rheology viscosity newtonian non-newtonian plastic pseudoplastic dilatant thixotropy rheopexy viscometers

1. RHEOLOGY
● Newtonian System
● Law of flow
● Kinematic viscosity
● Effect of temperature
● non-Newtonian system
● Pseudoplastic
● Dilatants
● Plastic
● Thixotropy
● Thixotropy in formulation
● Determination of Viscosity
NABEELA MOOSAKUTTY
ASST.PROFESSOR
DEPT OF PHARMACEUTICS
KTN COLLEGE OF PHARMACY

2. Rheology is the science of flow and deformation of matter under stress
It is the flow of liquids and deformation of solids
VISCOSITY
It is defined as resistance to the flow
The higher is the viscosity of a liquid, the greater is the resistance to flow
η is the coefficient of viscosity
η = F/G
F = Shearing stress
G = Rate of shear
Unit of viscosity = Poise or dyne.sec/cm2
2
Rheo -
To flow
Logos -
Science
INTRODUCTION

3. Concept of Viscosity
3
Block of liquid consisting of parallel layers of molecules
When the pressure is applied on the top
layer ‘A’, it moves at greater velocity and
induces flow in the second layer ’B’.
The velocity at ‘B’ is somewhat less than that
of first layer due to the viscous drag offered
by the 3rd layer ‘C’
The phenomenon continue and the bottom
layer ‘N’ remains stationary
Hence, Liquids resist flow when force is
applied and this resistance is expressed as
Viscosity

4. IMPORTANCE
▪ Manufacturing of dosage forms
4
▪ Materials undergo process such as mixing, flowing through pipes,
filling into the containers etc
▪ Flow related changes influence the selection of mixing equipment
▪ Formulation of medicinal and cosmetic creams, pastes and lotions
▪ Formulation of emulsions, suspensions, suppositories and tablet
coating
▪ Fluidity of solutions for injection
▪ Extrusion of paste or ointment from a tube
▪ Patient’s acceptability of the product
▪ Determination of standards of liquids
▪ As quality control tools for product evaluation
▪ As viscosity improving agents
▪ Identification of diseases
▪ Determination of molecular mass
▪ Proteins, enzymes and polysaccharides

5. IMPORTANT
TERMS
5
Shear
It is the movement of material relative to parallel layer
Shear stress (F’)
It is the force per unit area required to bring about flow (F/A)
The flow of liquids is induced by applying stress
Shear rate (G)
Difference in velocity (dv) between two planes of liquids separated by
distance (dr)
F/A 𝛂 dv/dr
Fluidity
It is the reciprocal of viscosity
It is the ability of a substance to flow
Φ = 1 / η

6. KINEMATIC VISCOSITY
6
It is a measure of a fluid’s internal resistance to flow under
gravitational forces
It is determined by measuring the time in seconds, required for
a fixed volume of fluid to flow a known distance by gravity
through a capillary within a calibrated viscometer at a closely
controlled temperature
It is the viscosity divided by the density of the liquid
Kinematic viscosity = η / ρ
Unit : Stokes or Centistokes
1 stoke = 10⁻⁴ m²/s
or
Where,
Kinematic viscosity (cSt)
Absolute viscosity (cP)
Fluid’s specific gravity (SG)
● This measurement is used mostly for Newtonian
liquids - liquids that do not change viscosity with
changes in applied force (shear rate)
● Testing lubricating oils
Applications

7. DYNAMIC
VISCOSITY
7
Dynamic viscosity is measured as the fluid’s resistance
to shear flow when an external and controlled force
(pump, pressurized air, etc.) is applied
It is otherwise known as Absolute viscosity
Applications:
▪ Most useful for liquids that change their apparent
characteristics as force or pressure is applied.
These liquids are known as non-Newtonian fluids
▪ In the design of pumping systems

8. EFFECT OF
TEMPERATUR
E
8
Viscosity of liquids decreases with increase in temperature
Viscosity of gases Increases with increase in temperature
The effect of temperature on the viscosity of a liquid is expressed by
Arrhenius equation
Viscosity depends
on Temperature
η = viscosity
A = constant depending on the mol.wt and molar volume of the liquid
E = activation energy required to initiate flow between molecules
T = temperature

9. TYPES OF FLOW 1. NEWTONIAN
2. NON-NEWTONIAN
Time independent
a. PLASTIC
b. PSEUDOPLASTIC
c. DILATANT
Time dependent
a. THIXOTROPY
b. RHEOPEXY
9

10. NEWTON’S
LAW
10
Higher the viscosity of a liquid,
the greater is the force per unit
area (shearing stress F) required
to produce a certain rate of
shear(G)
Rate of shear 𝛂 Shearing stress
F = η G

11. NEWTONIAN
FLOW
NEWTONIAN FLUIDS
lIQUIDS THAT OBEY NEWTON’S LAW OF FLOW
Rheogram / Consistency curve
▪ Shear stress-Shear rate relationship curve
▪ When data are plotted by taking F on x axis and G on y
axis a flow curve is obtained
▪ The rheogram passes through origin and the slope gives
the coefficient of viscosity
▪ So, Newtonian fluids follows a linear relationship and
the viscosity of such a fluid is constant at a given
temperature and pressure
▪ Ex: Water, Glycerin, Chloroform
11

12. NON-
NEWTONIAN
FLOW
12
lIQUIDS THAT DO NOT
OBEY NEWTON’S LAW OF
FLOW

13. PLASTIC
FLOW
13
● The curve doesn’t pass through the origin
● The substance initially behaves like an elastic body and fails to flow
when less amount of stress is applied
● Further increase in stress leads to a non-linear increase in the shear rate
and progressively gets linearised
Yield value
● The linear portion when extrapolated intersects at a point on x axis.
That point is called yield value
● Plastic flow resembles Newtonian flow above the yield value

14. Plastic
viscosity
U = [F-f] / G
F = shear stress N/m²
f = yield value N/m²
G = rate of shear s⁻¹
14
Plastic flow is associated with the presence of flocculated
particles in concentrated suspensions, butter, ointments
and gels
Mechanism
When the system is at rest - Floccules (aggregation of
particles) are maintained
Yield value represents the stress required to break the
inter-particle contacts - upon exceeding the yield value the
particles behave individually
Bingham bodies
Materials that exhibit plastic flow are called Bingham
bodies
Slope of rheogram is termed as mobility

15. PSEUDOPLASTIC
FLOW
15
The rheogram for a pseudoplastic flow begins at
the origin
As the shear stress increases progressively shear
rate also increases but it is not linear
It is exhibited by polymer dispersions such as
● Tragacanth in water
● Sodium alginate in water
● Methylcellulose in water
● Sodium carboxymethylcellulose in water
The materials are known as Shear thinning
materials

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Mechanism
Under normal storage conditions,
● The long chain molecules of the polymers are
randomly arranged in the dispersion
Upon applying a shear stress,
● The molecules begin to arrange their long axes in the
direction of force applied
● This stress induced orientation reduces the internal
resistance of the material
● In addition, the solvent molecules associated with the
polymer molecules will also released
● Thereby the effective conc. and size of the molecules
get lowered
● Then the material allows greater shear rate upon
progressive increase in shearing stress

17. 17
The rheogram can be described by
N
F = η’ G
N = number given to the exponent
η’ = viscosity coefficient
N is higher than 1, the flow becomes non-Newtonian
N = 1, the flow becomes Newtonian
Taking logarithms on both sides,
N log F = log η’ + log G

18. DILATANT
FLOW
18
● The system exhibits enhanced resistance to flow with increasing rate of
shear
● When sheared, these systems increase their volume hence they are
called as Dilatant
● It is also known as Shear thickening systems
● When the stress is removed, the system returns to its initial state of
fluidity
Dilatant flow is exhibited by
● Suspensions containing high conc of solids (>50%) of small
deflocculated particles
● Suspension of starch in water
● Inorganic pigments in water

19. MECHANISM
19
When the dilatant system is at rest,
● The molecules are closely packed [A minimum void volume is available]
● The amount of vehicle is sufficient to fill void volume
● The particles can move relative to one another
● Hence the system exhibits relatively low consistency
When shear stress is applied,
● Bulk of the system expands or dilates i.e; the void volume significantly
increases
● But the amount of vehicle is insufficient to fill this expanded void space
● Thus, the particles are not wetted or lubricated and thereby develop
resistance to flow
● The system show a paste-like consistency
● The sediment in the deflocculated suspension is dilatant and resists stirring
or shaking. This effect is known as caking or claying of suspension
● It follows the equation
Log G = N log F - log η’

20. THIXOTROPY
DEFINITION
It is a reversible, isothermal time dependent decrease in apparent viscosity when a
material is subjected to increased shear rate
That means the structure of a fluid is broken down under shear and rebuilt at rest
It is a shear thinning system, it takes longer time to recover compared to the time
taken for agitation
20
System : Gel
At rest, dispersion contain asymmetric particles that
through numerous point of contact set up a 3 dimensional
structure and will have rigidity
System : Sol
As the shear is applied the structure will breakdown and
become solution and the flow starts
System : Gel
Upon removal of stress the system regains its original state
very slowly
PARTICLE-PARTICLE INTERACTIONS-
TRANSFORMATIONS

21. 21
RHEOGRAM
Bulges
Concentrated aq.magma (gel) of bentonite produces hysteresis loop with a
characteristic bulge in the up-curve
Mechanism
Spurs
Procaine penicillin gel produces rheogram with a spur value
The structural breakdown is indicated by spur value, Y in up-curve

22. NEGATIVE
THIXOTROPY
22
It is also known as Anti-thixotropy
Ex: Magnesia magma
It shows sol-like properties
Upon shaking the system behaves like a gel
It represents an increase in consistency on down curve
Down curve shifts to the right of the up-curve

23. THIXOTROPY
IN
FORMULATIO
N
23
● Thixotropy is a desired property in liquid pharmaceutical system
Its have a high consistency upon storage and low consistency pon
shaking
● In suspension, the particles will not settle down in the container [gel
form]
It will become fluid [sol] upon shaking for a dose to dispense
Upon rest it will retain its consistency to maintain the particles
suspended
● This is also applied to emulsions, lotions and creams
● Ex: Parenteral suspensions used for intramuscular depot therapy
Procaine penicillin G (40 - 40-70% w/v in water)
When passed through the hypodermic needle, breakdown of the
structure occurred
● With regards to suspension stability- there is a relation between
degree of thixotropy and rate of sedimentation
Thixotropy ∝ [1 / rate of settling]
Greater the thixotropy,
Lower rate of settling
It provides stability
It enhances retention
time thereby increased
bioavailability

24. MEASUREMENT
OF
THIXOTROPY
24
1. In a thixotropic system, the hysteresis loop is formed by the up and down-
curves of the rheogram
The area of hysteresis loop - Its the measure of thixotropic breakdown
It can be obtained with the help of a planimeter
1. The nature of the rheogram depends on the rate at which shear is increased
or decreased
Consider a material that follows plastic flow
The shear rate is increased at a constant rate on the system upto the point ‘b’ and
then decreased then ‘abe’ rheogram is obtained
If the shear rate is maintained at ‘b’ for time ‘t₁’ seconds and then decreased then
‘abce’ rheogram is obtained
At point ‘b’ the shear rate is maintained for time ‘t₂’ seconds and then decreased
‘abde’ curve is obtained
Based on these rheograms, the thixotropic coefficient ‘B’ can be calculated by
B = [U1 - U2] / ln [t2/t1]
U1 and U2 = Plastic viscosities of the two down curves

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3. In this method, the system is subjected to different rates of shear [V1 and
V2] the resulting rheogram shows 2 hysteresis loops
The Thixotropic coefficient ‘M’ can be calculated by
M = 2 [U1-U2] / ln [V2/V1]²
Applications
It's a desirable property in emulsions, suspensions and creams
The greater the thixotropy, the higher is the physical stability of the
suspension
Parenteral suspension containing 40 to 70% of procaine penicillin G acting
as depot and maintaining sustained levels of drug in the body
Commonly used in the construction industry (liquid cements,liquid concrete,
drilling fluids etc)
Industrial applications (muds and paints)
Food industry (liquid dairy products, ketchup, yoghurts, mayonnaise)

26. RHEOPEXY /
RHEOPECTY
It is the rare property of some non-Newtonian fluids to show a time-
dependent increase in viscosity; the longer the fluid undergoes shearing
force, the higher its viscosity
Ex: Gypsum pastes and Printer inks
26
VISCOMEER
SINGLE POINT VISCOMETERS
MULTIPOINT VISCOMETERS
CAPILLARY VISCOMETER
FALLING SPHERE VISCOMETER
CUP AND BOB VISCOMETER
CONE AND PLATE VISCOMETER
● SINGLE RATE OF SHEAR
● NEWTONIAN FLUIDS
● SEVERAL RATES OF SHEAR
● non-NEWTONIAN FLUIDS
● NEWTONIAN FLUIDS

27. Capillary
Viscometer
27
It is used to determine the viscosity of a Newtonian liquid
Both Dynamic and Kinematic viscosity can be obtained
Principle
When a liquid flows by gravity, the time required for the liquid to pass
between two marks through a vertical capillary tube is determined
The time of flow of the liquid under test is compared with the time
required for a liquid of known viscosity (usually water)
The viscosity of unknown liquid can be estimated by
η₁ = [ρ₁t₁ / ρ₂t₂] η₂
η₁ = viscosity of the unknown liquid Pa.s
ρ₁ = density of the unknown liquid Kg/m³
t₁ = time of flow of unknown liquid s
ρ₂ = density of the known liquid Kg/m³
t₂ = time of flow of known liquid s
η₂ = viscosity of the known liquid Pa.s

28. Falling
Sphere
Viscometer
28
Principle
It's based on the Hoeppler viscometer
The apparatus consists of a glass tube positioned vertically
A constant temperature jacket with provision for water circulation is arranged
around the glass tube
The test liquid is placed in the glass chamber
A glass or steel ball is dropped into the liquid and allowed to reach equilibrium
with the temperature of the outer jacket
The tube with the jacket is then inverted, which places the ball at the top of the
inner glass tube
The time taken for the ball to fall between two marks is accurately measured
This process is repeated several times to obtain concurrent results
The viscosity of a newtonian liquid can be calculated by
η = t [Sb - Sf]B
t = time taken for the ball to fall between the two points
Sb = Specific gravity of the ball
Sf = Specific gravity of the test fluid
B = Constant for a particular ball
Can be used over a range of 0.5 to 20000 Pa.s
Constant
temperature
jacket

29. Cone and
Plate
Viscometer
29
Principle
The sample is placed at the center of the plate which is then raised into a position under
the cone
The cone is driven by a variable speed motor and the sample is sheared in the narrow
gap between the stationary plate and the rotating cone
The rate of shear in rpm is increased or decreased by a selector dial and the shearing
stress produced on the cone is read on the indicator scale
Thus one can construct a plot of rpm (rate of shear) versus scale reading (shearing
stress)
Advantages
The rate of shear is constant throughout the entire sample being sheared. Plug flow is
not observed
The sample required is small, 0.1 to 0.2ml
Cleaning and filling is easy
Less time is required for temperature equilibration
In Newtonian system, the viscosity is estimated by
C = instrument constant, T = torque reading, v = Speed of the cone
Plastic viscosity can be estimated by
Tf = Torque at the shearing stress axis
Cf = Instrumental constant
η = C [T/ v]
U = Cf [ (T-Tf) / v]
yield value = Cf x Tf

30. Cup and Bob
Viscometer
30
• This is a multipoint viscometer and belongs to the category of rotational
viscometers.
• The sample is placed in the cup and the bob is placed in the cup up-to
an appropriate height.
• The sample is accommodated between the gap of cup and bob.
• Cup or bob is made to rotate and the torque (shearing stress) from the
viscous drag is measured by a spring or sensor in the drive of the bob
Couette type: Revolving cup type - MacMichael viscometer
Searle type: Revolving bob type - Stormer viscometer
The apparent viscosity of a pseudoplastic system can be estimated by
η = Kv [w/v]
w = Weight placed on the hanger, shearing stress N/m²
v = rpm, shear rate s⁻¹
η = Apparent viscosity
Kv = Constant for the instrument

31. Plug flow
31
One of the Disadvantages of Cup and Bob Viscometer
● The sample is placed between the cup and bob
● During evaluation, when the bob is made to rotate, the amount of stress
exerted near the wall of the bob is relatively higher compared to the stress
observed at the inner wall of the cup that means
Different stresses are being exerted across the sample,
Hence the readings may not represent the stress on the entire sample
Ex: In plastic system,
Below yield value, the apparent viscosity is infinite
Above yield value, it posses a finite plastic viscosity
When the bob is made to rotate at lower rates of shear, the stress closer to the
rotating bob may be higher than yield value
But, at the inner wall of the cup, the stress may be below the yield value
So, the material at the zone remain as a solid plug
Minimised by
1. Using the largest bob possible in order to reduce the gap
2. Increasing the speed of rotation of the bob, so that the stress at outer wall
of the cup is above the yield value and the system undergoes laminar flow
It is undesirable for the
rheological evaluation
of dispersion system
It is important in
extrusion of toothpaste
and ointment from the
tube

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