This document discusses rheology, which is the science describing the flow and deformation of matter under stress. It defines key terms like viscosity, shear stress, shear rate, and classifies fluids as Newtonian or non-Newtonian based on their relationship between shear stress and shear rate. Newtonian fluids have a constant viscosity regardless of shear rate, while non-Newtonian fluids have variable viscosity. Plastic, pseudoplastic, and dilatant behaviors are described for non-Newtonian fluids. Thixotropy, which is a time-dependent decrease and recovery of viscosity under shear, is also discussed. The document concludes by explaining the operation and calibration of common viscometers.

1. UNIT 5
RHEOLOGY
KPJ HEALTHCARE UNIVERSITY
COLLEGE

2. RHEOLOGY
Science describing the flow and deformation
of matter under stress.
Rheo = the flow
Viscosity   is the resistance of a fluid
material to flow under stress. The higher the
viscosity, the greater the resistance.

3. Importance of rheology
– Formulation of medicinal and cosmetic creams,
pastes and lotion.
– Formulation of emulsion, suspension, suppositories
and tablet coatings.
– Fluidity of solutions for injection.
– In mixing and flow of materials, their packaging into
containers, their removal prior to use, whether by
pouring from a bottle, extrusion from a tube, or
passage through a syringe needle.
– Can affect patient acceptability, physical stability, and
even biological availability.

4. Viscosity
 Viscosity is an index of resistance of a liquid to
flow.
 The higher the viscosity the greater the
resistance
 Water and alcohol has the least resistance to
flow (lowest viscosity)

5. Types of viscosity
 Kinematic viscosity: It is defined as the
viscosity(neta) divided (row) of the liquid.
Viscosity is expressed as kinematic viscosity in
official pharmacopoeias. It is expressed as
kinematic viscosity=neta/row
The unit of kinematic viscosity is stokes (s) and
centistokes(cs)

6. Types of viscosity
 Relative viscosity: the coefficient, abbreviated,
neta r is defined as the ratio of viscosity of the
dispersion (neta) to that of the solvent neta0
(vehicle) it is mathematically expressed as
Relatively viscosity, nr =neta-neta0/neta0

7. Types of viscosity
 Specific viscosity: this term is defined as the
relative increase in the viscosity of the
dispersion over that of the solvent (vehicle)
alone. It is mathematically expressed as
Specific viscosity, neta sp=n-n0/n0
 Reduced viscosity: this term is defined as the
ratio of specific viscosity to the concentration
(c). It is mathematically expressed as
 Reduced viscosity=netasp/c

8. Types of viscosity
 Specific viscosity: this term is defined as the
relative increase in the viscosity of the
dispersion over that of the solvent (vehicle)
alone. It is mathematically expressed as
Specific viscosity, neta sp=n-n0/n0
 Reduced viscosity: this term is defined as the
ratio of specific viscosity to the concentration
(c). It is mathematically expressed as
 Reduced viscosity=netasp/c

9. Types of viscosity
 Intrinsic viscosity: the reduced viscosity is
determined at various concentrations of a
substance and the results are plotted. The
resulting line can be extrapolated to c=0 to
obtain the intercept. The intercept value is
known as intrinsic viscosity. This parameter is
useful to determine the molecular weight of
polymers.

10. Other important definitions
 Shear stress is defined as the force per unit area
F’/A, which is applied to bring about the flow
Shear stress, F=F’/A
 Velocity gradient or rate of shear, dv/dr is defined
as the change in the velocity, dv, with an
infinitesmal change in distance, dr.
Rate of shear, G=dv/dr
The higher the viscosity of the liquid the greater is
the force per unit area required to produce a certain
rate of shear.

11. Other important definitions
 Hence the relationship between shear stress
and rate of shear is given as follows
F’/A∞dv/dr
Or F’/A=neta dv/dr
Or F=netaG
In which neta is the coefficient of viscosity and
usually referred to as viscosity.
Viscosity is calculated by neta=F/G
This equation is called as Newtonian equation

12. Rheogram
G V neta=1
F
Rheogram: Rheogram is a plot of rate of shear Vs shearing stress.
For Newtonian liquid if G is plotted Vs F the flow curve gives straight
line passing through the origin and the slope is the coefficient of
viscosity and is equivalent to 1

13. Other important definitions
 Coefficient of viscosity is defined as the force
per unit area required to maintain unit difference
in velocity between two parallel layers in the
liquid, one centimeter apart
 Units of Viscosity:
In ISO system the unit of viscosity is the poise,
named after Poiseulle. It is practically expressed
as centipoise, cp (=0.01 poise)
In CGS system the units for viscosity is dynes/cm2

14. Other important definitions
 Poise: it is defined as the shearing stress
required to produce a velocity of 1cm/sec
between two parallel planes of a liquid each
1cm2 in area and separated by a distance of
1cm.
 Fluidity: this term fluidity ø is used to denote
the reciprocal of viscosity i.e. Fluidity ø=1/neta

15. Thixotropy and Antithixotropy
 “Change by touch”
 Thixotropy is defined as an isothermal and
comparatively slow recovery process on standing
of a material of a consistency lost through
shearing. This is applied for plastic and
pseudoplastic system. This is also called as gel to
sol to gel transformation.
 Antithixotropy: This is also called as negative
thixotropy, this represents an increase in
consistency on the down curve. The down curve
shifts to the right of the up curve. This is also called
as sol to gel to sol transformation

16. Classification of Rheological Systems
Newtonian System
Non- -Newtonian System

18. NEWTONIAN SYSTEMS
NEWTONIAN ‘S LAW OF FLOW

20. Shearstress
NEWTONIAN FLOW
Newton assumed that all materials have, at a given
temperature, a viscosity that is independent of the shear
rate.
In other words, twice the force would move the fluid twice
as fast.
Simple Newtonian Rheogram
Shear rate
viscosity

21. Shear: is the movement of material
relative to parallel layer.
Shear stress (F’): is the force per unit
area required to bring about flow (F/A)
Shear rate (S) difference in velocity dv,
between two planes of liquids separated
by distance dr (i.e. dv/dr)
F/A α dv/dr

22. Absolute (dynamic) viscosity
Viscosity=  = F’ = shear stress = dyn m-2 = dyn m-2 s
S shear rate sec-1
The fundamental unit of viscosity measurement is
the poise. A material requiring a shear stress of
one dyne per square centimeter to produce a
shear rate of one reciprocal second has a
viscosity of one poise, or 100 centipoise.

23. Definitions
Fluidity; it is the reciprocal of viscosity
Ø = 1/ 
Kinematic Viscosity:
It is the absolute viscosity divided by the density
of liquid at a specified temperature
Kinematic viscosity =   p
Where p is the density of the liquid
The unite is Stock (s) or centistock (cs)

24. Definitions
Relative viscosity:
Is the relation of the solution viscosity  to
the viscosity of the solvent “standard”  
 rel =    
_ Specific Viscosity
 sp =  rel-1

25. Example
A) The viscosity of acetone at 25°C is 0.313 cp, its density at
25°C is 0.788 g/cm3. What is its kinematic viscosity at
25°C?
B) Water is usually used as a standard of liquids. Its viscosity
at 25°C is 0.89 cp. What is the viscosity of acetone
relative to that of water (relative viscosity,  rel ) at 25°C?
Solutions:
a) Kinematic viscosity = 0.313 cp ÷ 0.788 g/cm3= 0.397 cs
b) Relative viscosity  rel = 0.313 cp ÷ 0.8904 cp = 0.352
(dimensionless)

26. Liquid Viscosity(cp)
Castoroil
Chloroform
Ethylalcohol
Glycerol
Oliveoil
Water
1000
0.563
1.19
400
100
1.0019
ABSOLUTE VISCOSITY OF SOME OF THE COMMONLY USED LIQUI

27. NON- -NEWTONIAN
SYSTEMS

28. NON- -NEWTONIAN SYSTEMS
A non- -Newtonian fluid is defined as one for
which the relationship between F’ and S is not a
constant.
In other words, when the shear rate is varied,
the shear stress doesn't vary in the same
proportion. The viscosity of such fluids will
therefore change as the shear rate is varied.
It can be seen in liquid and solid heterogeneous
dispersions such as colloids, emulsions, liquid
suspensions and ointments.

29. NON- -NEWTONIAN SYSTEMS
THREE CLASSES:
– Plastic flow
– Pseudoplastic flow
– Dilatant flow

30. 1.PLASTIC FLOW
Plastic flow is associated with the preparation of
flocculation or aggregations of particles in
concentrated suspension, also known as
Bingham bodies.
A Bingham body does not begin to flow until a
shearing stress corresponding to the yield value
is exceeded.
Yield value (f); is an indication of the force that
must be applied to a system to convert it to a
Newtonian System.
Examples; suspension of Zno in mineral oil,
certain paints, ointments

31. 1.PLASTIC FLOW

32. Plastic flow Rheogram
 Plastic flow
rate of shear yield value
(G)
Shearing Stress (F)

33. PLASTIC FLOW (CONT.)
The slope of the rheogram is termed
Mobility, analogous to fluidity in Newtonian
system, and its reciprocal is known as
Plastic viscosity, U
U= F – f
S
Where f is the yield value

34. PLASTIC FLOW (CONT.)
Problem
A plastic material was found to have a yield value of 5200
dyne.cm-2. At a shearing stress above yield value, F was
found to increase linearly with S. If the rate of shear was
150 sec-1 when F was 8000 dyne.cm-2. Calculate the
plastic viscosity of the sample.
Solution:
U = F – f = 8000 – 5200 = 18. .67 poise
S 150

35. 2. Pseudoplastic Flow (shear- -thinning)
The curve begins at the origin (or approach it),
there is no yield value.
Occurs in dispersion of polymers (e.g. syenthetic
or natural gum, cellulose derivatives)
As the shearing stress is increased, disarranged
molecules orient themselves to the direction of
flow. This orientation reduces internal friction
and resistance of the molecules and allows a
greater rate of shear at each shear stress.
Some of the solvent associated with molecules
will be released resulting in decreasing the
viscosity.
This type of flow behavior is sometimes called
shear- -thinning.

36. Pseudo- -plastic flow behavior; Structural reasons

37. Pseudo- -plastic flow behavior; Structural reasons

38. Pseudoplastic Flow
-Random arrangement
polymer chains
-Solvent interact with polymer
- Chain entalgment
Increased
stress
-Chains line up in the direction of the
Applied stress
-Layers move over each other more
easily
-More vehicle available

39. Pseudo-Plastic flow Rheogram
 Pseudo-Plastic flow
rate of shear
(G)
Shearing Stress (F)
The curve begins at (or near) the origin, there is no
yield value
-Apparent viscosity at any shear rate is determined
from the slop of a tangent to the curve at that point

40. 3. Dilatant Flow
(shear- -thickening)
Certain suspensions with a high percentage (up
to 50%) of deflocculated solids exhibit an
increase in resistance to flow with increasing
rate of shear.
Such systems actually increase in volume when
sheared and hence termed dilatant.
This type of flow behavior is sometimes called
shear--thickening.
When stress is removed, a dilatent system
returns to its original state of fluidity. E.g. corn
starch in water.

41. Dilatant flow Rheogram
 Dilatant flow
rate of shear
(G)
Shearing Stress (F)

42. Reasons for Dilatency
1. At rest particles are closely packed with minimal
inter- -particle volume (void), so the amount of
vehicle is enough to fill in voids and permits
particles to move at low rate of shear.
2. Increase shear stress, the bulk of the system
expand (dilate), and the particles take an open
form of packing.
3. The vehicle becomes insufficient to fill the voids
between particles. Accordingly, particles are no
longer completely wetted (lubricated) by the
vehicle.
4. Finally, the suspension will set up as a firm
paste.
5. This process is reversible.

43. Resting Sheared
-Closedpackparticles
-Minimumvoidvolume
-Sufficientvehicle
-Relativelylowconsistency
Openpackedparticles
Increasedvoidvolume
Insufficientvehicle
Relativelyhighconsistency
Characters of dilatent system

44. SIGNIFICANCE OF DILATENCY
Such behaviour suggests that appropriate precautions
should be used during processing of dilatent materials.
Mixing (powder+granulating liquid) is usually conducted
in high speed mixers, dilatent materials may solidify
under these conditions thereby damage the equipments.

45. Sum up of all types of material flow

46. THIXOTROPY
Non-Newtonian, Time Dependent behaviour.
Definition of Thixotropy:
It is the decrease in viscosity as a function
of time upon shearing, then recovery of
original viscosity as a function of time
without shearing.

47. THIXOTROPY
– A decrease in apparent viscosity with time under
constant shear rate or shear stress, followed by a
gradual recovery, when the stress or shear rate is
removed.
– Such system contain asymmetric particles forming a
loose network through sample. At rest, this structure
impart rigidity to system resembling gel. As shear
applied, the structure begin to break and the material
undergo Gel-to-Sol transformation. Finally, at rest the
structure is restored again (Sol-to Gel).
– It happens with pseudoplastic materials (shear-
thinner)

48. THIXOTROPY

49. Shearstress
THIXOTROPY
Shear rate

50. THIXOTROPY
Examples of thixotropic samples are ketchup,
consumer paints, yoghurts, mayonnaise.
Thixotropic samples break their structure under
shear rate and rebuilds the structure at rest. The
rebuild is occurring under a material specific
time scale. The rebuild speed is highest at rest
and slow at low shear rates.

51. Thixotropy in Formulation
In suspension, particles will not settle down in
the container (gel form), will become fluid (sol)
on shaking for a dose to dispense. At rest, it will
retain its consistency to maintain the particles
suspended. This is also applied to emulsions,
lotions and creams.
40-
Parenteral suspensions used for intramuscular
depot therapy, e.g. procaine penicilline G (40-
70% w/v in water)

52. Rheopexy
– An increase in apparent viscosity with time
under constant shear rate or shear stress,
followed by a gradual recovery when the
stress or shear rate is removed. Also called
Anti-thixotropy or negative thixotropy.

53. Operation of Capillary and
Cone & Plate Viscometers

54. Capillary Viscometer
 Select appropriate
capillary size to give
reasonable times
 Keep constant
temperature
 Time fluid falling
between two fiducial
marks (a) and (b)
 Avoid parallax
Also known as Ostwald (U-tube)

55. Brookfield Cone & Plate Viscometer
 Shallow angled cone in very close proximity
with a flat plate
 Important features
 Circulating bath to keep constant temperature
 Different cone sizes
 Level on the instrument
 Adjusting ring
 Motor speed in RPM
 Operation
 Adjust cup so pins barely not making contact
 Measure torque needed to overcome viscous
resistance

56. Calibrations

57. Calibration
 Capillary Viscometer
 Second term neglected for sufficiently long times
(>60 sec)
 Fluid of known viscosity used to determine
parameter B
2
'
t
B
tB



=

58. Calibration
Brookfield
Standard
Density
(g/mL)
Viscosity
(cP @
25°C)
Average
time (sec)
Parameter B
(cP*mL/g*sec)
Fluid 100 0.974±
0.005 (2)
96.6 89.84±
0.22 (1)
1.104±
0.006 (2)
Fluid 50 0.971±
0.005 (2)
47.9 44.74±
0.14 (1)
1.102±
0.006 (2)
Cannon-Fenske Routine Capillary Viscometer:
Size 400 with T=25°C
(1) Standard deviation (2) Propagated error

59. Calibration
 Brookfield cone and plate viscometer with cone
size CP-41 and T=28.5°C
y = 1.1221x - 1.8099
y = 1.1405x - 1.4843
0
20
40
60
80
100
120
30 40 50 60 70 80 90 100
Measured Viscosity (cP)
ActualViscosity(cP)
6 RPM 12 RPM Linear (6 RPM) Linear (12 RPM)

60. Viscosity of an
Unknown Fluid

61. Unknown Fluid
 Capillary Viscometer
 Accuracy: 0.7% vs ±0.2% reported
 Reproducibility: 0.19% vs ±0.1%
Average Time
(sec)
Density
(g/mL)
Viscosity
(cP)
89.89±0.17 (1)
0.974±0.005 (2)
96.7±0.7 (2)
(1) Standard deviation (2) Propagated error

62. Unknown Fluid
Motor speed
(RPM)
Viscosity
Reading (cP)
Viscosity (cP)
6 85.8 94.5
12 86.0 96.6
 Brookfield Cone and Plate Viscometer
 Average viscosity=95.5±1.5 cP (st dev)
 Accuracy: 1.6% vs ±1%

63. Results
 Unknown fluid determined to be Brookfield Fluid
100 (μ=96.6 cP)
 Capillary Viscometer (25°C)
 96.7±0.7 cP
 Error of 0.10%
 Cone and Plate Viscometer (28.5°C)
 95.5±1.5 cP
 Error of 1.1%
 Student’s T Test
 84.4% Probability they are the same

64. Determination of Viscosity
U-tube viscometers
Falling sphere viscometers
Rotation viscometers

65. .1Cappilary viscometers
Also known as Ostwald (U-tube(
viscometer of glass cappilary viscometer.
Used for Newtenian flow
Classified as direct flow
and reverse flow viscomenters

66. .2Falling sphere viscometers
A glass or steel ball of known size and density is
allowed to descend through the liquid hold
stationary in a vertical glass tube.
The rate at which the ball
falls inversely proportion
to the viscosity.
- Electrical sensor is used for
opaque liquids

67. 3. rotational Rheometers
1. Concentric cylinder rheometer
A viscometer in which the liquid
whose viscosity is to be measured
fills the space between two vertical
coaxial cylinders, the inner one
suspended by a torsion wire; There is
two types:
The outer cylinder is rotated at a
constant rate, and the resulting
torque on the inner cylinder is
measured.
The inner cylinder is rotated at a
constant rate, and the resulting
torque on the outer cylinder is
measures

68. 2. Cone and plate type

69. Important notes
 Flocculated suspensions exhibit plastic flow
 Newtonian fluids are expressed in terms of
viscosity whereas non Newtonian fluids are
expressed apparent (viscosity)
 Fluidity is a term associated with Newtonian
fluids, whereas mobility is the term used for
fluids exhibiting plastic flow
 Dilatant flow is characterized as a reverse
phenomenon of pseudoplastic fluids

70. Important notes
 Deflocculated suspensions containing high
concentration of the dispersed solids exhibits
dilatant flow
 In antithixotropy the down curve is frequently
positioned to (with respect to up curve) right
 At equillibrium, the thixotropic behaviour of a
pseudoplastic system exhibit the state of a Sol
 Viscosity, body and slip, and spreadability are
the rheological properties whereas surface
tension is not a rheological property

71. Important notes
 Pseudoplastic flow behaviour can be explained by
apparent viscosity
 High viscosity indicates stronger intermolecular
attractions
 An o/w emulsion has the viscosity greater than that of
the internal phase
 A system which undergoes gel to sol transformation is
known as shear thinning
 Ostwalds viscometer measures kinematic viscosity
 When the IM injection of procaine penicillin G is given, a
process of ‘depot’ formation occurs due to rapid
thixotropic recovery