This document discusses rheology, the science of deformation of matter under stress. It defines tensile and shearing stresses and explains reversible and irreversible deformations. Viscosity is introduced as the resistance of fluids to flow, with Newtonian fluids obeying the law of proportionality between stress and shear rate. Non-Newtonian fluids are divided into time-dependent categories like thixotropy and time-independent types including plastic, pseudoplastic and dilatant flows. Specific examples and rheograms are provided to illustrate different fluid behaviors.

1. RHEOLOGY

2. RHEOLOGY
 Rheology is the science concerned with the deformation
of matter under the influence of stress
 Stress applied perpendicular to the surface of a body is
known as Tensile Stress
 If tangentially to the surface of a body is known as
Shearing Stress
Tensile Stress Shearing Stress

3. RHEOLOGY
 Deformation that result from the application of stress
divided into two types:-
• Reversible Deformation (Elastic Deformation) When the
body returns to its original shape after the removal of
applied stress
• Irreversible Deformation (Permanent Deformation)
When the body does not returns to its original shape
after the removal of applied stress

4. RHEOLOGY
 Viscosity is a property of fluids that indicates resistance to
flow. Newton's Law states that the shear stress (the force
divided by area parallel to the force, F/A) is proportional to
the shear rate (V/H). The proportionality constant is known
as the Coefficient of Viscosity (η).
 The ratio of applied shear stress to the Rate of Shear is
known as Coefficient of Viscosity (η).
η = Shear Stress/ Rate of Shear
 On the basis of Newton’s Law fluids can be divided into
two types:
• Newtonian Fluids
• Non-Newtonian Fluids

5. NEWTONIAN FLUIDS
 Fluid which obey Newton’s Law is called Newtonian Fluids
(rate of flow of liquid is directly proportional to applies
stress).
 Flow of this type of fluid can be illustrated by hypothetical
cube of fluid containing infinite layer of liquid (laminae).
 When tangentially stress is applied the rate of movement of
laminae very strong a maximum value in layer adjacent to
the upper plan to a value that is close to zero in the layer
adjacent to the lower plane.

6. NEWTONIAN FLUIDS
• Thickness of Cube = x
• Stress = S
• Velocity difference = µ
• Applied Stress = F/A
• Rate of Shear = µ/x
• Viscosity = Applied Stress/ Rate of Shear
η = F/A/dµ/dx
• Unit of η is Ns/m2 other unit of η poise (P) & centipoise
(cP) 1cP = 10-3 ns/m2
 Rheogram
ShearRate
Shear Stress

7. NEWTONIAN FLUIDS
• Straight line of graph shows direct relation of shear
stress with shear rate.
• The slope of which is equal to reciprocal of viscosity of
the fluid a value to as fluidity.
ϕ = 1/η
 Examples of Newtonian Fluids:-
• Water
• Simple Organic Liquids
• True Solutions
• Dilutes Suspensions
• Emulsions

8. NON-NEWTONIAN FLUIDS
 The fluid which do not obey Newton Law’s they are termed
as Non-Newtonian Fluids.
 Types of Non-Newtonian Fluids:-
Time
Dependent
Thixotropy Rheopexy
Time
Independent
Plastic
Flow
Pseudo
Plastic Flow
Dilatant
Flow
Non-Newtonian Fluids

9.  Time Dependent Effects These are properties which
depend on duration of shear.
• Thixotropy means change by touch.
 Any reversible time dependent decrease in Viscosity
that result form the application of shearing stress.
 The decrease in Viscosity arise from a breakdown of
structure within a system when it is sheared after the
shearing force are remove a time lag occurs before
structural reformation is complete.
 The rheogram for this system is:-
NON-NEWTONIAN FLUIDSShearrate
Shear Stress

10.  Example of Thixotropy
• Bentonite gel
• Hydrated Bentonite Stress Particular elongated aligning
themselves with respect to flow (parallel to flow liquid)
this orderly arrangement breaks the interparticle
links and therefore apparent viscosity decreases
• On removal of shearing force the arrangement of
dispersed particle gradually become less orderly and the
gel network reform after a time lag.
 Irreversible Thixotropy
There is structural deformation to that extend they cannot
go to original state on removal of shear stress. Bentonite
Solution .
NON-NEWTONIAN FLUIDS

11. Thixotropy
NON-NEWTONIAN FLUIDS

12.  Negative Thixotropy
• Samyn and Wan 1967 suggest that Negative Thixotropy
observed on clay suspension was caused breakdown of
relatively large compact produced, which therefore an
increase in apparent viscosity.
• When the system subjective to stress time depend
increase in viscosity.
• ReasonLarge compact flocules by the application of
stress change into smaller flocules and its orientation
change and increase in the friction between them so
viscosity increases.
NON-NEWTONIAN FLUIDS

13.  Rheopexy
• The time lag occurs when stress is removed and system
reformed. This time lag is reduced by application of mild
rolling or drumming motion. This motion provide a mild
turbulence that aids particle of the system to a random
orientation when reformation can occurs. This whole
effect is known as Rheopexy.
• Negative Rheopexy Reversible deformation by the
application of stress. When stress is removed time lag
for reformation increased.
NON-NEWTONIAN FLUIDS

14.  Time Independent Fluids
• Plastic Flow. The rheogram for plastic flow show that
the line does not pass through the origin of the graph
but rises at some point on the shear stress axis. This
indicate that certain shearing stress must be exerted
before flow began. These stress is termed the Yield
Value. If the stress is applied is lower than yield value
the system exhibit elastic deformation that are
reversible when these small stress removed.
NON-NEWTONIAN FLUIDS
Shear Stress
ShearRate

15.  Bingham Bodies.
• Material that shows plastic behaviour are often known
as Bingham Bodies. The quantitative behaviour of these
system usually expressed in terms of Bingham
Equations.
U or ηp = S — fB
du/dx
fB = Bingham Yield Value
U = Plastic Velocity,
du/dx = Shear Rate,
S = Shear Stress
NON-NEWTONIAN FLUIDS

16. • This equation employs that flow diagram is straight line
that arises on the shear stress axis at yield value. In
practice usually occurs at the lower stress. (Yield Value
fH = Higher Yield Value to which the flow curve become
linear) When System extremely plastic fL is used in place
of fB
NON-NEWTONIAN FLUIDS

17.  Pseudoplastic Flow
• It can be seen that the curve arises at the origin of the graph
so no yield value exist.
• As soon as stress applied system will began to flow, the slop
of curve gradually increases until it reach maximum value
since the apparent of viscosity at any shear rate is given by
the reciprocal of the slope, that apparent viscosity decreases
as the shear rate increases until a constant value is reached.
• An empirical equation for this system is Sn = k du/dx (K & n
are constant) if n=1 the it is similar to Newtonian Equation.
NON-NEWTONIAN FLUIDS

18. • At the high value of stress the graph of plastic and
pseuds plastic are superimposable. So to differentiate
between them we applied less stress.
 Why increasing stress viscosity decreases?
• Dependent on the nature of the liquid.
• When stress increases in concentrated suspension
aggregates of particles are break/ disperse and the
friction between particles decreases, so viscosity
decreases.
NON-NEWTONIAN FLUIDS

19.  Dilatant Flow
• Dilatnacy is usually exhibited by concentrated
dispersion of deflocculated particle. .
• At lower shear rate in these systems the particle are
arrange in a state of close packing and the small amount
of liquid present is sufficient to fill the narrow spaces
between adjacent particles.
NON-NEWTONIAN FLUIDS
Lower Shear Rate High Shear Rate

20. • These thin liquids films allow the system to flow like a
liquid.
• At higher shear rate the particle will become displace
from their close pack arrangement which result in the
formation of large white spaces in the system.
• The liquid continuous medium is now insufficient to fill
all the spaces between particles, hence the movement of
particle relative to each other involves a greater amount
of friction and the apparent viscosity therefore
increases.
• This effect may be trouble some in high speed milling
process because the viscosity of dilatant suspension
may increase so much that led to overloading of the
motors.
NON-NEWTONIAN FLUIDS

21. • The Rehogram for Dilatant Flow
• The slope of this curve gradually decreases to a
constant value which indicate that the apparent
viscosity must increase with increase in shear rate up to
a maximum value.
NON-NEWTONIAN FLUIDS
ShearRate