Rheology

Definition:
• The branch of physics, which deals with deformation
and flow of matter.
• Rheology governs the circulation of blood & lymph
through capillaries and large vessels, flow of mucus,
bending of bones, stretching of cartilage, contraction
of muscles.
• Fluidity of solutions to be injected with hypodermic
syringes or infused intravenously, flexibility of tubing
used in catheters, extensibility of gut.

From the rheological viewpoint systems are:
• Solid if they preserve shape & volume.
• Liquid if they preserve their volume.
• Gaseous if neither shape nor volume remains constant when
forces are applied to them.

To the pharmacist:
• Flow of emulsions through colloid mills,
• Working of ointments on slabs or roller mills.
• Trituration of suspensions in mortar and pestle.
• Mechanical properties of glass or plastic containers & of
rubber closures.
To the consumer:
• Squeezing toothpaste from a collapsible tube.
• Spreading lotion on his skin.
• Spraying liquids from atomizers or aerosol cans.

Types of Flow:
The choice depends on whether or not their flow properties
are in accordance to Newton's law of flow.
Newtonian Non - Newtonian

Representation of flow of liquid

Newton Law of Flow:
• Laminar or Stream line: The bottom layer is
considered to be fixed in place. If the top plane of
liquid is moved at a constant velocity, each lower
layer will move with a velocity ∞ to its distance
from the stationary layer.
• Velocity gradient or rate of shear , dv / dr.
• The rate of shear indicates how fast the liquid flows
when a shear stress is applied to it. Its unit is sec-1
.
• The force per unit area (F'/A) required to bring about
flow is called the shearing stress and its unit is
dyne/cm2
.

F'/A = η dv / dr (1)
Where η is the viscosity.
Equation (1) is frequently written as:
η = F/G (2)
Where F = F'/A & G = dv/dr.
For Newtonian System is shown in the figure. A
straight line passing through the origin is
obtained.

Units of Absolute Viscosity:
 The Poise (p), is the shearing force required to produce a
velocity of 1 cm/sec. between two parallel planes of liquid each
1 cm2
in area & separated by a distance of 1 cm.
 The Centipois (cp), 1 cp = 0.01 poise.
 Fluidity (φ) is the reciprocal of viscosity:
(φ) = 1/η (3)
 Kinematic viscosity : is the absolute viscosity divided
by the density of the liquid
 Kinematic viscosity = η/ρ (4)
The units of kinematic viscosity are the stoke (s( &
the centistoke (cs(.

Effect of Temperature on Viscosity:
 Viscosity of a gas increases with the increase of
temperature.
 Viscosity of liquid decreases as the temperature is raised
& the fluidity of a liquid, increases with temperature.

Non-Newtonian Systems:
• 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.

Plastic Flow:
Materials exhibiting plastic flow are known asMaterials exhibiting plastic flow are known as Bingham bodiesBingham bodies..
 The plastic flow curve does not passThe plastic flow curve does not pass
through the origin & it intersects thethrough the origin & it intersects the
shearing stress axis (or will if theshearing stress axis (or will if the
straight part of the curve isstraight part of the curve is
extrapolated to the axis) at a particularextrapolated to the axis) at a particular
point referred to aspoint referred to as yield valueyield value.. (f)
 A Bingham body does not begin toA Bingham body does not begin to
flow until a shearing stress,flow until a shearing stress,
corresponding to the yield value, iscorresponding to the yield value, is
exceeded.exceeded.

• The slope of the rheogram = mobility, ( fluidity in
Newtonian systems(.
• Its reciprocal is known as the plastic viscosity .
U = ( F-f ) / G (5)
• where f is the yield value, or (intercept, on the shear
stress axis in dynes cm-2
(.
• U is the plastic viscosity.

• Plastic flow is associated with the presence of flocculated particles
in concentrated suspensions.
continuous structure is set up.
• The yield value is present due to contacts between adjacent particles
(brought about by Van der Waal's forces).
• Consequently, the yield value is an indication of the force of
flocculation, the more flocculated the suspension, the higher will be
the yield value.
• Frictional forces between moving particles can also contribute to the
yield value.
• Once the yield value has been exceeded, any in shearing stress
(i.e. F-f ) brings about a directly proportional increase in G, the rate
of shear.
• Aplastic system resembles a Newtonian system at shear
stresses > the yield value.

Pseudoplastic Flow:
Polymers in solution, natural & synthetic
gums, e.g. liquid dispersions of tragacanth,
sodium alginate, methylcellulose.
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.
In contrast to Bingham bodies, there is no
yield value no part of the curve is
linear, one cannot express the viscosity of a
pseudoplastic material by any single value.

FN
= η' G (6)
 The exponent N rises as the flow becomes increasingly non-
Newtonian.
 When N = 1, equation (6) reduces to equation (2) & the flow
is Newtonian. F= η' G
The term η' is a viscosity coefficient.
 Following rearrangement, equation (6) may be written in the
logarithmic form:
log G = N log F - log η' (7)
 This is an equation for a straight line. Many pseudoplastic
systems fit this equation when log G is plotted as a function of
log F.

Shearing stress
Coiling & entanglement Alignment & disentanglement
Random & Brownian motion
in fluids
Shear stress applied to the fluid
Due to

• As the shearing stress the 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 the concentration and size of dispersed molecules.
• An equilibrium exists between the shear induced changes and
random coiling tendency caused by Brownian motion which
entraps water inside the coils. The rate of entanglement and
randomization by Brownian motion is constant, while the rate
of disentanglement and alignment increases with increasing
shear stress.
• The viscosity diminishes as the shear is increased, so they
known as “shear thinning systems”.

FN
= η' G (6)
 The exponent N rises as the flow becomes increasingly
non-Newtonian.
 When N = 1, equation (6) reduces to equation (2) and
the flow is Newtonian. The term η' is a viscosity
coefficient.
 Following rearrangement, equation (6) may be written in
the logarithmic form:
log G = N log F - log η' (7)
 This is an equation for a straight line. Many pseudoplastic
systems fit this equation when log G is plotted as a
function of log F.

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.

• FN
= η' G (6)
• N is always < 1 and decreases as the degree of dilatancy
increases.
• As N approaches 1, the system becomes increasingly
Newtonian in behavior.
• Substances possessing dilatant flow properties are
invariably suspensions containing a high concentration
(about 50 % or greater) of small, deflocculated particles.

At rest:
Particles are closely packed with small interparticle
volume. The amount of vehicle in the suspension
is enough to fill this volume. The particles move
relative to one another at low rates of shear.

Applying shear stress
Particle ,
s arrangement is expanded, particles take an open form
of packing (dilate). The amount of vehicle in the suspension
is constant & becomes insufficient to fill the inter-particles voids.
The resistance to flow increases, the particles are no longer
completely wetted or lubricated by the vehicle.
Eventually, the suspension will set up as a firm paste.

Time-Dependent Behaviour:
Thixotropy:
• Newtonian systems: If the rate of shear was reduced
once the desired maximum rate had been reached, the
down curve would be identical with & superimposed on
the up-curve.
• Non Newtonian systems:
With shear-thinning systems (i.e., plastic &
pseudoplastic), the down - curve is frequently displaced
to the left of the up-curve.This means 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
phenomenon is known as Thixotropy.

 Definition:
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 .

Gel structure
Asymmetric particles, many points of contact,
network structure & rigid structure.
Sol structure
Breakdown of structure, flow starts, particles are
aligned and transform to sol (shear thinning)
Removal of Shearing stress
Shearing stress
Gel structure
Rebuild of the gel structure by brownian motion
(time is not defined)

• An aqueous dispersion of 8% w /w sodium bentonite
sets to gel within an hour or two after preparation when
undisturbed, but flows & can be poured within many
minutes after it had been stirred above the yield value.
After prolonged rest it reverts to a gel.
• Thixotropic systems usually contain asymmetric particles
which, possess numerous points of contact & set up a
loose three-dimensional network.
• At rest, this structure confers some degree of rigidity on
the system & it resembles a gel.
• As shear is applied & flow starts, this structure begins to
break down. Points of contact are disrupted & the
particles become aligned.
• The material a gel-to-sol transformation &

• Upon removal of the stress, the structure starts to
reform. This process is not immediate. It is a progressive
restoration of consistency as the asymmetric particles
come into contact with each other by undergoing random
brownian movement.
• The rheograms obtained with thixotropic materials are
dependent on:
1- The rate at which shear is increased or decreased.
2- The time for which a sample is subjected to any one
rate of shear.

Choice ofViscometer
“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

“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

:Falling SphereViscometer
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.
For newtonian liquids:
B ( Sb – Sf ) η = t

• t= the time interval in sec.
• Sb & Sf are the specific gravities of the ball & fluid under
examination at the temperature being used.
• B is a constant for a particular ball and is supplied by the
manufacturer.
• The instrument can be used over the range 0.5 to 200,000
poise.

:Cone and PlateViscometer
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 or
shearing stress may be plotted.

C is an instrumental
constant.
T is torque reading.
V is speed in revolution /
minute.
C T / V= η
U = C (T - T f ) / V
f = T f x C f C f is constant
Plastic materials

Advantages :
• The rate of shear is constant throughout the entire sample
being sheared. As a result, any change in plug flow is avoided.
• Time saved in cleaning & filling.
• Temperature stabilization of the sample during a run.
• The cone and plate viscometer requires a sample volume of 0.l
to 0.2 ml. This instrument could be used for the rheological
evaluation of some pharmaceutical semisolids.

Factors Affecting Rheological Properties in
Pharmaceutical Products:
Chemical Factors:
(a) Degree of Polymerization:
• Suspending agents, and emulsion stabilizers act in low
concentrations to produce viscous solutions (high molecular
weight).
• Lower concentrations of the high molecular weight grades of
synthetic & modified natural gums are used to obtain the
desired viscosity.

(b) Extent of Polymer Hydration:
• In hydrophilic polymer solution the molecules are completely
surrounded by immobilized water molecules forming a solvent layer.
Such hydration of hydrophilic polymers gives rise to an increased
viscosity.
• The solvate layer is strongly bound to the macromolecule
viscosity will be insensitive to pH changes or low concentrations of
electrolytes.
• Loose solvate around the macromolecules, pH & electrolytes will
produce variations in viscosity.

(c) Impurities, Trace Ions and Electrolytes
• Changing the viscosity of natural polymers, e.g. in
sodium alginate solution, the viscosity to the
gelling point traces of calcium are present
the formation of calcium alginate.
• At concentrations, electrolytes do not change the
viscosity of natural colloids in aqueous solution.
• concentrations, the salts compete for the adsorbed
water molecules, surrounding the hydrated polymer,
due to the affinity of the salt ions for water.
• As the polymer molecules become dehydrated, their
dispersions decrease in viscosity & precipitation
occurs

)d) Effect of pH:
• Changes in pH greatly affect the viscosity & stability of
the hydrophilic natural & synthetic gums.
• The natural gums usually have a relatively stable
viscosity plateau extending over 5 or 4 pH units. Above
and below this stable pH range viscosity decreases
sharply.
• Methyl cellulose has a stable pH range of 3 to 12.
• Sodium salts polymers are unstable in acid medium due
to the separation of the acid form of the polymer, e.g.
sodium alginate.

(E) Sequestering Agents and Buffers:
• Sequestering agents have a stabilizing effect on viscosity in
some polymer solutions, which are decomposed by traces of
metals.
Examples:
• Calcium ions the viscosity of sodium alginate. Addition of
sequestering agents i.e. EDTA or hexameta-phosphate will
viscosity in sodium alginate solutions.
• Tragacanth solution also suffers a rapid loss in viscosity,
regardless of the pH, in systems, which bind calcium ions,
i.e citrate buffers.

Physical Factors:
(a) Aeration:
• Aerated products usually result from high shear milling.
Aerated samples are more viscous or have more viscous
creamed layer than non-aerated samples.
• Some aerated emulsions will be less viscous & less stable
than un-aerated samples due to concentration of the
surfactant or emulsion stabilizer at the air liquid interface &
thus deletion of the stabilizer at the oil - water interface.
De-aeration is done:
• Mechanically by roll milling, which squeezes out the air.
Heat the aerated system.

(b) Light:
• Various hydrocolloids in aqueous solutions are reported to be
sensitive to light.These colloids include carbopol, sodium
alginate & sodium carboxymethyl cellulose.
• To protect photosensitive hydrocolloids from decomposition:
• The use of light-resistant containers,
• Screening agents, antioxidants.
• In the case of carbopol, the use of sequestering
agents.

(c) The Degree of Dispersion and
Flocculation:
• In concentrated suspensions of 3% solids & higher, a
decrease in particle size of the solid phase, produce an
increase in the viscosity of the system.
• This viscosity increase to immobilization of the
vehicle with an increase in the fraction of the
suspension volume effectively occupied by the solid.
• The addition of insoluble solids to a Newtonian vehicle
non-Newtonian flow properties in system.
• The smaller the particle size of the dispersed solid phase,
the lower the concentration of the solids required to
produce non-newtonian flow and thixotropy.

Flocculation of a suspension system:
• Flocculation viscosity & thixotropy.
• The flocs or aggregates are held weakly together and
are capable of forming extended networks which give
the flocculated suspension its structural properties.
• Immobilization of a portion of the dispersing media in
the network & between the flocs viscosity.

Pharmaceutical and Biological Applications of
Rheology:
1- Prolongation of Drug Action:
• The rate of absorption of an ordinary
suspension differs from thixotropic suspension.
• Example: procaine penicillin G, a form of
penicillin, of relatively low water solubility.
Aqueous suspensions containing between 40 and
70% w/v of milled or micronized procaine
penicillin G + small amount of sodium citrate &
polysorbate 80 are thixotropic pastes & are of depot
effect when injected intramuscularly.

Ordinary suspension of
pencillin G
Thixotropy suspension of
pencillin G
I.M injection
Forms no depot, fast dispersion&
absorption so maintain therapeutic
Level for short time
Forms spherical deposits at site of
injection which resists disintegration
by tissue fluids& Small surface area
(absorption) so maintain therapeutic
Level for longer time
The formation of depot depends on: a- high yield value
b-fast thixotropic recovery after injection.

(2) Effect on Drug Absorption:
• The viscosity of creams and lotions may affect the rate of
absorption of the products by the skin.
• A greater release of active ingredients is generally possible
from the softer, less viscous bases.
• The viscosity of semi-solid products may affect absorption of
these topical products due to the effect of viscosity on the
rate of diffusion of the active ingredients.

(3)Thixotropy in Suspension and Emulsion
Formulation:
• Thixotropy is useful in the formulation of
pharmaceutical suspensions and emulsions. They
must be poured easily from containers (low viscosity)
• Disadvantages of Low viscosity:
• Rapid settling of solid particles in suspensions and rapid creaming of
emulsions.
• Solid particles, which have settled out stick together, producing
sediment difficult to redisperse ("caking or claying").
• Creaming in emulsions is a first step towards coalescence. (break down
of emulsion)

• A thixotropic agent such as sodium bentonite magma,
colloidal silicon dioxide, is incorporated into the suspensions
or emulsions to confer a high apparent viscosity or even a
yield value .
• At rest :
• High viscosities retard sedimentation & creaming .
• Yield values prevent them altogether; since there is no flow
below the yield stress, the apparent viscosity at low shear
becomes infinite

Pouring the suspension or emulsion from its container:
• Shaking at shear stresses above the yield value
• The agitation breaks down the thixotropic structure so
reducing the yield value to zero & lowering the apparent
viscosity.This facilitates pouring.
• Back on the shelf, the viscosity slowly increases again and the
yield value is restored as Brownian motion rebuilds the house-
of-cards structure of bentonite.

Rheology

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