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.