Rheology

Dept. of pharmaceuticsFaculty of Pharmacy

King Abdulaziz University 1

What is Rheology anyway?

• Rheology is the study of deformation and flow.

• Oil and water flow in familiar, normal ways, whereas mayonnaise, peanut butter, and chocolate flow in complex and unusual ways.

• In rheology, we study the flows of unusual materials.

Approach to explain the tendency of material to flow:

• When you open a partly used jar of mayonnaise, the top surface retains the shape created by the last person who made a sandwich.

• Well, compare that observation with the behavior of honey. The top surface of honey in a jar is always smooth. Within a few seconds of serving yourself from a honey jar, the surface is flat again.

• Honey is able to flow and become flat quite rapidly, while the mayo, even after months, fails to flow, and it retains the last shape carved into it by a knife.

• The difference in behavior of mayonnaise and honey is related to their viscosity.

• Rheology: has been derived from Greek words rheo “to flow” and logos “science”.

• Viscosity is an expression of the resistance of a fluid to flow. The higher the viscosity, the greater the resistance.

• Rheology may thus be defined as: The science concerned with the study of the deformation of matter under the influence of stress, which may be applied perpendicularly to the surface of a body (tensile stress) or tangentially to the surface of a body (a shearing stress) or at any other angle to the surface of the body..

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Importance of Rheology:

Rheology is involved in the:• In preparation, development and evaluation of

pharmaceutical dosage forms e.g., suspensions, emulsions, pastes, suppositories, tablets coating, …., etc.

• Mixing and Flow of materials• Packaging into containers• Removal prior to use

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Classification of Materials according to the types of flow:

1) Newtonian Systems They obey Newton’s law of flow.Example: Water, Ethanol, Benzene.

2) Non-Newtonian SystemsThey fail to follow Newton’s law of flow.Examples: Colloidal Solutions, Emulsions, Liquid Suspensions, Gels and Ointments.

1. Newtonian systems Newton's law of flow:

1. Let us consider a block of liquid consisting of parallel plates of molecules.

2. The bottom layer is considered to be fixed in place.

3. If the top plane of liquid is moved at constant velocity, each lower layer will move with a velocity directly proportional to its distance from the stationary bottom layer.

4. The velocity difference, dv, between two planes of liquid separated by distance, dr, is the rate of shear (G) = dv/dr.

5. The force per unit area required to cause flow (F'/A) is called the shearing stress (F).

6. Newton recognized that: the higher the viscosity of a liquid, the greater the force per unit area (shearing stress) required to produce a certain rate of shear.

7. Thus, the rate of shear is directly proportional to the shearing stress.

F'/A α dv/dr F'/A = η dv/dr (1)where η is a constant known as viscosity η = F / G (2)

The unit of viscosity is poise or dyne.sec.cm-2.

Laminar shear field due to applied Shear stress

Velocity ,V

Force,F

Thickness , X

Area , A

Newtonian systems have constant viscosity where η = F / G.

• When we plot a rheogram of G against F, then a straight line is obtained passing through the origin, the slope of which is equal to the reciprocal of viscosity, a value referred to as the fluidity Φ,

Φ = 1 / η• Newtonian systems like water, simple organic liquids, true

solutions and dilute suspensions and emulsions.

Shearing stress (F)

Shear rate (G)

Slope = Φ = 1 / η

Rheogram of a Newtonian liquid

The passage through the origin indicates that even a mild force can induce flow in these systems.

The linear nature of the curve shows that the viscosity (η) of a newtonian liquid is a constant unaffected by the value of the rate of shear.

Thus a single determination of viscosity from the shear stress at any given shear rate is sufficient to characterize the flow properties of a Newtonian liquid.

Kinematic Viscosity (S):The kinematic viscosity of a liquid is its absolute viscosity divided by the density at a definite temperature. kinematic viscosity (s) = η /ρ

The units of kinematic viscosity are the stoke (s) and the centistoke (cs).

Relative Viscosity (ηr):

It is the ratio of solution viscosity (η) to the viscosity of the solvent (ηo ) (in pharmaceutical products it is often water).

FLOW CHARACTERISTICS OF NON-NEWTONIAN SYSTEMS

Do not follow the simple Newtonian relationship i.e., when F is plotted against G the rheogram is not a straight line passing through the origin i.e., viscosity is not a constant value.

Such as colloidal dispersions, concentrated emulsions and suspensions, ointments, creams, gels, etc.

These rheograms represents three types of flow: 1. Plastic 2. Pseudoplastic 3. Dilatant.

1. Plastic Flow:Such materials are called Bingham bodies

• The curve is linear over most of its length corresponding to that of a Newtonian fluid.

• However, the curve does not pass through the origin but rather intersects the shearing stress axis (or will if the straight part of the curve is extrapolated to the axis) at a particular point referred to as the Yield value or Bingham Yield value.

Contrary to a Newtonian liquid that flows under the slightest force, a Bingham body does not flow until a definite shearing stress equal to the yield value is applied.

Below the yield value the system acts as an elastic material.

Plastic systems resembles Newtonian systems at shear stresses above the yield value.

The slope of the rheogram is termed mobility, analogous to fluidity in Newtonian systems and its reciprocal is known as the Plastic viscosity, U.

U = (F - f) G

• Plastic flow is associated with the presence of flocculated particles in concentrated suspensions, however ointments and creams are common examples for that system.

• A yield value exists because of the contacts between adjacent particles (brought about by van der Waals forces), which must be broken down before flow can occur.

• Consequently, the yield value is an indication of force of flocculation: The more flocculated suspension, the higher will be the yield value.

• Plastic systems are shear-thinning systems

Mechanism of Plastic Flow

2. Pseudoplastic Flow:

A large number of pharmaceutical products, including natural and synthetic gums, e.g., liquid dispersions of tragacanth, sodium alginate, methyl cellulose, and Na CMC show pseudoplastic flow.

As a general rule pseudoplastic flow is exhibited by polymers in solution, in contrast to plastic systems which are composed of flocculated particles in suspension

• Curve for a pseudoplastic material begins at the origin consequently, in contrast to Bingham bodies, there is no

yield value.

• Since no part of the curve is linear, one can not express the viscosity of a pseudoplastic material by any single value.

• The viscosity of a pseudoplastic substance decreases with increasing rate of shear (shear-thinning systems).

• As the shearing stress is increased, the normally-disarranged molecules begin to align their long axes in the

direction of flow.

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• Plastic Flow: Pseudoplastic Flow:

Flocculated particles Polymers in

in Suspensions. Solution

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• Rheogram of a pseudoplastic material begins at the origin, there is no yield value.

The viscosity of a pseudoplastic substance decreases with increasing rate of shear, why?

oNewtonian system is completely described by η the viscosity. oPlastic system is described by the yield value and the plastic

viscosity. oPseudoplastic systems which can not be described by a

single value are expressed by: F N = η’ G

When N = 1, the flow is Newtonian As N rises the flow becomes increasingly non Newtonian. The term η’ is a viscosity coefficient.

The logarithmic form is a straight line equation log G = N log F – log η’A straight line is obtained when log G is plotted against log F

3. Dilatant Flow:

Dilatant systems exhibit an increase in resistance to flow (viscosity) with increasing rates of shear, “shear thickening systems”.

Such systems actually increase in volume when sheared and are hence termed dilatant. When the stress is removed, a dilatant system returns to its original state of fluidity.

• Dilatant flow is the reverse of that possessed by pseudoplastic systems.

• Substances possessing dilatant flow properties are invariably suspensions containing a high concentration (about 50 percent or greater) of small, deflocculated particles.

• Particulate systems of this type which are flocculated would be expected to possess plastic, rather than dilatant flow characteristics.

Dilatant behavior may be explained as follows:

• At rest, the particles are closely packed with the interparticle volume, or voids being at a minimum.

• The amount of vehicle in the suspension is sufficient, however, to fill this volume and permits the particles to move relative to one another at low rates of shear.

• Thus, one may pour a dilatant suspension from a bottle since under these conditions it is reasonably fluid.

As the shear stress is increased, the bulk of the system expands or dilates, hence the term dilatant.

The particles, in an attempt to move quickly past each other, take on an open form of packing. Such an arrangement leads to a significant increase in the interparticle void volume.

The amount of vehicle remains constant and at some point, becomes insufficient to fill the increased voids between the particles.

Accordingly, the resistance to flow increases because the particles are no longer completely wetted or lubricated by the vehicle.

Thus, the suspension will set up as a firm paste.

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Closed packed particles open packed particlesminimum void volume increase void volume sufficient vehicle insufficient vehiclelow viscosity high viscosity

Common flow behaviours

Newtonian Pseoudoplastic DilatantS

hear

str

ess

Sh

ear

str

ess

Sh

ear

str

ess

Shear rate Shear rate Shear rate V

iscosit

y

Vis

cosit

y

Vis

cosit

y

Shear rate Shear rate Shear rate

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• How can characterize the following systems:

• Newtonian systems• Non- Newtonian systems:a- plastic substanceb- pseudoplastic substancec- dilatant

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Thixotropy• Thixotropy is a property exhibited by certain gels

(semisolid, jellylike colloids).• A thixotropic gel appears to be solid and maintains a

shape of its own until it is subjected to a shearing force or some other disturbance, such as shaking. It then acts as a sol (a semi-fluid colloid) and flows freely.

• If the rate of shear was increased and then was reduced once the desired maximum rate had been reached and plotted against the resultant shear stress, the down-curve would be identical with and superimposed on the up-curve in case of Newtonian systems.

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• The down curve for non-Newtonian systems (plastic and pseudoplastic) displaced to the left of the up curve, showing that the material has a lower consistency at any one rate of shear on the down-curve than it had on the up-curve. This indicates a breakdown of structure that does not reform immediately when the stress is reduced or removed.-------- Thixotropy

• Thixotropic behavior is reversible, and when allowed to stand undisturbed the sol slowly reverts to a gel.

• Common thixotropic gels include certain paints

and printing inks. Ketchup and yoghurt displays thixotropic

properties

• So, Thixotropy as a term means “to change by touch”.

• It is usually referred to as isothermal gel-sol-gel transformation.

• It is characterized by a breakdown of structure with agitation and followed by the reformation of the rigid structure when the material is allowed to stand undisturbed for some time.

• The breakdown of the structure does not reform immediately when the stress is reduced or removed.

Thixotropy, may be defined as

• an isothermal and comparatively slow-recovery of a consistency lost through shearing, on standing of a material,.

• Thixotropy may only be applied to plastic and pseudoplastic flow systems (shear-thinning systems).

• Factors affecting rheogram of thixotropic substance:1- Rate at which shear is increased or decreased.2- Length of time a sample is subjected to any one rate of shear.

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Negative Thixotropy• It is also called antithixotropy, which represents

an increase rather than a decrease in consistency when the system is sheared (shear thickening).

• It results from an increased collision frequency of dispersed particles or polymer molecules in suspension, resulting in increased interparticle bonding with time.

• Negative Thixotropy differed than dilatancy

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Dilatant system is deflocculated and contains more than 50% by volume of solid dispersed phase.

• Antithixotropic system has low solids content (1 to 10%) and are flocculated.

• At rest it is sol.

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Rheograms of thixotropic fluids

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Measurement of Thixotropy:

1- The most apparent characteristic of a thixotropic system is the hysteresis loop, formed by the up- and down-curves of the rheogram.

This area of hysteresis has been proposed as a measure of thixotropic breakdown; it may be obtained readily by means of a Planimeter.

2- Determine the structure breakdown of plastic bodies at constant shearing rate and different time.

B = U1-U2/ (ln t2/t1)

B= thixotropic coefficient, U1 and U2 are plastic viscosity of two down curves after shearing at a constant rate for t1 and t2 second.

3- Determine the viscosity due to increase shearing rate

M = U1-U2/ (ln 2/ 1) M is the thixotropic coefficient, the rate of shear

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Thixotropy in formulation1- A well formulated thixotropic suspension will not settle out readily in the container, will become fluid on shaking, and will remain long enough for a dose to be dispersed.

2- Similar behavior is desired with emulsion, lotions, creams, ointments and parenteral suspension to be used

as intramuscular depot therapy.

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Determination of Rheological Properties

• The rate of shear in a Newtonian system is directly proportional to the shearing stress, thus one can use instruments that operate at a single rate of shear.

• For non-Newtonian system, the instrumentation used must be able to operate at a variety of rates of shear and so, only by the use of “multi-point” instruments it is possible to obtain the complete rheogram for these systems.

• So, the choice of viscometer to determine the viscosity is important, all viscometers can be used to determine the viscosity of Newtonian systems, while non- Newtonian systems need viscometer with variable shear stress.

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1- Capillary Viscometer: Used for Newtonian system by determine the time required for the liquid to pass between two marks as it flows by gravity through a vertical Capillary tube known as Ostwald Viscometer

η 1/ η2= t1/t2

Where η 1 / η 2 is called the relative viscosity

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2-Falling Sphere Viscometer

• Stokes' law is the basis of the falling sphere viscometer,

V = 2r2 g ( ρ - ρo) / 9 ηo

V is the velocity of sedimentation of spherical particles, ρ is the density of the spherical particles, ρo is the density of the medium, ηo is the viscosity of the medium and g is the acceleration due to gravity.

For description, the fluid is stationary in a vertical glass tube and a sphere of known size and density is allowed to descend through the liquid. The time for the ball to fall between two marks is accurately measured and repeated several times .

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η = t(Sb-Sf)B where:t is the time in second for the ball to fall between two marksSb , Sf are the specific gravity of the ball and the liquid B constant for particular ball

N.B: Specific gravity is the ratio of the density (mass of a unit volume) of a substance to the density (mass of the same unit volume) of a reference substance

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3- Cup And Bob Viscometer:

In the cup and Bob viscometer the sample is sheared in the space between the outer wall of

the bob and the inner wall of the cup into which

the bob fits.

The various instruments available differ mainly in whether the torque set up in the bob results from the cup or from the bob being caused to resolve.

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The torque resulting from the viscous drag of the system under examination is generally measured by a spring or sensor in the drive to the bob. Stormer instrument should be used with systems having a viscosity below 20 cps.

Ω = 1 T (1/R2b -1/R2

c) η 4h Ω = (omega) T = torque in dyne cm h= depth to which the bob is immersed in the liquid R2

b R2c are the radii of the cup and bob

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4- Cone and Plate ViscometerThe 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 and the sample is sheared

in the narrow gap between stationary plate and rotating cone.

The rate of shear is controlled by a selector dial and the torque

(shearing stress) produced on the cone is read on indicator scale

cone

plate

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For Newtonian systems η = C T/

C = instrumental constantT = Torque reading= speed of the cone per minute

For Plastic systems η = C (T-Tf /)Tf is the torque at shearing stress axis (yield value)

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Viscoelasticity:

• The viscosity can be measured for both liquid and solid

• For liquid : η = F/G the behavior expressed by flow properties of the liquid

• For solid: E= F/ E = elastic modules (dyne/cm) = the strain F = the stress (dyne/cm)

the behavior expressed by elasticity properties of the solid

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Temperature dependence and the theory of viscosity:

The viscosity of the gas increases with increasing the temperature since, in gases the cohesive forces between the molecules is lesser, while molecular momentum transfer is high. As the temperature of the gas is increased the molecular momentum transfer rate increases further which increases the viscosity of the gas

The η of the liquid decreases with increase the temp. and the fluidity increase.

The dependence of the η on temp. can be expressed by Arrhenius equation

η = AeEv/RT

A = constant depend on molec. Wt and molec. Volume of the liquid Ev = activation energy required to initiate energy between molec.

The viscosity of a liquid usually decreases with rise in temperature. The amount of such a decrease is often of the order of 1 to 10 % per °C.

Physical Factors affecting Viscosity

1.Temperature

• A temperature increase usually produces a rapid viscosity decrease, with the exception of certain synthetic polymers such as methyl cellulose, whose aqueous solutions gel with temperature for a short period, due to hydration.

• Prolonged heating may produce drastic decrease in viscosity due to decomposition of the polymer, e.g., gelatin.

2. Aeration

• Aerated products usually result from high shear milling. Aerated samples appear to be more viscous or have more viscous creamed layer than non-aerated samples.

• Some aerated emulsions will be less viscous and less stable than unaerated samples due to concentration of surfactant or emulsion stabilizer at the air-liquid interface and depletion of it at the oil-water interface.

• Deaeration may be carried out either

– mechanically by roll milling, which squeezes out the air or by – heating the aerated system.

3. Light

• Various hydrocolloids in aqueous solutions are reported to be sensitive to light. These colloids include carbopol, Na alginate, and Na CMC.

• To protect photosensitive hydrocolloids from decomposition and resultant viscosity change use light-resistant containers, antioxidants or in case of carbopol, the use of sequestering agents.

Pharmaceutical and Biological Applications of Rheology

(1) Prolongation of Drug Action

• There is a great difference in the rate of absorption of an ordinary suspension and the same when it is thixotropic.

• The suspension is shaken before administration to be easily injected but in the body it forms a compact, spherical deposits at the site of injection. These deposits resist disintegration by tissue fluids because of their high consistency which leading to prolonged or depot action as in case of procaine penicillin G.

(2) Effect on Drug Absorption• The viscosity of creams and lotions may affect the rate of

absorption. A greater release of active ingredients is generally possible from the softer, less viscous bases.

(3) Thixotropy and good Suspension Formulation• Thixotropy is particularly useful in suspensions. These must

be poured easily from containers, which requires low viscosity.

• It is possible to minimize or completely eliminate sedimentation and coagulation of insoluble particles to give a uniform dosage simply by agitation.

(4)Thixotropy and Drug Stability• Another useful aspect of thixotropy is that substances,

which are susceptible to decomposition, such as vitamins, are found to be stable for longer periods of time in thixotropic preparations, as such substances are in a state of complete rest, in a solid gel.

(5) Rheology and Diagnosis of Disease

• Several studies have been made to correlate the rheology of body fluids and the diagnosis of disease, determination of fertility, determination of blood composition and blood flow through normal and constricted arteries.

• The rheology of blood is of interest in the studies of normal and abnormal blood and vascular states.

• The viscosity changes of the cervical fluid appear to be related to ovulation in women.

(6) Effect on bioavailability:

• The rate of dissolution of a drug particle will be decreased as the viscosity of the dissolution medium is increased.

• The use of hydrocolloids will exhibit non-newtonian behavior such as in case of griseofulvin in concentrations of methylcellulose, which will exhibit pseudoplastic behavior and delay absorption.

• The absorption of drugs by the skin and from injection sites will be decreased by increase in the viscosity of the vehicle.

Thank you