscosity with increasing shear stress (shear thinning) are known as pseudo plastics.It is an example of non Newtonian fluid and it's behavior is as shown in the figure-1.

  Examples: Lava,Blood, paint and nail polish.

 Dialatant

A dialatant material is one which shows increase in viscosity with increasing shear stress(Shear thickening). It is an example of non Newtonian fluid and it's behavior is as shown in the figure-1.

Examples: Quick sand.