Newtons law of viscosity

newtonian and non-newtonian fluids

1. NEWTON’S LAW OF VISCOSITY
Newton’s law of viscosity states that “shear stress is directly proportional to velocity gradient”.
The shear stress between the two adjacent layers of fluid is directly proportional to the negative
value of the velocity gradient between the same two adjacent fluid layers.
Mathematically the law can be stated as:-
τyx = - µ dVx / dy
Where µ is the constant of proportionality known as dynamic viscosity having units n.s / m2.
NEWTONIAN FLUIDS
The fluids that obey the newton’s law of viscosity are known as Newtonian fluids.
NON NEWTONIAN FLUIDS
The fluids that do not obey newton’s law of viscosity are called as Non-Newtonian fluids.
TYPES OF NON NEWTONIAN FLUIDS
Non-Newtonian fluids are divided into two broad categories on the basis of their shear
stress/shear rate behavior as:-
Those whose shear stress is dependent on time.
Those whose shear stress is independent of time.


FIGURE 1 SHEAR DIAGRAM F O R NEWTO NIAN AND TIME-INDEPENDENT NON-NEWTO NIAN FLUIDS
NON-NEWTONIAN FLUIDS (SHEAR STRESS IS INDEPENDENT OF
TIME)

BINGHAM PLASTIC FLUIDS
These are the simplest types of Non-Newtonian fluids. They differ from Newtonian fluids only
in the linear relationship that they do not pass through origin.
Examples:

2. Soap
Toothpaste
Paper Pulp
Sewage Sludge
Chocolate Mixtures


PSEUDO PLASTIC FLUIDS
The majority of non-Newtonian fluids are included in this category. Flow behavior of pseudo
plastic fluids show and decrease in apparent viscosity with increase in shear rate.
Examples:
Polymer Solutions
Greases
Starch Suspensions
Biological Fluids
Detergent Slurries


DILATANT FLUIDS
These fluids are less common than pseudo plastic fluids. Flow behavior of dilatant fluids show
an increase in apparent viscosity with increase in shear rate.
Examples:
Corn Flour Sugar Solutions
Wet Beach Sand
Starch In Water
Potassium Silicate In Water


FIGURE 2 VISCOSIT Y SHEAR OVERTIME DIAGRAM FOR T IME-DEPENDENT NON-NEWT ONIAN FLUIDS
NON-NEWTONIAN FLUIDS (SHEAR STRESS IS DEPENDENT OF TIME)

THIXOTROPIC FLUIDS

3. These fluids exhibit a reversible decrease in shear stress with time at a constant shear rate.
Examples:
Polymer Solutions,
Food Materials
Paints

RHEOPECTIC FLUIDS
These fluids are quite rare in occurrence. These fluids exhibit a reversible increase in shear stress
with time at a constant shear rate.
Examples:
Bentonite Clay Suspensions
Solutions and Clay Suspensions

VISCOELASTIC FLUIDS
In addition to these Non-Newtonian fluids some Non-Newtonian fluids exhibit elastic behavior
and are called as viscoelastic fluids.
Examples:
Flour Dough
Polymer Melts