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RHEOLOGY

M.Balamurugan. M.Pharm., Ph.D.,

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LEARNING OUTCOMES

At the end of this chapter the students shall be able to:

define rheology.

apply the principles of rheology in the pharmaceutical sciences.

define the following concepts: shear rate, shear stress, deformations,

viscosity, kinematic viscosity, viscoelasticity, fluidity, Non-Newtonion

flows, thixotropy, hysteresis loop, rheopexy.

describe temperature dependence and the theory of viscosity

explain the characteristics of Newtonian and Non-Newtonian

materials.

interpret the rheograms of Newtonian and Non-Newtonian

materials.

explain the working of various viscometers.

differentiate the rheology of emulsions, suspensions, and gel. 2

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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

response to a stress is

known as Rheology.

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STRESS

Tensile Stress: stress applied perpendicularly to the surface of a body.

Shearing stress: stress applied tangentially to the surface of a body.

Stress applied at any other angle to the surface of a body

Tensile Stress

Shearing stress 4

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DEFORMATIONS

Elastic deformation: It is spontaneous and reversible.

The work spent for the deformation is recoverable

when the body returns to the original position.

Plastic deformation: It is permanent and irreversible. The

work spent for the deformation is dissipated as heat.

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VISCOSITY : is an expression of the resistance of a liquid to flow.

Higher the viscosity greater the resistance.

Some liquids like water, alcohol, chloroform flow readily whereas syrup, glycerin flow slowly.

This rate of flow is depends on the internal resistance involved when moves over another layer.

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.

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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.

The viscosity of certain liquid preparations is increased in order to improve pourability or to make the preparation more palatable.

Paints are made more viscous so that they remain in contact with skin for long time e.g. glycerin 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.

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.

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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

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• 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.,

For Semi-solids

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• Powder flow from hopper to die cavities & flow of powder into capsules

• Packageability of powdered or granular solids

For Solids

• Production capacity & correct choice of production efficiency

• Processing efficiency

Processing

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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.

Liquid Temperature C Kinematic viscosity (centistokes)

Light liquid paraffin 37.8 > 30

Liquid paraffin 37.8 64

PEG 4000 100 76 & 100

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• 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

As a method for controlling or maintaining batch to batch quality to ensure its stability on storage and ease of use.

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Instruments which measure the visco-elastic properties of solids, semi-solids and fluids are named “Rheometers”

Instruments which are limited in their use for the measurement of the viscous flow behavior of fluids are described as “Viscometers”

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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.

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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.

• G=f F

Rheogram is produced by Newtonian systems, which follow the equation for a straight line passing through the origin:

The slope, f is known as fluidity and is the reciprocal of viscosity, n : f=1/η

The greater the slope of the line, the greater is the fluidity or conversely, the lower is the viscosity.

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NEWTONIAN SYSTEMS

Representation of the shearing force required to produce a definite velocity gradient between the parallel planes of a block of material.

Consider a “block” of liquid consisting of parallel plates of molecules, similar to a deck of cards …..

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.

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.

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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 . 17

TEMPERATURE DEPENDENCE & 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. 18

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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. 19

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.

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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

NON-NEWTONIAN SYSTEMS

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PLASTIC FLOW

The 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. 22

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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

U=𝑭−𝒇

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) 23

A plastic material was found to have a yield value of 5200 dynes/cm2.

At shearing stresses above the yield value, F was found to increase

linearly with G. If the rate of shear was 150 sec-1 when F was 8000

dynes/cm2, calculate U, the plastic viscosity of the sample.

• U=(8000-5200)/150

• =18.67 poise 24

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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. 25

PSEUDO-PLASTIC 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.

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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. 27

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

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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.

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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

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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.

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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.

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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.

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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.

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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) 36

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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)

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Viscoelastic materials possess both viscous flow and elasticity.

Two basic elements of mechanical models used to represent its behavior.

• Helical spring- gives the elastic behavior

• 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.

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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.

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(1) By gradually increasing the shearing stress on plastic or pseudo-plastic 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 SHEARING STRESS

REMOVING SHEARING STRESS

The conversion of sol to gel is not instantaneous but requires some time lag

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(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.

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 dependent effect is called thixotropy

which means ‘change by touch’.

APPLYING SHEARING STRESS

REMOVING SHEARING STRESS

SOL GEL

The conversion of gel to sol is not immediate but requires some time lag.

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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. 42

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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.

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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.

THIXOTROPY IN PLASTIC &

PSEUDOPLASTIC SYSTEMS 44

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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.

RA

TE O

F SH

EAR

SHEARING STRESS

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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.

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DETERMINATION OF THE VISCOSITY

Ostwald

viscometer

Falling sphere viscometer

Cone and plate viscometer

Ubbelhode viscometer

Rotational viscometer

Ferranti - Portable

viscometer ( for bulk liquids)

The viscosity of the liquid is measured by comparing with a liquid of known viscosity. 47

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(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.

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Viscous drag on the sphere= force responsible for downward

motion due to gravity

Rearranging the equation

Where 𝜂= coefficient of viscosity, d= diameter of the sphere, g= acceleration due to gravity,

u= terminal velocity, 𝜌𝑠= density of the sphere, 𝜌𝑙= density of the liquid

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.

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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

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Ostwald ‘s Viscometer

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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.

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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:

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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

ARM

RIGHT ARM

T

H

I

R

D

A

R

M

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.

Phase volume ratio

globule size distribution

Viscosity of the internal phase

Aggregation of globules

Nature & proportion of emulsifying agents

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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.

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.

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Most emulsions display both plastic and pseudoplastic flow behaviour rather than simple

Newtonian flow.

The pourability, spreadability and ‘syringeability’ of an emulsion determined by its rheological

properties.

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 -decrease in viscosity, resulting

in improved ease of injection. 58

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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.

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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.

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RHEOLOGY OF GEL

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. 61

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. 62

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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.

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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.

the change in plastic viscosity and thixotropy of petrolatum and plastibase as a function of temperature. The modified Stormer viscometer used.

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THE EFFECT OF RHEOLOGICAL PROPERTIES ON BIOAVAILABILITY

understanding of rheological behavior, both in the formulation and, if possible, at

the absorption site, is essential in any evaluation of bioavailability.

E.g. the rate of dissolution of a drug particle will be decreased

as the viscosity of the dissolution medium is increased.

absorption of drugs by the skin and from injection sites will be

decreased by an increase in the viscosity of the vehicle 65

THANK YOU

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