It contains a full and explainable method.
It notes to contain the following item made explainable.
the note prepare of different authors book.
Rheology
Dr. Balajee chari .,
Department of Pharmaceutics
Faculty of Pharmacy
Maharana pratap college of
pharmacy
E-mail: [email protected]
.
9 1
Unit II Rheology
Introduction:- Reo+logos
Reo= Flow of liquid/material/deformation
Logos= Science
Rheology is branch of science that is with mechanical
property of material having liquid and solid properties
intermediate technology and natural product. The
flow of liquid and the deformation of solid take place
when shearing stress is applied. When the force is
applied in solid the deformation take place by
changing volume and its shape.
Fundamentals of Rheology
i. Manufacturing of dosage forms: Materials
undergo process such as mixing, flowing through
pipes, filling into the containers etc. Flow related
changes influence the selection of mixing
equipment.
ii. Handling of drugs for administration: The
syringibility of the medicines, the pouring of the
liquids from containers, extrusion of ointment from
tubes, all depend on the changes in flow behavior of
dosage forms.
3
Applications of rehology
Standards of liquid:- The term of expressing the flow
of liquid/fluid by viscosity. It is common parameter of
liquid.
Manufacturing of doses form
Handing of drug for administration
Quality control tools for product evaluation
Determination of molecular weight
Identification of diseases
Model of treatment.
Concept of viscosity
Resist the deformation and regain the size and shape in solid when
force exclude
Resist the flow of liquid and fluid not regain the size and shape
In general, in any flow, layers move at different
velocities and the fluid’s viscosity arises from the shear
stress between the layers that ultimately opposes any
applied force. The relationship between the shear
stress and the velocity gradient can be obtained by
considering two plates closely spaced at a distance y,
and separated by a homogeneous substance.
Assuming that the plates are very large, with a large
area A, such that edge effects may be ignored, and that
the lower plate is fixed,
Concept of viscosity
let a force F be applied to the upper plate. If this force
causes the substance between the plates to undergo
shear flow with a velocity gradient u (as opposed to
just shearing elastically until the shear stress in the
substance balances the applied force), the substance is
called a fluid. The applied force is proportional to the
area and velocity gradient in the fluid and inversely
proportional to the distance between the plates.
Combining these three relations results in the
equation:
Conti……..
Hence, through this method, the relation between the
shear stress and the velocity gradient can be obtained.
Hence, through this method, the relation between the shear
stress and the velocity gradient can be obtained.
Note that the rate of shear deformation is x/y which can be
also written as a shear velocity, du/dy .
James Clerk Maxwell called viscosity fugitive elasticity
because of the analogy that elastic deformation opposes
shear stress in solids, while in viscous fluids, shear stress is
opposed by rate of deformation.
conti…..
F=ʮ A.u/y
where μ is the proportionality factor called viscosity.
This equation can be expressed in terms of shea shear
stress ʈ=F/A
Thus as expressed in differential form by Isaac
Newton for straight, parallel and uniform flow, the
shear stress between layers is proportional to the
velocity gradient
in the direction perpendicular to the layers:
Hence, through
Diagram of viscosity
Relations
Types of viscosity
Fluidity :- The term fluidity ø is used to denote
the reciprocal of viscosity .
Fluidity=ø= 1/η.
Kinematic viscosity:-
Viscosity(η) divided by the density ( ) of
the liquid. Kinematic viscosity=װ/ρ
Kinematic viscosity is expressed in m2/s.
1 stoke(s) =10-4m2/s
1centi stoke=10-6m2/s
1 poise (kg/m3)=1centistoke(cs). It has
great importance in IP.BP,and USP and
national formulary
Types of Viscosity
Most of the dispersion do not obey Newton flow. These are
discussed under the heading
Of non-newtonian flow.
In order to describe these changes the following terminology is
used.
Relative Viscosity:
The coefficient abbreviated װr, The ratio of dispersion(η) to
that of solvent װo
Relative Viscosity ηr=װ/ηo
Specific Viscosity
The term defined as the relative increase in the viscosity
of the dispersion over that of the solvent alone
Specific Viscosity= װ-ηo/ηo
Reduce viscosity:-Reduce viscosity
(ηred)=ηsp/C
This term is defined as the ratio of
specific viscosity to the concentration C
Reduce Viscosity ηred =ηsp/C
Intrinsic Viscosity:-
The reduced viscosity is determined at
various concentrations of a substance
the result are plotted the resulting line
can be extra plotted to C=0 to obtained
intercept. The intercept value is known
as intrinsic viscosity.
Factor influencing the viscosity
Molecular size, shape and Intermolecular forces
influences the viscosity
Molecular weight :- liquid with large and irregularly
shaped molecular are generally known to be viscous as
compared to small and symmetric molecules. Molecular
collision between larger molecular molecules are not
elastic i.e. involve loss of kinetic energy. As a result
,intermolecular interactions are stranger and the
molecular tend to stick to each other there by increasing
the viscosity of the liquid.
Extrinsic Factor
Pressure temperature and added substances also influence
the viscosity. An increase in pressure enhances the
cohesive forces of interaction leading to an increase in the
viscosity. In general small quantities of non electrolytes
namely sucrose, glycerin and alcohol when added to the
water the solution exhibits increased viscosity .similarly
polymers and other macromolecules enhance the viscosity
of solvent such as water. On the other hand small amount
of strong electrolytes decrease the viscosity Alkali metals
and ammonium ions are a few examples temperature is an
important factor that needs elaborate discussion
Temperature:-As the temperature increases ,the
system acquires thermal energy which facilitates the
breaking of the cohesive forces. The viscosity of liquid
decreases. In case of gases ,an increase in temperature
increases the viscosity owing to the increased
molecular collisions and interactions . The relationship
between viscosity and temp. may be expressed as :
η= AeE v/RT where A is a constant which depends on the
molecular weight and molar volume ,and Ev is an
activation energy required to initiate the flow
between the molecules. Flow of liquid explained by the
movement of molecules. Liquid are assumed to posses
a number of holes or vacancies. Energy is required to
create a hole in the liquid. This energy is related to the
energy of vaporization. Energy of vaporization is
defined as the energy required to remove molecule
from liquid.
Shear Time : The stress –strain relationship
depends on the time scale of the experiment.
When shear stress is applied on the fluid shear
thinning my result. At end when stress is
removed the material must regain its original
structure completely. In some case
rhodestruction is irreversible. Therefore the
exposure of stress is important factor for
understanding the recovery of the rheological
behavior.
Newtonian and
Non-Newtonian Flows
Rheology
Newtonian Non – Newtonian
2
3
Types of Flow
•Newtonian (Newtonian Law of Flow)
•Non Newtonian
1. Newtonian system
•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”
shearing force
•A shearing force is applied to the
top of the rectangle while the
bottom is held in place. The
resulting shear stress, F, deforms
the rectangle into a parallelogram.
The area involved would be the top
of the parallelogram.
The difference in the velocity gradient (dv)
between two plan of liquid separated by
distance (dx) is the rate of shear (dv/dx)
and it symbol is G.
•The force per unit area required to bring
about flow is called the shearing stress ant
its given a symbol F
•F α G F = η . G
η is the viscosity of the liquid
η = ????????
•Increased viscosity = increased shear force or
shear stress required to produce a certain rate
of shear (Rate of shear should be directly
proportional to the shearing stress)
•A certain shear stress with produce a certain
rate of she
Newtonian Flow
• Newton was the first to study the flow properties of
liquids in quantitative terms. Liquids that obey
Newton’s law of flow are called as Newtonian fluids.
F=nG
G
F
•In common terms, this means the fluid continues
to flow, regardless of the forces acting on it. For
example, water is Newtonian, because it
continues to exemplify fluid properties no
matter how fast it is stirred or mixed.
•For a Newtonian fluid, the viscosity, by
definition, depends only on temperature and
pressure (and also the chemical composition
of the fluid if the fluid is not a pure
substance), not on the forces acting upon it
Non-Newtonian Flow
Non –Newtonian phenomena may be time independent
or time dependent
• Non – Newtonian bodies are those substances, which
fail to follow Newton’s law i.e. liquid & solid ,
heterogeneous dispersions such as colloidal solutions,
emulsions, liquid suspensions and ointments.
They are classified into 3 types of flow:
• Plastic.
• Pseudoplastic.
• Dilatant.
• Time dependent 1-Thixotropy 2-Rheopexy
NON-NEWTONIAN SYSTEMS
•A non-Newtonian fluid is a fluid whose flow properties
are not described by a single constant value of viscosity.
•Many polymer solutions and molten polymers are non-
Newtonian fluids, as are many commonly found
substances such as ketchup, starch suspensions, paint,
blood and shampoo.
•Most pharmaceutical fluids do not follow Newton’s
equation: because the viscosity of fluid varies with the
rate of shear. therefore a single determination of viscosity
at any one rate of shear cannot yield the entire
rheological profile
A In a non-Newtonian fluid, the relation
between the shear stress and the strain rate is
nonlinear, and can even be time-dependent.
Therefore a constant coefficient of viscosity
cannot be defined.
•A ratio between shear stress and rate of strain (or
shear-dependent viscosity) can be defined, this
concept being more useful for fluids without time-
dependent behavior.
Rheograms of different fluids
3
3
Plastic Flow
• The plastic flow curve does
not pass through the origin
& it 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 yield value. (f).
9
•A Bingham body does not begin to flow until a
shearing stress, corresponding to the yield value,
is exceeded.
•If stress is less than the yield value, the system
behaves like a solid and exerts elastic
deformations that are reversible.
•The quantitative behaviour of these bodies is best
described by the Bingham Equation where fB is
the Bingham yield value:
Newtonian F = η . G
η=F
G
–
Non-Newtonian η pl = F -fb (dyne/cm2)
(plastic viscosity) G
• In practice, deformation and flow usually
occurs at a lower shear stress value and this
accounts for the curved portion of the
curve.
• The viscosity decreases initially and then
remains constant.
• In a highly flocculated system, there is
interaction between flocs which results in a
structured system and plastic flow is
associated with these systems e.g highly
flocculated suspensions.
The yield value is present because of the
contacts between adjacent particles (caused
by van der Waals forces which may be capable
of withstanding weak stresses) which must
be broken down before flow can occur.
•Consequently, the yield value is an indication
of the degree of flocculation; the more
flocculated the suspension, the higher will
be the yield value.
•This type of behaviour is also exhibited by
creams and ointments
Pseudoplastic Flow
• The curve for a pseudoplastic
material begins at the origin (or
at least approaches it at low
rates of shear).
• The curved rheogram for
pseudoplastic materials is due
to shearing action on the long
chain molecules of materials
such as linear polymers.
40
Polymer dispersion generally shows pseudo plastic
flow. some of the example of pseudo
Plastic flow are :
1-sodium alginate in water
2-Tragacanth in water
3-sodium CMC in water
4-methylcellulose in water
5-Acacia water
6Ethyl cellulose in water
Mechanism
polymers long chain molecular remains randomly arranged in the
dispersion
Under normal condition. however ,if a shear stress is applied ,the
molecular alignTheir long axes in the direction of applied force
.This alignment (orientation) of
The molecular caused due to stress ,there by, reduces the material ̕s
internal resistance.
Futher ,the molecules of solvent existing in close association with
the polymer molecules
Will also get detached and released free. Therefore ,the molecules
size and concentration
Gets decreased .However ,on progressive increase in the shearing
stress, the material
allows greater rate of shear.
The curve commences at the origin and there is no yield value.
• No part of the curve is linear,
so viscosity cannot be expressed
by any single value.
• The apparent viscosity may be
obtained at any rate of shear from
the slope of the tangent to the
curve at the specified point.
• The viscosity decreases with an
increasing rate of shear
(shear-thinning systems).
•Pseudoplastic flow cannot be satisfactorily expressed by
fundamental equations.
•The following empirical equation correlates most closely with
experimentally observed flow not involving stress over vast ranges:
η´ = ????????
G
η’ is a apparent coefficient.
•The exponent N rises as the flow
becomes increasingly non-Newtonian.
•When n = 1, this equation reverts to
the classic Newton equation and the
flow is Newtonian.
1/η = gradient
(changes with S)
At the Particulate level:
• The curved rheogram for pseudoplastic materials results
from a shearing action on the long-chain molecules which
become entangled and associated with immobilized
solvent.
• As the shearing stress is increased, the randomly
arranged particles tend to become disentangled and align
their long axes in the direction of flow.
• This orientation reduces the internal resistance of the
material and offers less resistance to flow. Some of the
entrapped water will also be released.
•Both of these account for the lower viscosity. Once stress
is removed, the structures reform spontaneously
Dilatant Flow
• Certain suspensions with a high
percentage of dispersed solids
exhibit an in resistance to flow
with increasing rates of shear.
• Such systems actually increase in
volume when sheared & are called
dilatant.
• Dilatant materials “shear thickening
systems.”
• When the stress is removed, a
dilatant system returns to its original
state of fluidity.
• Dilatant flow – usually suspensions containing a high
concentration (>50%) of small, deflocculated particles.
•Exhibit an increase in resistance to flow with increasing rates of
shear.
•Systems increase in volume when
sheared – termed dilatant.
• The reverse of pseudoplastic systems.
• Pseudoplastic systems –
shear-thinning systems,
Dilatant materials –
shear-thickening systems.
• The same equation can be used to
describe dilatancy in quantitative terms:
η´ = FN
G
N<1
• N is always less than 1
•Decreases as the degree of
dilatancy increases.
•As N approaches 1, the system
becomes increasingly Newtonian
in behaviour.
Dilatants flow :
The effect of a dilatants flow can be seen where the particles packed
in close vicinity are combined with sufficient liquid to fill up the
void spaces , At higher velocities the viscosity of fluid increases due
to increase in friction( among the particles), thus ,restricting the
filling of gaps between the particles. However at low velocities ,the
liquid works as a lubricating agent causing the dilatants to flow
easily .Mixture of corn-starch and water (oobleck) includes high
velocity particle which work in a counter intuitive manner when
thrown or struck against the surface.
The consistency curve having a dilatants flow. The system possesses
increased flow resistance with increase shear rate .however ,the
volume of the system get increased when they are sheared and thus
are called as dilatants.
These dilatants materials are also known’s as shear
thickening systems due to enhanced the apparent
viscosity at increased shear rates. The initial state
of fluidity of the system get restore after the
removal of stress, example of materials exhibiting
the dilatants flow are:
1-suspension of starch dissolved in water
1-suspension s having high concentration of solid
(>50%) consisting of small and deflocculated
particles.
3-inorganic pigments dissolved in water e.g. ,zinc
oxide(30%) in water 12%kaloin in water
At the particulate level:
•At rest:
– particles closely packed
– voids at a minimum.
•Vehicle:
– sufficient to fill this volume
– allows the particles to move relative to one another at low rates of
shear.
•Can pour a dilatant suspension from a bottle without shaking as it
is relatively fluid without shear stress applied.
•If the shear stress is increased by shaking, the bulk expands or
dilates as the particles move quickly past each other and take an
open form of packing.
• Such an arrangement results in a significant
increase in the void volume, with the vehicle
now being insufficient to fill the voids
between the particles.
• The resistance to flow increases since the
particles are no longer completely wetted or
lubricated by the vehicle and eventually the
suspension will set up as a firm paste.
• Caution must be taken in processing
dilatant materials.
– Usually, the processing of dispersions
containing solid particles is facilitated by the
use of high speed mixers, blenders or mills.
– Dilatant materials may solidify under these
conditions of high shear, thereby
overloading and damaging the processing
equipment.
Thixotropy
Thixotropy can be defined is time dependent change in
the viscosity of plastic,psudo plastic and dilatants system
at given temp and different shearing stresses. shear
thinning system when agited and kept aside are expected
to return to its original state of fluidity,
However it takes longer time to recover compared time of
taken agitation.
This behavior is called thixotropy.Thixotropy is defined
as an isothermal and comparatively slow recovery on
standing of material of consistency lost through shearing.
Thixotropy in plastic and
pseudo-plastic systems
It is a comparatively slow
recovery, on standing of a
material which lost its
consistency through shearing.”
Thixotropy is only applied to
shear-thinning systems. This
indicates a breakdown of
structure (shear-thinning), which
does not reform immediately
when the stress is removed or
reduced .
1
2
Thixotropy in plastic and
pseudo-plastic systems
An anygiven Temperature, the shearing stress
gradually decreases the viscosity
of these system When the shearing stress is
removed the system re-gain there viscosity after
certain time lag. This phenomena is known
thixotropy which can be describe as reversible
isothermal transformation gel to sol
Application of Removal of shear stress
shear stress gel
gel sol
Rheogram for such a system will given hypothesis loop
when rate of different shearing stress is plotted . Up curve
is obtain when the shearing stress is increased whereas
when the shearing stress is gradually decreased then we
get down curve as result. Up curve and down curve do not
superimpose each other. The left side shift of down-curve
indicate lower viscosity of the down curve as compare to
up curve. This indicate that to regain the viscosity it takes
time
For most non-Newtonian systems:
•The flowing elements, whether particles or
macromolecules, may not adapt immediately
to the new shearing conditions.
•When subjected to a particular shear rate,
the shear stress and consequently the
viscosity, will decrease with time.
•Therefore the down-curve can be displaced
with regard to the up-curve.
Shear-thinning systems (plastic and
pseudoplastic)
• down-curve is frequently displaced to the left
of the up-curve rheogram exhibits a hysteresis
loop.
i.e. the material has a lower consistency at any one rate of shear on
the down-curve than it had on the up-curve.
•Indicates a breakdown of structure that does not reform
immediately when the stress is removed.
•This phenomenon is known as thixotropy and may be defined as:
•“An isothermal and comparatively slow recovery, on
standing of a material whose consistency is lost through
shearing”.
•According to this definition, thixotropy can only be applied to
shear-thinning systems.
The rheograms obtained with thixotropic materials are:
– highly dependent on the rate at which shear is
increased or decreased
-the length of time a sample is subjected to any one
rate of shear.
-Example of plastic and pseudo plastic system include:
-1) Plastic system : Bentonite get petrolatum act,
-2)pseudo-plastic system: Dispersion of synthetic
suspending agents
-Thixotropy in Dilatants systems:
-An increase in viscosity (apparent) in the dilatants
systems at a given temperature results from an increase in
the shearing stress. However, The viscosity of the system
Decreases after a certain time period of removing the
shearing stress. This phenomenon, knows thixotropy in
dilatants system, which can be described as a reversible
isothermal transformation form solution to gel .
Application of
shear stress Removal of shear stress
soln Gel soln
Phenomena related to thixotropy
The different phenomena related to thixotropy
discussed
1- Irreversible thixotropy(deformation not
regain its original position
2-Rheopexy(reformation of gel from
deformation of gel}
3=Negative Rheopexy
4- anti thixotropy and negative thixotropy
Measurement of thixotropy
Main characteristic of a thixotropic system is the hysteresis
loop.
•The area of hysteresis has been proposed as a measure of
thixotropic breakdown.
•Two approaches:
– determine the structural breakdown with time at a constant
rate of shear.
– determine the structural breakdown due to increasing shear
rate.
• Limitations:
-Does not taken into account the shape of the up- and down-
curves. So
– Two different materials may produce loops of similar area but
which have completely different shapes representing totally
different flow behaviour.
•Rheogram of white soft paraffin
•This is typical of a loop obtained with
some samples of white soft paraffin
where the up-curve exhibits a
number of bulges.
•Lower shear rates
– the bulges are thought to be
associated with the initial loss of
3-D structure.
•Higher shear rates
– the smoother deviations here are
associated with molecular
reorientation.
Rheopexy
•This is a characteristic exhibited by some
thixotropic systems.
•A phenomenon where a sol forms a gel more
readily when gently shaken than when allowed
to form the gel while the material is kept at
rest.
•The rocking motion provides a mild turbulence
which aids in returning de-randomised particles to
a random orientation.
•The gel is the equilibrium form.
Thixotropy in formulation
• Thixotropy is a desirable property in liquid
pharmaceutical systems that ideally should have:
• A high consistency in the container yet pour or
spread easily.
• e.g.
-a well formulated suspension will not settle out readily in
the container
-will become fluid on shaking and will remain so long
enough for a dose to be dispensed.
-will regain consistency rapidly enough so as to maintain
the particles in a suspended state.
• Also desirable with emulsions, lotions, creams,
ointments and parenteral suspensions to be used for
intramuscular depot therapy.
Instrumentation
Viscometer
Single/One point: Multipoint:
At a single rate of shear one Several rates of shear many
point on the curve points on the curve
Equipment: Equipment:
1) Ostwald viscometer 1) Cup and bob
2) Falling sphere viscometer 2) Cone and plate
Applications: Applications:
• Newtonian fluids • Non-Newtonian fluids
• Newtonian fluids
73
Instrumentation
“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.
• Used for Newtonian fluids.
• Since the rate of shear is directly proportional to the
shearing stress.
• The capillary and falling sphere are for use only with
Newtonian materials.
74
Ostwald Viscometer
• Ostwald viscometer is used to determine the viscosity
of a Newtonian liquid. Both dynamic and kinematic
viscosities can be obtained.
• When a liquid flows by gravity, the time required for
the liquid to pass between two marks (A and B shown
in Figure) through a vertical capillary tube is
determined.
75
Instrumentation
“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.
• Used for Newtonian fluids.
• Since the rate of shear is directly proportional to the
shearing stress.
• The capillary and falling sphere are for use only with
Newtonian materials.
76
Capillary viscometer
The Low Viscosity of Newtonian fluid can be
accurately measured by the capillary viscometer.
The Time taken by the fluid to flow under the gravity
in the capillary column from one marked point
say(A)to other is measured. The time taken to pass
between the two point by the fluid under test is
compared to that of fluid of known viscosity(generally
water).
Let ρ1 and ρ2 be the densities of the unknown and
stand liquid and η1and װ2 Be the viscosity of the
liquid ,and t1 and t2 be the respective flow times in
second.
By substituting the experimental value in the below
equation ,the absolute viscosity of unknown liquid (η1)
can be determine.
η1/η2 =ρ1t1/ρ2t2 the value η1/η2 =ηrel is called relative
viscosity of the test liquid .
The equation described above is based on the puiseuille̕ s
Law for a liquid get flows through a capillary tube.
=װπ r²t.ΔP/8LV
Where r=Radius of the inside capillary
t=Time of the flow, ΔP=Pressure head in dyne/cm2 under
which the liquid flows.
L=Length of the capillary.
V= Volume of fluid flowing.The equation can also be
written as :
=װKt. ΔP K= constant
Ostwald Viscometer
79
Procedure: of oswald viscometer
Through the left arm ,the liquid is introduced
into the viscometer till it reaches the level up to
mark A
The viscometer is then allowed to attain the
desired temp by vertically fixing
It in the thermostat bath
The volume of sample is adjusted and the liquid
is plown or stucked into the right arm till it
reaches the meniscus just above the B mark
Lastly, the pressure or suction is released and the
time taken by the lower meniscus to fall from
marked B to C is noted.
Falling Sphere Viscometer
• The sample & ball are placed in the inner glass tube
& allowed to reach temperature equilibrium with the
water in the surrounding constant temperature
jacket.
• The tube & jacket are then inverted, which
effectively places the ball at the top of the inner
glass tube.
• The time for the ball to fall between two marks is
accurately measured & repeated several times.
81
Falling sphere viscometer
Name of instrument: hoeppler falling sphere(ball)
viscometer.
Viscometer consists of glass or steel ball that rolls
down in a vertical glass tube.
The inner glass tube contains the ball and the sample.
Surrounding a jacket filled by water which helps to
maintain the temperature.
The jacket and the tube are then turned upside-down
which set the ball effectively at the top of the inner
glass tube.The time required by the ball to fall
between the two points.This process is repeat two or
three times.
Falling Sphere Viscometer
83
Cont—-
The viscosity of the Newtonian liquid can be calculated by
the following equation.
=װt(Sb-St )B
Where.
t=Time interval in seconds for the ball to fall between
the two points.
Sb =specific gravity of the ball.
St = Specific gravity of the fluid
B = constant for a particular ball
Range of 0.5-2,00,000 poise. Time taken less than 30
sec. ball is used variety of glass and different diameter
Instrumentation
“Multi-point” instruments
• Used with non-Newtonian systems.
• The instrumentation used must be able to operate at a
variety of rates of shear.
• Cup and Bob , Cone and Plate viscometers may be
used with both types of flow system.
• These instruments called rotational viscometer in
which the torque required to turn an object in a fluid
is a function of the viscosity of that fluid. They
measure the torque required to rotate a disc or bob in
a fluid at a known speed.
Cup and Bob Viscometer
Cup and Bob Viscometer
• 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.
Cup and bob viscometer
The two type of cup and bob viscometers are
1)couette type :revolving cup type-Macmichael viscometer
2)Searle type : revolving bob type-Stormer viscometer
The number of revolution (rpm) and the torque represent the
rate of shear and shearing stress, respectively. The following
equation is used to calculate the apparent viscosity of a
pseudo plastic system. η=kv W /Y
Where W= weight placed hangar ,shearing stress N/m2(pa)
V= rpm( shear rate),η=Apparent viscosity of the
liquid.KV =constant for the instument.apparent
viscosities can be obtained at several points of
shearing stress.
Cone and Plate Viscometer
23
Cone and Plate Viscometer
• The sample is placed at the center of the plate which
is then raised into position under the cone.
• The cone is driven by a variable speed motor & the
sample is sheared in the narrow gap between the
stationary plate and the rotating cone.
• The rate of shear in rev./min. is increased &
decreased by a selector dial & the torque (shearing
stress) produced on the cone is read on the indicator
scale.
• A plot of rpm or rate of shear versus scale reading
(shearing stress) may be plotted.
91
Newtonian systems :-The viscosity is estimated by
the equation
η=c.T/v where T is the instrument constant ,T is
the torque reading and v is the speed of the
cone(rpm)
Plastic viscosity : The plastic viscosity (U) is
estimated using equation
U =Cf.T-Tf/V
And yield value (f) =Cf x Tf
In which Tf is the torque at the shearing stress
axis (extrapolated from the linear portion of the
curve),and
Cf is an instrumental constant.
