14 rheology

Learning Outcomes
Students should be able to understand and explain:
• General Introduction to the concept of Rheology,
• The classification of liquid into different types of flow,
• The characteristics of Newtonian and Non-Newtonian liquids,
• The reasons a liquid shows certain type of flow,
• The advantages and disadvantages of a flow type compared to another,
• The methods to characterize types of flow & the calculations involved,
• The interpretations of rheograms,
• Thixotropy phenomena and their importance,
• Factors affecting the rheological properties of dispersed systems.
• ways to modify and improve a problematic dispersed formulation.
2

Rheology: has been derived from Greek words logos“science”
and Rheo “to flow”.
Viscosity is an expression of the resistance of a fluid to flow. The
higher the viscosity, the greater the resistance.
Rheology may thus be defined as:
The science concerned with the deformation of matter under the
influence of stress, which may be applied perpendicularly to the
surface of a body (tensile stress) or tangentially to the surface of
a body (a shearing stress) or at any other angle to the surface of
the body.

5
The deformation that results from the application of a
stress may be divided into two types:
i) Elastic Deformation :
It is a spontaneous and reversible deformation.
Exhibited by elastic bodies
ii) Plastic Deformation :
It is a permanent or irreversible deformation.
Plastic deformation is exhibited by viscous bodies.

6
S LOW OF FLOW’NEWTONIAN
Let us consider a block of liquid consisting of parallel
plates of molecules as shown in the figure.
The bottom layer is considered to be fixed in place.
 If the top plane of liquid is moved at constant velocity,
each lower layer will move with a velocity directly
proportional to its distance from the stationary bottom layer
Representation of shearing force
acting on a block of material

7
☻Rate of Shear dv/dr = G
Is the velocity difference dv between two planes of liquid
separated by an infinite distance dr.
Indicates how fast a liquid flows when a stress is applied on it
☻The Shearing Stress F'/A = F
Is the force per unit area required to cause flow.
☻ Newton recognized that:
The higher the viscosity of a liquid, the greater the force per
unit area (shearing stress) required to produce a certain rate
of shear. Thus, the rate of shear is directly proportional to the
shearing stress.
F'/A α dv/dr
F'/A = η dv/dr (1)
where η is a constant known as viscosity
η = F / G. (2)
The unit of viscosity is poise or dyne.sec.cm-2 .

8
Poise
Is the shearing force required to produce a velocity of 1 cm/sec
between two parallel planes of liquid each 1 cm2 in area and
separated by a distance of 1 cm.
(cp)Centipoises
= 0.01 Poise.
Rheogram
To express the rheological properties of liquids
Graphs showing the variation of shear rate with shear stress
(obtained by plotting F versus G)

9
Newtonian systems
• These systems have constant viscosity where
• η = F / G.
• When we plot a rheogram of G against F then we become a strait
line passing through the origin, the slope of which is equal to the
reciprocal of viscosity, a value referred to as the fluidity Φ, Φ =
1 / η
• Newtonian systems like water, simple organic liquids, true solutions
and dilute suspensions and emulsions
Shearing stress
Shearing rate
Slope = Φ = 1 / η
Rheogram of a
Newtonian liquid

10
The linear curve for newtonian liquids passing through the origin
1. The passage through the origin indicates that even a mild force
can induce flow in these systems.
2. The linear nature of the curve shows that the viscosity (η) of a
Newtonian liquid is a constant unaffected by the value of the
rate of shear.
Thus a single determination of viscosity from the shear stress at
any given shear rate is sufficient to characterize the flow
properties of a Newtonian liquid.
Shear rate
viscosity

11
Kinematic Viscosity
The kinematic viscosity of a liquid is its absolute
viscosity divided by the density at a definite
temperature.
kinematic viscosity (s) = η /ρ
The units of kinematic viscosity are the stoke (s) and the
centistoke (cs)
Relative Viscosity
Relative Viscosity (η r) is the ratio of
solution viscosity (η) to the viscosity of the solvent (ηo )
(in pharmaceutical products it is often water).

12
FLOW CHARACTERISTICS OF NON-NEWTONIAN SYSTEMS
 Do not follow the simple Newtonian relationship
i.e. when f is plotted against G the rheogram is not a
straight line passing through the origin
i.e. viscosity is not a constant value.
 Such as colloidal dispersions, emulsions, suspensions
and ointments, etc.
 There rheograms represents three types of flow:
- plastic
- pseudoplastic
- dilatant.

13
1. Plastic Flow (Such materials are called Bingham bodies)
Rheogram for a plastic material
• The curve is linear over most of its length corresponding to that of a
Newtonian fluid.
• However, the curve does not pass through the origin but rather intersects
the shearing stress axis (or will if the straight part of the curve is
extrapolated to the axis) at a particular point referred to as the Yield value
or Bingham Yield value
f Shear stress
Shear strain

14
 Contrary to a Newtonian liquid that flows under the
slightest force, a Bingham body does not flow until a definite
shearing stress equal to the yield value is applied. Below the
yield value the system acts as an elastic material.
plastic systems resembles Newtonian systems at shear
stresses above the yield value.
 The slope of the rheogram is termed mobility, analogous to
fluidity in Newtonian systems and its reciprocal is known as
the Plastic viscosity, U.
U = (F - f)
G
 Plastic systems are shear-thinning systems

15
Explanation of Plasticity:
• Flocculated particles in a concentrated suspensions
usually show plastic flow
• The yield value is because the van der Waals forces
between adjacent particles, which must be broken first
before flow can occur
 The more flocculated the suspension the higher will be
the yield value
Shear

16
2-Pseudoplastic Flow
•A large number of pharmaceutical products, including
natural and synthetic gums, e.g. liquid dispersions of
tragacanth, sodium alginate, methyl cellulose, and
Na-carboxymethylcellulose show pseudoplastic flow.
•As a general rule pseudoplastic flow is exhibited by
polymers in solution, in contrast to plastic systems
which are composed of flocculated particles in
suspension.

17
• Curve for a pseudoplastic material begins at the origin
consequently, in contrast to Bingham bodies, there is no yield value.
Since no part of the curve is linear, one can not express the viscosity
of a pseudoplastic material by any single value.
• The viscosity of a pseudoplastic substance decreases with increasing
rate of shear. (shear-thinning systems)
• As the shearing stress is increased, the normally-disarranged
molecules begin to align their long axes in the direction of flow.
Shear stress
Shear strain Rheogram of a
pseudoplastic system

18
• Newtonian system is completely described by η, the viscosity.
• Plastic system is described by the yield value and the plastic
viscosity.
• Pseudoplastic systems which can not be described by a single value
are expressed by:
FN = η’ G
When N = 1, equation the flow is Newtonian
As N rises the flow becomes increasingly non Newtonian.
The term η’ is a viscosity coefficient.
The logarithmic form is a straight line equation
log G = N log F – log η’
A straight line is obtained when log G is plotted against log F

19
3-Dilatant Flow
Dilatant systems exhibit an increase in resistance to flow
(viscosity) with increasing rates of shear. “ shear
thickening systems”.
Such systems actually increase in volume when sheared
and are hence termed dilatant. When the stress is
removed, a dilatant system returns to its original state of
fluidity

20
Shear stress
Shear strain Rheogram of a dilatant
system
Dilatant flow is the reverse of that possessed by pseudoplastic
systems.
The equation: FN = η’ G
can be used to describe dilatancy in quantitative terms. In this case,
N is always less than 1 and decreases as the degree of dilatancy
increases.
as N approaches 1, the system becomes increasingly Newtonian in
behaviour

21
• Substances possessing dilatant flow properties are invariably
suspensions containing a high concentration (about 50 percent or
greater) of small, deflocculated particles.
• As discussed previously, particulate systems of this type which are
flocculated would be expected to possess plastic, rather than
dilatant flow characteristics.
Dilatant behavior may be explained as follows:
• At rest, the particles are closely packed with the antiparticle
volume, or voids, being at a minimum.
• The amount of vehicle in the suspension is sufficient, however, to
fill this volume and permits the particles to move relative to one
another at low rates of shear.
• Thus, one may pour a dilatant suspension from a bottle since
under these conditions it is reasonably fluid.

22
 As the shear stress is increased, the bulk of the system expands or dilates, hence
the term dilatant. The particles, in an attempt to move quickly past each other,
take on an open form of packing. Such an arrangement leads to a significant
increase in the antiparticle void volume.
 The amount of vehicle remains constant and at some point, becomes insufficient
to fill the increased voids between the particles. Accordingly, the resistance to
flow increases because the particles are no longer completely wetted or
lubricated by the vehicle. Thus, the suspension will set up as a firm paste

23
Time dependant behaviour
Thixotropy
When shear stress is reduced after it reaches its maximum desired
value:
Newtonian flow: The down-curve is identical with the up curve
Pseudoplastic and plastic flow: down curve is displaced to the left of
the up curve
The breakdown of the structure does not reform immediately
when the stress is reduced or removed
Shear stress
Shear strain

24
Thixotropy, may be defined as:
an isothermal and comparatively slow-recovery, on standing of a
material, of a consistency lost through shearing”. As so defined,
thixotropy may only be applied to shear-thinning systems.
Antithixotropy
Is the slow loss of consistency that was gained by shearing. It is
associated with dilatant systems
Measurement of Thixotropy
The most apparent characteristic of a thixotropic system is the
hysteresis loop, formed by the up- and down-curves of the
rheogram.
This area of hysteresis has been proposed as a measure of
thixotropic breakdown; it may be obtained readily by means of a
planimeter

25
Flow Behaviour
DILATANT
S
PSEUDOPLASTICS
IDEAL
FLUIDS
TYPES of
FLUIDS
FLOW
behaviors
OSTWALD
DRY
STEIGER
OSTWALDNEWTONMODELS
DIFFERENT
FLOW
behaviors/
FUNCTION
OF SHEAR
RATE
Moving
sands,
High
concentrate
d
suspension
Cellulosi
c Ethers
Solution
Emulsion,
Toothpaste
, Blood
Salt
Solutions,
gases
Pure
Liquid
INDUSTRIAL
EXEMPLES

26
THIXO-
TROPICS
PLASTICSTYPES of
FLUIDS
FLOW
behaviors
MODELS
DIFFERENT
FLOW
behaviors/
FUNCTION OF
SHEAR RATE
Alkyd
Paints
Tomatoes
Sauce
Fruit juices
INDUSTRIAL
EXEMPLES

29
Choice of Viscometer:
1. Newtonian systems:
 The rate of shear in a Newtonian system is directly proportional to the shearing
stress, thus one can use instruments that operate at a single rate of shear.
 These “one point” instruments provide a single point on the rheogram;
extrapolation of a line through this point to the origin will result in the
complete rheogram.
 The problem is the prior knowledge that the flow characteristics of the material
are Newtonian.
 Capillary & falling sphere viscometers
2. Non-Newtonian systems:
 The instrumentation used must be able to operate at a variety of rates of shear.
 Only by the use of “multi-point” instruments is it possible to obtain the
complete rheogram for these systems.
 Cup and bob & cone and plate viscometers

30
Capillary viscometer
The viscosity of a Newtonian liquid
may be determined by measuring the
time required for the liquid to pass
between two marks as it flows by
gravity a vertical capillary tube,
known as a Ostwald viscometer

31
Modern adaptation of the original Ostwald viscometer
The time flow of the liquid under test is compared with the time for
a liquid of known viscosities (usually water) to pass between the two
marks.
1 1 t1
2 2 t2
1 and 2 : the viscosities of the unknown and the standard
liquids.
1 and  2 : the densities of the liquids.
t1 and t2 : the respective flow times in seconds.
1/2 = re is the relative viscosity of the liquid under test

32
Equation is based on Poiseuille's law for a liquid flowing
through a capillary tube.
=  r4 t P
8 l V
r : radius of the inside of the capillary,
t : time of flow
P : pressure head in dyne/ cm2 under which the liquid flows
l : length of the capillary
V : volume of liquid flowing

33
The Hoeppler
viscometer
1) The sample and ball are placed in the inner glass tube and allowed to
reach temperature equilibrium with the water in the surroundings
constant temperature jacket
2) The tube and jacket are then inverted
3) The time for the ball to fall between two marks is accurately
measured and repeated several times .
Falling sphere Viscometer:
In this type of viscometer, a glass or steel ball rolls down an
almost vertical glass tube containing the test liquid

34
At a known constant temperature for a ball of a particular
density and diameter, the rate at which it falls is an inverse
function of viscosity of the sample
The viscosity of a Newtonian liquid is then calculated from:
= t (Sb-Sf) B
t : the time interval in seconds for the ball to fall between the two
points
Sb and Sf : the specific gravity of the ball and fluid under
examination at the temperature being used
B : a constant for a particular ball and is supplied by the
manufacturer

35
Cup and bob viscometers
In cup and bob
viscometers the sample is sheared
in the space between the outer
wall of a bob and the inner wall of
a Cup into which the bob fits .
•The principle is illustrated in figure
the various instruments available
differ mainly in whether the torque
set up in the bob results from the
cup or the bob being caused to
revolve
•The viscous drug on the bob due to
the sample causes it to turn the
resultant torque is proportional to
the viscosity of the sample

36
Cone and plate viscometer cone
plate
The cone is driven by a speed motor and the
sample is sheared in the narrow gap between
the stationary plate and the rotating cone
Advantages over cup and bob viscometer
1. Time saved in cleaning
2. The small sample size
3. More suitable for semisolid preparations
4. Rate of shear is constant throughout the sample

37
Factors affecting rheological properties
1. Chemical factors
A- Degree of polymerization
the longer polymer molecules may be susceptible to shear depolymerization will be
accompanied by decrease in viscosity as was found for sodium alginate.
B- Extent of Polymer Hydration
In hydrophilic polymer solution the molecules are regarded as completely
surrounded by immobilized water molecules forming a solvent layer. Such
hydration of hydrophilic polymers gives rise to an increased viscosity.
C- Impurities, Trace Ions and Electrolytes
Chemical impurities are the major factors in changing the viscosity of natural
polymers e.g. in Na alginate solution, the viscosity increase if traces of Ca are
present, due to the formation of calcium alginate.
D- Effect of pH
Changes in pH greatly affect the viscosity and stability of the hydrophilic natural
and synthetic gums. The natural gums usually have a relatively stable viscosity
plateau extending over 5 or 4 pH units. Above and below this pH range viscosity
decreases sharply.

38
2- Physical Factors
A- Temperature
A temperature increase usually produces a rapid viscosity decrease,
with the exception of certain synthetic polymers such as methyl
cellulose,
B- Aeration
Aerated products usually result from high shear milling. Aerated
samples appear to be more viscous or have more viscous creamed
layer than non-aerated samples
(c) Light
Various hydrocolloids in aqueous solutions are reported to be
sensitive to light. These colloids include carbopol, Na alginate, and
Na CMC. To protect photosensitive hydrocolloids from
decomposition and resultant viscosity change use light-resistant
containers

39
(4) Thixotropy and Suspension Formulation
• Thixotropy is particularly useful in suspensions and emulsions.
These must be poured easily from containers, which requires low
viscosity.
• Low viscosity, however, causes rapid settling of solid particles in
suspensions and rapid creaming of emulsions.
• A thixotropic agent such as microcrystalline cellulose is
incorporated into the suspensions or emulsions to give a high
viscosity.
• High viscosities retard sedimentation and creaming. When it is
desired to pour some of the suspension or emulsion from its
container, it is shaken well.
(5) Rheology and Diagnosis of Disease
Several studies have been made to correlate the rheology of body
fluids and the diagnosis of disease, e.g. The rheology of blood is of
interest in the studies of normal and abnormal blood and vascular
states.

Rheology
• Part of mechanics that deals with the flow of rocks,
or matter in general
• Deals with the relationship of the following:
(in terms of constitutive equations):
– stress, s
– strain, e
– strain rate e
.
(hence time, t)
– material properties
– other external conditions
• Rocks flow given time and other conditions!

Linear Rheologies
The ratios of stress over strain or stress over
strain rate is constant, e.g.:
• Elastic behavior: s = Ee
• Viscous behavior: s = ηe
.

Rheological Behavior of some materials
• Drop onto a concrete floor four objects:
– a gum eraser
– a cube of halite [commonly known as rock salt, is the mineral form of sodium chloride (NaCl)]
– a ball of soft clay
– one cm3 of honey
• When they fall, they behave the same by following the
Newton’s Second Law (F = mg)
• Their difference is when they reach the ground:
– The eraser rebounds and bounces (elastic)
– The clay flattens and sticks to the floor (ductile)
– The halite fractures and fragments scatter (brittle)
– The honey slowly spreads on the floor (viscous)

Material Parameters for Rheological behaviors
• Rheological dependents:
– Extrinsic (external) conditions such as:
• Pressure, Temperature, time, physicochemical
nature of the environment
– Intrinsic (internal) material properties such as:
• rock composition, mass, density

Material Parameters
• Are actually not purely “material constants”
• Are related to the rheological properties of a body, e.g.:
– rigidity
– compressibility
– viscosity, fluidity
– elasticity
• These depend on external parameters
• Are scalars in isotropic material and tensors of higher
order in anisotropic material

Constitutive Equations
• Mechanical state of a body is specified by:
• Kinematic quantities such as:
– strain, e
– displacement, d
– velocity, v
– acceleration, a
• Dynamic quantities such as:
– force, F
– stress, σ

Constitutive Equations, Example
F = ma
s = E e
• The constitutive equations involve both
mechanical and material parameters:
f (e, e
.
, s, s
.
, ……, M ) = 0
• M is material property depending on P, T, etc.

Law of Elasticity - Hooke’s Law
• A linear equation, with no intercept, relating stress
(s) to strain (e)
• For longitudinal strain:
s = E e (de/dt = 0)
• The proportionality constant ‘E’ between stress and
longitudinal strain is the Young’s modulus
• Typical values of E for crustal rocks are on the
order of 10-11 Pa
• Elasticity is typical of rocks at room T and pressures
observed below a threshold stress (yield stress)

Characteristics of Elasticity
• Instantaneous deformation upon application of a
load
• Instantaneous and total recovery upon removal of
load (rubber band, spring)
• It is the only thermodynamically reversible
rheological behavior
• Stress and strains involved are small
• Energy introduced remains available for returning the
system to its original state (internal strain energy)
– It does not dissipate into heat; i.e., strain is recoverable
• Typically, elastic strains are less than a few percents of
the total strain

Shear Modulus
• For shear stress and strains
ss = Gg
• The proportionality constant G between stress
and shear strain is the shear modulus (rigidity)

Bulk Modulus
• For volume change under pressure:
P = Kev
• K = P/ev is the bulk modulus; ev is dilation
• K is the proportionality constant between
pressure and volumetric strain
• The inverse of the bulk modulus is the
compressibility:
k = 1/K

Units of the proportionality constants
• The proportionality constants ‘E’, ‘G’, and ‘K’ are
the slope of the line in the s-e diagram
(slope = s/e)
• Since ‘E’, ,’G’, and K’ are the ratio of stress over
strain (s/e), their units are stress (e.g., Pa, Mpa,
bar) because ‘e’ is dimensionless

Ideal (Newtonian) Viscous Behavior
• Viscosity theory deals with the behavior of a liquid
• For viscous material, stress, s, is a linear function of
strain rate, e
.
=e/t, i.e.,
s = e
.
where  is the viscosity
• Implications:
• The s - e
.
plot is linear, with viscosity as the slope
• The higher the applied stress, the faster the
material will deform
• A higher rate of flow (e.g., of water) is associated
with an increase in the magnitude of shear stress
(e.g., on a steep slope)

Viscous Deformation
• Viscous deformation is a function of time
s = e
.
= e/t
• Meaning that strain accumulates over time (next slide)
• Viscous behavior is essentially dissipative
• Hence deformation is irreversible, i.e. strain is
– Non-recoverable and permanent
• Flow of water is an example of viscous behavior
– Some parts of Earth behave viscously given the large
amount of geologic time available

Ideal Viscous Behavior
• Integrate the equation s = e
.
with respect to time, t:
sdt = e
.
dt  st = e or s = e/t or e = st/
• For a constant stress, strain will increase linearly
with time, e = st/ (with slope: s/)
• Thus, stress is a function of strain and time!
s = e/t
• Analog: Dashpot; a leaky piston that moves inside a
fluid-filled cylinder. The resistance encountered by
the moving perforated piston reflects the viscosity

Viscosity, 
• An ideally viscous body is called a Newtonian
fluid
• Newtonian fluid has no shear strength, and its
viscosity is independent of stress
• From s = e/t we derive viscosity ()
 = st/e
Dimension of : [ML-1 T-2][T] or [ML-1 T-1]

Units of Viscosity, 
Units of  : Pa s (kg m -1 s -1 )
s = e
.
 (N/m2)/(1/s)  Pa s
s = e
.
 (dyne/cm2)/(1/s)  poise
If a shear stress of 1 dyne/cm2 acts on a liquid, and gives
rise to a strain rate of 1/s, then the liquid has a  of 1
poise
poise = 0.1 Pa s
  of water is 10-3 Pa s
• Water is about 20 orders of magnitude less viscous than
most rocks
  of mantle is on the order 1020-1022 Pa s

Nonlinear Behavior
• Viscosity usually decreases with temperature
(effective viscosity)
• Effective viscosity: not a material property but a
description of behavior at specified stress, strain rate,
and temperature
• Most rocks follow nonlinear behavior and people
spend lots of time trying to determine flow laws for
these various rock types
• Generally we know that in terms of creep threshold,
strength of salt < granite < basalt-gabbro < olivine
• So strength generally increases as you go from crust
into mantle, from granitic-dominated lithologies to
ultramafic rocks

Plastic Deformation
• Plasticity theory deals with the behavior of a solid
• Plastic strain is continuous - the material does not
rupture, and the strain is irreversible (permanent)
• Occurs above a certain critical stress
(sy, yield stress = elastic limit) where strain is no
longer linear with stress
• Plastic strain is shear strain at constant volume, and
can only be caused by shear stress
• Is dissipative and irreversible. If applied stress is
removed, only the elastic strain is reversed
• Time does not appear in the constitutive equation

Elastic vs. Plastic
• The terms elastic and plastic describe the nature of
the material
• Brittle and ductile describe how rocks behave
• Rocks are both elastic and plastic materials,
depending on the rate of strain and the
environmental conditions (stress, pressure, temp.)
– Rocks are viscoelastic materials at certain conditions

Plastic Deformation
• For perfectly plastic solids, deformation does not
occur unless the stress is equal to the threshold
strength (at yield stress)
• Deformation occurs indefinitely under constant
stress (i.e., threshold strength cannot be exceeded)
• For plastic solids with work hardening, stress must
be increased above the yield stress to obtain larger
strains
• Neither the strain (e) nor the strain rate (e
.
) of a
plastic solid is related to stress (s)

Brittle vs. Ductile
• Brittle rocks fail by fracture at less than
3-5% strain
• Ductile rocks are able to sustain, under a
given set of conditions, 5-10% strain
before deformation by fracturing

Strain or Distortion
• A component of deformation dealing with shape and volume
change
– Distance between some particles changes
– Angle between particle lines may change
• Extension: e=(l’-lo) / lo = l/ lo [no dimension]
• Stretch: s = l’/lo =1+e = l½ [no dimension]
• Quadratic elongation: l = s2 = (1+e)2
• Natural strain (logarithmic strain):
e =S dl/lo = ln l’/lo= ln s = ln (1+e) and since s = l½ then
e = ln s = ln l½ = ½ ln l
• Volumetric strain:
ev = (v’-vo) / vo = v/vo [no dimension]
• Shear strain (Angular strain) g = tan 
•  is the angular shear (small change in angle)

Factors Affecting Deformation
• Confining pressure, Pc
• Effective confining pressure, Pe
– Pore pressure, Pf is taken into account
• Temperature, T
• Strain rate, e
.

Effect of T
– Increasing T increases ductility by activating
crystal-plastic processes
– Increasing T lowers the yield stress (maximum
stress before plastic flow), reducing the elastic
range
– Increasing T lowers the ultimate rock strength
• Ductility: The % of strain that a rock can take without
fracturing in a macroscopic scale

Strain Rate, e
.
• Strain rate:
• The time interval it takes to accumulate a
certain amount of strain
– Change of strain with time (change in length per
length per time). Slow strain rate means that
strain changes slowly with time
– How fast change in length occurs per unit time
e
.
= de/dt = (dl/lo)/dt [T-1]
e.g., s-1

Shear Strain Rate
• Shear strain rate:
g
.
= 2 e
.
[T-1]
• Typical geological strain rates are on the
order of 10-12 s-1 to 10-15 s-1
• Strain rate of meteorite impact is on the
order of 102 s-1 to 10-4 s-1

Effect of strain rate e
.
• Decreasing strain rate:
– decreases rock strength
– increases ductility
• Effect of slow e
.
is analogous to increasing T
• Think about pressing vs. hammering a silly putty
• Rocks are weaker at lower strain rates
• Slow deformation allows diffusional crystal-plastic
processes to more closely keep up with applied stress

Strain Rate (e
.
) – Example
• 30% extension (i.e., de = 0.3) in one
hour (i.e., dt =3600 s) translates into:
e
.
= de/dt = 0.3/3600 s
e
.
= 0.000083 s-1 = 8.3 x 10-5 s -1

Strain Rate (e
.
) – More Examples
• 30% extension (i.e., de = 0.3) in 1 my
(i.e., dt = 1000,000 yr ) translates into:
e
.
= de/dt
e
.
= 0.3/1000,000 yr
e
.
= 0.3/(1000000)(365 x 24 x 3600 s)= 9.5 x 10-15 s-1
• If the rate of growth of your finger nail is about 1
cm/yr, the strain rate, e
.
, of your finger nail is:
e = (l-lo) / lo = (1-0)/0 = 1 (no units)
e
.
= de/dt = 1/yr = 1/(365 x 24 x 3600 s)
e
.
= 3.1 x 10-8 s-1

Effect of Pc
• Increasing confining pressure:
– inreases amount of strain before failure
• i.e., increases ductility
– increases the viscous component and
enhances flow
– resists opening of fractures
• i.e., decreases elastic strain

Effect of Fluid Pressure Pf
• Increasing pore fluid pressure
– reduces rock strength
– reduces ductility
• The combined reduced ductility and strength
promotes flow under high pore fluid pressure
• Under ‘wet’ conditions, rocks deform more
readily by flow
– Increasing pore fluid pressure is analogous to
decreasing confining pressure

Strength
• Rupture Strength (breaking strength)
– Stress necessary to cause rupture at room
temperature and pressure in short time
experiments
• Fundamental Strength
– Stress at which a material is able to withstand,
regardless of time, under given conditions of T, P,
and presence of fluids, without fracturing or
deforming continuously

Factors Affecting Strength
• Increasing temperature decreases strength
• Increasing confining pressure causes significant
– increase in the amount of flow before rupture
– increase in rupture strength
• (i.e., rock strength increases with confining
pressure
• This effect is much more pronounced at low T (< 100o)
where frictional processes dominate, and diminishes at
higher T (> 350o) where ductile deformation processes,
that are temperature dominated, are less influenced by
pressure

Factors Affecting Strength
• Increasing time decreases strength
• Solutions (e.g., water) decrease strength,
particularly in silicates by weakening bonds
(hydrolytic weakening) (OH- substituting for O-)
• High fluid pressure weakens rocks because it
reduces effective stress

Flow of Solids
• Flow of solids is not the same as flow of liquids, and is not
necessarily constant at a given temperature and pressure
• A fluid will flow with being stressed by a surface stress –
it does response to gravity (a body stress)
• A solid will flow only when the threshold stress exceeds
some level (yield stress on the Mohr diagram)

Rheid
• A name given to a substance (below its melting point) that
deforms by viscous flow (during the time of applied stress)
at 3 orders of magnitude (1000 times) that of elastic
deformation at similar conditions.
• Rheidity is defined as when the viscous term in a
deformation is 1000 times greater than the elastic term (so
that the elastic term is negligible)
• A Rheid fold, therefore, is a flow fold - a fold, the layers of
which, have deformed as if they were fluid

81
The term RHEOLOGY, from the Greek RHEO
(to flow) and LOGOS (science)was suggested
by Bingham & Crawford to describe the flow
of liquids and the deformation of solids.
Different materials deform differently under the same state of
stress. The material flow response to a stress is known as
Rheology.
RHEOLOGY
RHEO (GREEK) = to flow; LOGOS = SCIENCE  TO
DESCRIBE THE LIQUID FLOW AND DEFORMATION OF
SOLID
•VISCOSITY = AN EXPRESSION OF THE RESISTANCE OF A FLUID TO
FLOW ( VISCOSITY   RESISTANCE)
•(EASY FLOWING  DILUTE FLUID, MORE DIFFICULT TO FLOW
(VISCOUS FLUID)

Rheologyisused
inthestudyof
Paints, Doughs
Cosmetics (Lotion, Cream, Paste)
Road building materials
Inks
Dairy products
Emulsions, Suspensions, Suppositories, Coating
Materials
Mixing and flow of materials, packaging into
containers, pouring from the bottle, extrusion
from a tube, passage through a syringe needle

83
(a)Tensile Stress: a stress applied
perpendicularly to the surface of a
body.
(b) Shearing stress: a stress applied
tangentially to the surface of a body.
(c) Also Stress can be applied at any
other angle to the surface of a body.

84
The deformations are of two types:
(I)Elastic deformation: It is
spontaneous and reversible.
The work spent for the
deformation is recoverable
when the body returns to the
original position.

85
(II) Plastic deformation: It
is permanent and
irreversible. The work
spent for the deformation
is dissipated as heat.

TYPES OF FLOW &
DEFORMATION
NEWTONIAN
NON-NEWTONIAN
(Viscous structure)
F
d
x
D
v
NEWTON EQUATION
F/A =  . dv/dx or  = F / G
= Coefficient of Viscosity or Viscosity
produce a velocity of 1 cm/sec between
two parallel planes of liquid each 1 cm2
in area and separated by a distance of 1
cm
dyne.sec/cm2 or g/cm.sec
LAMINAR flow
A
F’/A = F = shearing stress
dv/dx = G = rate of shear

TERMINOLOGY
FLUIDITY  = 1/
Centipoise, cps = 0,01 poise
Dynamic viscosity = 
Kinematic viscosity = /
(Stokes, s or centistokes, cs)
ARRHENIUS equation =
Temperature dependence of viscosity
 = A.eEv/RT
A : a constant depending on molecular
weight and molar volume of the liquid,
Ev : an activation energy required to
initiate flow between the molecules.
RHEOGRAM
A representative flow curve, obtained by
plotting (F) versus (G)
Rheogram Newtonian
F = F’/A
G=dv/dx
C
1
C
3
C
2
1
D
2
D
1
D
3

2

Rheogram Newtonian
F = F’/A
G=dv/dx 

2
PURE SOLVENTS or
TRUE SOLUTION
(water, organic solvents,
liquid paraffin, melted
fatty oil and melted
vaseline)
F = shearing stress; G = rate of shear; rate of deformation

NON-NEWTONIAN SYSTEMS
(are those substances that fail to follow the Newton’s equation of flow)
= colloidal solutions, emulsions, liquid suspensions, ointments 
(1) plastic, (2) pseudoplastic and (3) dilatant
1
3
2
G
f
F
F
Vaseline, flocculated
suspensions, lotions,
viscous emulsions 1. BINGHAM body
2. CASSONS body
3. Plastic dilatant
2
0
1
U = (F - f)/G

PSEUDOPLASTIC
FLOWD
12



1 F = k.Gn; n>1 (Ostwald)
2 F = a.F3+c.F; c>0 (Steiger Ory)
Shear
thinning
system
Liquid dispersions of tragacanth,
methyl-cellulose, sodium alginate,
sodium CMC , in low
concentration

(are those substances that fail to follow the Newton’s
equation of flow)
G
G F
D
Suspended amylum
in water, suspension
of bolus in glycerol,
paste 50% w/v
Shear
thickenin
g system
Deflocculated
systems

equation of flow)
F
G
G
F
Cellulose gel, bentonite gel,
aerosil gel
CELLULOSE
pseudoplastic
plastic
Hydrogen
bonding
Electrostatic B

U1 – U2
B = 
ln t2/t1
MEASUREMENT OF THIXOTROPY
U1 and U2 = the plastic
viscosities of the two down-
curves, after shearing at a
constant rate for t1 and t2
seconds.

CRYSTALLITE of FIBER MICELL
Fiber
molecules
with some
contact points
Fiber
molecules
with more
contact points
Fiber molecules
with parallel
position 
crystalline str
(cellulose)
Structure of
laminar particles
(bentonite)
Structure of
needle particles Structure of
sferoid particles
(Aerosil)

ANTI-THIXOTROPY
NEGATIVE-THIXOTROPY
Magma magnesium 1-10%
and flocculated
G > 30 / sec
G < 30 / sec
THIXOTROPY
SOLE  GEL  SOLE
COLLISION BETWEEN PARTICLES >>>
D
PF



RHEOPEXY
equation of flow)
PEG, bentonit sole
SOLE of SOLIDS  GEL  SOLE
SLIGHTLY
SHAKED

98
o Higher the viscosity greater the resistance
o Some liquids like water, alcohol, chloroform flow readily whereas
syrup, glycerin flow slowly
o This rate of flow is depends on the internal resistance involved
when moves over another layer
VISCOSITY : is an expression of the resistance
of a liquid to flow.

99
Viscosity of liquid decreases with rise in temperature, while it
increases with fall in temperature.
Measurement of viscosity:
In C.G.S system the viscosity of a liquid is measured in dyne-second/square
centimeter. It is also known as poise. Each poise is further divided in to 100
centipoises.
In S.I. system it is measured in Newton-second/ square meter.
The viscosity of the water is one centipoise. The viscosities of liquids are
normally expressed as relative to water.

100
Applications in Pharmacy
Viscosity plays an important role in the stability of emulsions and
suspensions.
Ophthalmic preparations are made viscous to prolong the contact time of
the drugs e.g. methyl cellulose is used for this purpose.
Paints are made more viscous so that they remain in contact with skin for
long time e.g. glycerine is included in paint formulation to increase the
viscosity.
Certain pharmaceutical formulations are standardized on the basis of its
viscosity e.g. liquid extract of liquorice.
The viscosity of certain liquid preparations is increased in order to improve
pourability or to make the preparation more palatable.
Fats, waxes and other viscous substances are filtered at higher
temperature. It is due to the fact that at higher temperature, there is
decrease in viscosity and hence rate of filtration can be increased.

101
- Mixing of liquids
- Particle size reduction of
disperse system with shear
- Passage through orifices:
including pouring, packaging in
bottles, and passage through
hypodermic needles
- Physical stability of disperse
systems
- Fluid transfer
For fluids

102
For semi-solids
-Acceptable
consistency and
smoothness
- Spreading and
adherence on to
the skin
- Removal from jars or
extrusion from tubes
- Capacity of solids to mix
with miscible liquids
- Fluid transfer
- Physical stability
etc.,

103
For solids
Powder flow from
hopper to die cavities
& flow of powder
into capsules
Packageability of
powdered or granular
solids
Processing
Production capacity
& correct choice of
production efficiency
Processing efficiency

• As a method for determining the quality of materials of products.
• In cases when other chemical, physical or biological methods are not
available. / As an alternative for other existing methods.
• Quality may be determined based on the viscosity values.
104
Liquid Temperature C Kinematic
viscosity
(centistokes)
Light liquid paraffin 37.8 > 30
Liquid paraffin 37.8  64
PEG 4000 100 76 & 100

• As a method for controlling or maintaining batch to batch quality to
ensure its stability on storage and ease of use.
– For solutions- most appropriate flow is Newtonian
– Parameter relate to the consumer preference is viscosity
– For dispersed system- must be stable on storage, easy to be taken out
of the container.
– The most appropriate flow is plastic with thixotropy followed by
plastic, pseudo-plastic with thixotropy and lastly pseudo-plastic
 Instruments which measure the visco-elastic properties of solids,
semi-solids and fluids are referred to as “Rheometers”.
 Instruments which are limited in their use for the measurement of
the viscous flow behavior of fluids are described as “viscometers”.
105

106
Kinematic Viscosity is the absolute viscosity divided by the density of the liquid
at a specific temperature.
Kinematic Viscosity = η/ ρ
The units of kinematic viscosity are the stoke (s) and the centistoke (s)
When classifying materials according to types of flow and deformation, it is
customary to place them in one of two categories:
Newtonian or Non-Newtonian systems
The choice depends on whether or not their flow properties are in accord with
Newton’s law of flow.

FLUIDITY
• A rheogram is a plot of shear rate G, as a function of shear stress ,F.
• rheogram : is a consistency curve or flow curves.
• Rheogram is produced by Newtonian systems, which follow the equation
for a straight line passing through the origin:
G=f F
• The slope, f is known as fluidity and is the reciprocal of viscosity, n : f=1/n
• The greater the slope of the line, the gretare is the fluidity or conversely,
the lower is the viscosity.
107

108
Newtonian Systems
Consider a “block” of liquid consisting of parallel plates of molecules, similar to a
deck of cards …..
The difference of velocity, dv, between
two planes of liquid separated by an
infinitesimal distance dr is the velocity
gradient or rate of shear, dv/dr
The force per unit area, F’/A,
required to bring about flow is
called the Shearing stress and is
given the symbol F.
If the bottom layer is fixed in place and
the top plane of liquid is moved at a
constant velocity, each layer will move with
a velocity directly proportional to its
distance from the stationary bottom layer.

109
Newton was the first to study flow properties of liquids in a
quantitative way.
He recognized that the higher the viscosity of a liquid, the
greater is the force per unit area (shearing stress) required to
produce a certain rate of shear.
Rate of shear is given the symbol G. Hence, rate of shear should
be directly proportional to shearing stress, or
F’/A= η dv/dr --------- (1)
in which η is the Coefficient of Viscosity, usually referred to
simply as Viscosity.
Equation (1) is frequently written as η= F/G, Where F=
F’/A and G= dv/dr. A representative flow curve, or
Rheogram, obtained by plotting F versus G for a
Newtonian system .

110
TEMPERATURE DEPENDENCE AND THE THEORY OF VISCOSITY
The viscosity of a gas increases with temperature (due to molecular collisions &
interactions), that of a liquid decreases as temperature is raised, and the fluidity
of a liquid (the reciprocal of viscosity) increases with temperature.
The dependence of the viscosity of a liquid on temperature is expressed
approximately for many substances by an equation analogous to the Arrhenius
equation of chemical kinetics.
η = Ae Ev RT
Where A is a constant depending on the molecular weight and molar volume
of the liquid.
Ev is an “ activation energy” required to initiate flow between molecules.

111
The energy of vaporization of a liquid is the energy required to
remove a molecule from the liquid, leaving a ‘hole’ behind in equal
size to that of the molecule that has departed.
A hole must also be made available in a liquid if one molecule is
to flow past another.
The activation energy for flow has been found to be about one-
third that of the energy of vaporization, and it can be concluded
that the free space needed for flow is about one-third the volume
of the molecule.

112
More energy is required to break bonds and permit flow
in liquids composed of molecules that are associated
through hydrogen bonds.
These bonds are broken at higher temperatures by
thermal movement, however, and Ev decreases markedly.

113
Non-Newtonian systems
The majority of fluid pharmaceutical products are not simple liquids and do not
follow Newton’s law of flow. These systems are referred to as non-Newtonian.
Non-Newtonian behavior is generally exhibited by liquid and solid
heterogeneous dispersions such as colloidal solutions, emulsions, liquid
suspensions and ointments.
When non-Newtonian materials are analyzed in a rotational viscometer and
results are plotted, various consistency curves, representing three classes of flow,
are recognized:
Plastic flow , Pseudo-plastic flow, Dilatant flow

114
Plastic flow
The following curve represents a body that exhibits plastic flow; such
materials are known as Bingham bodies.
Plastic flow curves do not pass through the origin, but
rather intersect the shearing stress at a particular point
referred to as the yield value.
A Bingham body does not begin to flow until a shearing
stress corresponding to the yield value is exceeded. At
stresses below the yield value, the substance acts as an
elastic material.

115
The rheologist classifies Bingham bodies, that is, those substances that exhibit
a yield value, as solids, whereas substances that begin to flow at the smallest
shearing stress and show no yield value are defined as liquids.
The slope of the rheogram is termed as mobility, analogous to the fluidity in
Newtonian systems, and its reciprocal is known as the plastic viscosity, U. The
Equation describing the plastic flow is
F-f
U = -------
G
Where f is the yield value, or intercept, on the shear stress axis in dynes/cm2,,
and F is shearing stress and G is Rate of shear.
Plastic flow is associated with the presence of flocculated particles in
concentrated suspensions. (including certain ointments, pastes & gels)

116
Dilatant Flow (a), Pseudoplastic Flow (b), Plastic Flow; Bingham model (c),
Plastic Flow; Casson model (d)

• For Casson model the line is curved all the way and is
shown by most creams and ointments.
• The Casson model shows both yield stress and shear-thinning
non-Newtonian viscosity. For materials such as blood and food
products, it provides better fit than the Bingham plastic mode.
• For Bingham model only the initial part of the line is
curve and the liquid behaves almost similar to
pseudoplastic fluid.
– The rest of the line is linear behave similar to
Newtonian liquid.
117

Advantages of preparations having plastic flow
• Easy to process due to lower η when higher stress is applied.
• Very stable because no flow if stress is lower than F1
• Stop flowing immediately after being applied thus very
suitable for paints, lip sticks, dental preparations, and other
topical preparations including make-ups.
118

119
Pseudoplastic Flow
Many pharmaceutical products, including liquid dispersions of
natural and synthetic gums like
Tragacanth
sodium alginate
methyl cellulose
sodium carboxy methyl cellulose etc., exhibit pseudoplastic flow.

120
Pseudo plastic flow is typically exhibited by polymers in solution.
the consistency curve for a pseudo plastic material begins at the
origin (or at least approaches it at low rates of shear).
no yield value.
no part of the curve is linear.
the viscosity of a pseudo plastic material
cannot be expressed by any single value.

121
The curved Rheogram for pseudo plastic materials
results from a shearing action on long chain molecules of
materials such as linear polymers.
water
stress
Polymers at rest
Random arrangement
Water is bound
Polymers under flow
Alignment on long axes
Water is released

122
As shearing stress is increased, normally disarranged molecules
begin to align their long axes in the direction of flow.
This orientation reduces the internal resistance of the material
and allows a greater rate of shear at each successive shearing
stress.
In addition some of the solvent associated with the molecules
may be released, resulting in an effective lowering of both the
concentration and the size of the dispersed molecules. This, too,
will decrease apparent viscosity.

123
Objective comparisons between different Pseudo plastic systems are more
difficult. These are discussed by the exponential formula
FN= η’ G--------------- (1)
The exponent N rises as flow becomes increasingly non-Newtonian.
When N=1, the above equation reduces to the equation η = F/G and the flow is
Newtonian. The term η’ is a viscosity coefficient. Following rearrangement, we
can write the equation (1) in the log form
log G =N log F- log η’-------------- (2)
This is an equation for a straight line. Many Pseudo plastic systems fit this
equation when log G is plotted as a function of log F.
η’ = the force/unit area required to maintain unit difference in
velocity between 2 parallel layers in the liquid, 1cm apart

125
Dilatant flow
Certain suspensions with a high
percentage of dispersed solids exhibit
an increase in resistance to flow with
increasing rates of shear. Such systems
actually increase in volume when
sheared and are hence termed Dilatant.

126
This type of flow is the inverse of that possessed by
pseudoplastic systems. Whereas pseudoplastic materials
are frequently referred to as ‘ Shear thinning systems’,
Dilatant materials often termed ‘Shear thickening
systems’.
When the stress is removed, a dilatant system returns
to its original state of fluidity.

127
The equation FN= η’ G can be used to describe dilatancy in quantitative terms.
In this case, N is always less than 1 and decreases as degree of dilatancy
increases.
As N approaches 1, the system becomes increasingly Newtonian behavior.
Substances possessing dilatant flow properties are invariably suspensions
containing a high concentration (about 50% or greater) of small, deflocculated
particles.

128
Dilatant behavior can be explained as follows:
At rest, particles are closely packed with minimal inter-particle
volume (voids).
The amount of vehicle in the suspension is sufficient, however, to
fill voids and permits particles to move relative to one another at
low rates of shear.
Thus, a dilatant suspension can be poured from a bottle because
under these conditions it is reasonably fluid.
As shear stress is increased,
the bulk of the system
expands or dilates; hence the
term dilatant.
The particles, in an attempt to
move quickly past each other,
take on an open form of
packing.

129
Such an arrangement leads to a significant increase in inter-
particle void volume.
The amount of vehicle remains constant and, at some point,
becomes insufficient to fill the increased voids between particles.
Accordingly, resistance to flow increases because particles are no
longer completely wetted, or lubricated, by the vehicle.
Eventually, the suspension will set up as a firm paste.
E.g., suspensions of starch in water, inorganic pigments in
water(kaolin 12% in water, zinc oxide 30% in water)

Viscoelasticity
• Materials which exhibits viscous properties of
liquids & elastic properties of solids are called
viscoelastic materials.
• Creams, ointments, suppositories,
suspensions, emulsifying and suspending
agents.
• Biological materials such as blood, sputum and
cervical fluid also show viscoelastic properties.
(VISCOMETER USED: ROTATIONAL
VISCOMETERS)
130

131
Viscoelastic materials possess both viscous flow and elasticity.
Two basic elements of mechanical models used to represent its
behavior.
1. Helical spring- gives the elastic behavior
2. Dashpot- cylindrical container with a loosely fitting piston filled
with a Newtonian liquid which gives the viscous flow.
Viscoelastic behavior can be described by the above combination.

132
Two types of mechanical
models:
Maxwell element & Voigt-
Kelvin element
Maxwell element is
obtained by connecting a
spring and dashpot in
series and when they are
connected in parallel, the
form Voigt-Kelvin element
Maxwell element Voigt-Kelvin element
Spring and Dashpot models for
visco-elasticity

133
THIXOTROPY
The plastic, pseudoplastic and dilatant systems at a given temperature, change
their viscosities at varying shearing stresses. The behavior of such systems are
time dependent.
(i) By gradually increasing the shearing stress on plastic or pseudoplastic
systems, the apparent viscosity gradually decreases as a result of progressive
breakdown of structure in the liquid medium at a given temperature.
After removing the shearing stress, the viscosity is regained due to slow
rebuilding of structure by Brownian motion, but not immediately but after
some time lag. Consider the conversion of gel to sol and then sol to gel after
removing the stress applied.
GEL SOL
APPLYING
SHEARINGSTRESS
REMOVING
SHEARINGSTRESS
The conversion of sol to gel is not instantaneous but requires some time lag.

134
(ii) By increasing the shearing stress on dilatant system, the
apparent viscosity gradually increases at a given temperature. After
removing the shearing stress, the viscosity is decreased but not
immediately but after some time.
APPLYING
SHEARING STRESS
REMOVING
SHEARING STRESS
SOL GEL
The conversion of gel to sol is not immediate but requires some t
All the three systems, i.e. plastic, pseudoplastic and dilatant
systems will change their viscosities gradually with respect to time
even if a constant shearing stress is applied. Such a time
dependant effect is called thixotropy which means ‘change by
touch’.

135
Thixotropy is defined as a reversible isothermal transition
from gel to sol in the case of shear thinning systems like
plastic and pseudoplastic systems
&
from a sol to gel in the case of shear thickening systems like
dilatant system, and the transition is time-dependent.
The thixotropy exhibited by plastic and pseudoplastic
systems is called positive thixotropy and that of dilatant
system is called negative thixotropy or antithixotropy.

136
A rheogram is obtained for a shear thinning system by plotting the rate of
shear at various shear stresses. The curve is called ‘up curve’.
By reducing the shearing stress gradually on the above system, a ‘down-
curve’ is obtained.
Both the ‘up curve’ and ‘down curve’ are not super-imposable.
The down curve is shifted to left side. This means the flow property of the
system is not the same before and after the initial determination
Hence the viscosity of the sample depends upon its previous history.
Therefore, the viscosities of the ‘down curve’ are lower than the viscosities of
the ‘up curve’.
As a result, the ‘down curve’ is shifted to the left side of the ‘up curve’ in the
rheogram.

137
Thixotropy in plastic and pseudoplastic systems
The loop between the ‘up curve’ and the ‘down curve’ is called
‘hysteresis loop’. The area of the loop indicates the extent of
structural breakdown.

138
RATEOFSHEAR
SHEARING STRESS
The time period to regain its original viscosity may be reduced by applying a
gentle rolling or rocking motion (tumbling) to the system in a container. This is
called ‘rheopexy’ and it helps in bringing the particles to the original state.
The rheopexy with the shear thinning system is called positive rheopexy and
with the shear thickening system, it is called negative rheopexy.
Examples of systems showing antithixotropic
behavior are magnesium magma and clay.
The isothermal transition from gel to sol or sol to
gel takes some time. It may range from a short
period to very long period may be months. Any
thixotropic system which takes undue time is
considered practically irreversible.

141
Determination of the viscosity
The viscosity of the liquid is measured by comparing with
a liquid of known viscosity.
Some of the Instruments used to determine viscosity are:
 Ostwald viscometer
 Falling sphere viscometer
 Cone and plate viscometer
 Ubbelhode viscometer
 Rotational viscometer
 Ferranti - Portable viscometer ( for bulk liquids)

SINGLE POINT VISCOSIMETER
1. CAPILLARY VISCOSIMETER
2. FALLING SPHERE VICOSIMETER
MULTI POINT VISCOSIMETER
1. STORMER VISCOSIMETER
2. BROOKFIELD VISCOSIMETER
1 1 t1
 = 
2 2 t2
1/2 : relative viscosity
OSTWALD VISCOSIMETER

FALLING SPHERE VISCOSIMETER
HOEPPLER VISCOSIMETER

CUP AND BOB VISCOSIMETER
SEARLE VISCOSIMETER
A stationary cup and rotating bob
Based on the Searle principle
= Kv T/
Kv : constant for the instrument
 : a function of (v), the rpm generated by the
weight (w), in grams, that is proportional to (T)
 = Kv w/v

HAAKE ROTOVISCO VISCOSIMETER
G is selected manually or programmed for automatic plotting of up- and
down-curves. Its value in sec-1 is proportional to the speed of the bob shaft,
dialed in and read as  on the console. The shear stress is read on the scale S or
obtained from the rheogram, plotted on the X-Y recorder

CONE AND PLATE VISCOSIMETER
FERRANTI-SHIRLEY CONE PLATE
VISCOSIMETER
-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 revolutions per minute
is increased and decreased by a selector dial
and the viscous traction or torque (shearing
stress) produced on the cone is read on the
indicator scale
- a plot of rpm or G vs scale reading or (F)
may thus be constructed in the ordinary
manner
For Newton liquid   = C T/v
C : an instrumental constant
T : the torque reading
v : the speed of he cone in rpm
For plastic flow  U = C (T-Tf) /v

148
(HOEPPLER ) FALLING BALL VISCOMETER
• As per Stoke’s law, a body falling through a
viscous medium experiences a resistance or
viscous drag that opposes the motion of the body.
• When the body falls through a liquid under the
influence of gravity during which acceleration of
the motion occurs at the initial period but when
the gravitational force is balanced by the viscous
drag, the body falls down at a uniform terminal
velocity which can be determined in the falling ball
viscometer.

A
B
Air vent
Falling sphere
Liquid under test
Water bath
(thermostat)
• Two markings A and B on the outer
surface of the sampling tube.
• Tube is filled with the sample.
• Remove air bubbles.
• Steel sphere is allowed to fall in a
particular temperature.
• Time ‘t’ taken for the sphere to fall
from A to B is noted.
• By substituting all the values in the
equation, the coefficient of viscosity is
calculated. 149

150
• The equation is given assuming that the sphere is falling through
a medium of infinite dimension. But in the experiment the liquid is
contained in a cylinder.
• A correction factor (F) is introduced to nullify the effect of wall on
the fall of the sphere.
F= 1-2.104d/D+2.09d3/D3
Where d= diameter of the sphere, D= diameter of the tube & the
corrected viscosity = n×F
The instrument can be used over a range of 0.5 to 200,000 cp./
The ball (density) should be such that it takes not less than 30sec
to fall from A to B

152
Construction:
It consists of ‘U’ tube having two bulbs X and Y. A capillary tube CD of a suitable
bore is fitted to one arm of U tube. The viscometer is placed vertically in a
thermostatically controlled bath.
Working:
A liquid whose viscosity is to be determined is placed in arm Y to fill the tube to
mark E. It is then sucked or blown-up to a point 1cm above A.
The time (t1) for the liquid to fall from mark A to B is measured. The density of
liquid (d1) is determined.
The whole procedure is repeated with a liquid of known viscosity and time(t2) is
noted for the fall of liquid from mark A to B.

153
If n1 is the viscosity, d1 is the density of the liquid and t1
is the time in second of the unknown liquid
&
n2 is the viscosity, d2 is the density of the liquid and t2 is
the time in second of the known liquid, then the
viscosity of the unknown liquid can be determined by:

154
UBBELHODE VISCOMETER
 Modified Ostwald’s viscometer
 Third arm is attached to the bulb below the capillary part of
the right arm parallel to ‘U’ tube.
 pour the sample into the left arm
 Close the left arm and the third arm, suck the liquid into the
right arm, just above the point B.
 now close the central arm with thumb after removing the
thumbs from the other two arms and that keeps the level of
the liquid just above the mark B.
 as the liquid below the capillary tube is ventilated down by
the third arm, the volume of liquid in the right arm remains
constant.
 The rest is similar as Ostwald’s viscometer.
B
C
L
E
F
T
A
R
M
RIGHT ARM
T
H
I
R
D
A
R
M

155
Pharmaceutical & Biological Applications of Rheology
(1) Prolongation of Drug Action
There is a great difference in the rate of absorption of an ordinary
suspension and the same when it is thixotropic. The suspension is
shaken before administration to be easily injected but in the body it
becomes high consistency leading to prolonged action.
(2) Effect on Drug Absorption
The viscosity of creams and lotions may affect the rate of absorption.
A greater release of active ingredients is generally possible from the
softer, less viscous bases.
(3) Thixotropy and Drug Stability
Another useful aspect of thixotropy is that substances, which are
susceptible to decomposition, such as vitamins, are found to be stable
for longer periods of time in thixotropic preparations, as such
substances are in a state of complete rest, in a solid gel.

Rheology-Emulsions
• Volume of the dispersed phase is less than 0.05- the
system exhibits Newtonian flow
• Concentration increased, the system experience
resistant to flow- exhibits pseudo-plastic flow
• At sufficient concentration- exhibits plastic flow
• The fraction of volume concentration approaches
0.74- phase inversions may occur with sizable change
in viscosity
• Reduction in mean globule size increases viscosity
156
• Phase volume
ratio
• globule size
distribution
• Viscosity of the
internal phase
• Aggregation of
globules
• Nature &
proportion of
emulsifying agents
The high viscosity of water-in-oil emulsions leads to problems with
intramuscular administration of injectable formulations.
Conversion to a multiple emulsion (water-in-oil-in-water) leads to a dramatic
decrease in viscosity and consequent improved ease of injection.

Rheology-Emulsifying agent
Affect the particle flocculation and interparticle attractions-will
modify the flow.
Greater the concentration of emulsifying agent, the higher will be the
viscosity.
The physical & electrical properties of the films also effect the
viscosity.
Given amount of oil soluble component, water soluble ionic
surfactants produce stiffer creams than equal molar concentration of a
non-ionic surfactants.

158
Rheology-Suspensions
A suspension should have a high viscosity at low shear rates and a low
viscosity at high shear rates.
Under storage, the only shear is due to the settling of particles.
At this low shear rates, the viscosity of the suspension must be high.
Shaking the bottle a high shear rate is produced, the viscosity will fall to
a low value.
Such property may be derived from pseudo-plastic substances such as
tragacanth, sodium alginate and NaCMC which are used as suspending
agents.
A suspending agent which is thixotropic as well as pseudo-plastic may
have the property of forming a gel on standing becoming fluid when
shaken..
Thus a suspension containing such as combination of suspending
agents may prove to be ideal one.
Combination of such property can be obtained from a mixture of
bentonite (thixtropic), & CMC which is pseudo-plastic.

159
Organogel:
Petrolatum is a semisolid gel consisting of a liquid component
together with a ‘prosubstance’ and a crystalline waxy fraction.
The crystalline waxy fraction provides rigidity to the gel structure.
Prosubstance or the gel former stabilizes the system and thickens the
gel.
Polar organogels include the PEG of high molecular weight known as
carbowaxes.
Rheology of Gel

160
Hydrogels:
 Bases includes organic & inorganic ingredients that are
colloidally dispersible or soluble in water.
 Includes natural & synthetic gums such as tragacanth,pectin, Na
alginate, methylcellulose, & Na carboxy methylcellulose.
 Bentonite mucilage is an inorganic hydrogel.

16
1
•Best instrument: any rotational viscometer
•Addition of water into hydrophilic
petrolatum has lowered the yield point.
(from 520 to 340g).
•The plastic viscosity (reciprocal of the
slope of the down curve) and the thixotropy
(area of the hysteresis loop) are increased
by the addition of water to hydrophilic
petrolatum.

162
• In fig-1, both bases show same temperature coefficient of plastic viscosity-the
bases have same degree of ‘softness’ when rubbed between fingers.
• In fig-2, shows the alternation of thixotropy with temperature that
differentiates the two bases.
• The waxy matrix of petrolatum is probably broken down considerably as the
temperature is raised, whereas the resinous structure of plastibase withstands
temperature changes.
shows the change in
plastic viscosity and
thixotropy of petrolatum
and plastibase as a
function of temperature.
The modified Stormer
viscometer used.

Air 1,8 x 10-2 mPa.detik
Water 1,002 mPa.detik
Ethanol 1,2 mPa.detik
Glycerol 1500 mPa.detik
1 cP = 1 mPa.detik

Study Questions
• Define the following terms:
[Rheology, viscosity, elasticity, Viscoelasticity, plasticity, ductility, pseudoplasticity, stress, shear, strain,
pressure, poise, rheogram, dilatant, flocculation, deflocculation, suspension, solution, emulsion, lotion,
dilatation, dispersion, thixotropy, hysteresis, viscometer, polymerization, hydration, filtration, sterilization,
aeration, extrinsity, intrinsity, rigidity, compressibility, fluidity, linearity, dimension, deformation, distortion,
disaggregation, orientation, prolongation, rheidity, fibre, semifluid, semisolid, gradiency, coefficiency, rheidity,
fibre, semifluid, semisolid, gradiency, coefficiency, rheopexy, etc]
• Respond to the following questions:
 Illustrate with examples material deformations that results when there is an application of a stress
 Describe what a Newtonian system is using its typical characteristics
 What is viscosity and its relation with fluids
 Describe the characteristic flow types of non-Newtonian system with an example
 Explain what should be considered when choosing the type of viscometer for practical use
 Describe with explanations the factors affecting rheological properties of material substance
 Describe the material parameters for rheological behaviour of material substance
 Explain some of the characteristics of elasticity for any affected material substance
 Describe the rheological deformation behaviours in response to any form of applied force
 Describe some key phase changes of materials substance when exposed to some form of external forces
 Describe the practical factors that are prominent on the deformation of material substance in response to applied force
 Describe the practical factors that are prominent on the strength of material substance in response to applied force
 State and describe different pharmaceutical applications of rheological materials with examples
 State and explain some of the advantages and disadvantages of pharmaceutical materials with plastic flow characteristics
 State some of the instruments that can be used to measure and determine the viscosity of material substance
 State and explain some the pharmaceutical and biological applications uses of rheology as material substance behaviour

• Group work discussional questions:
 Describe the practical and rheological deformation behaviours in response to any form of applied force
on deformable substance
 Describe some key phase changes of materials substance when exposed to some form of external forces
 Describe the practical factors that are prominent on the deformation of material substance in response
to applied force
 Describe the practical factors that are prominent on the strength of material substance in response to
applied force
 State and describe different pharmaceutical applications of rheological materials with examples
 State and explain some of the advantages and disadvantages of pharmaceutical materials with plastic
flow characteristics
 State some of the instruments that can be used to measure and determine the viscosity of material
substance
 State and explain some the pharmaceutical and biological applications uses of rheology as material
substance behaviour

14 rheology

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14 rheology