RHEOLOGY
Definition:

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
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:

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
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
()
is the reciprocal of viscosity:
() = 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.
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Plastic Flow:
Materials
exhibiting plastic flow are known as Bingham bodies.
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)

A Bingham body does not begin to
flow until a shearing stress,
corresponding to the yield value, is
exceeded.

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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.
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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 nonNewtonian.
 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
Due to
Random & Brownian motion
in fluids
Shear stress applied to the fluid

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:

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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

N is always < 1 and decreases as the degree of dilatancy
increases.
As N approaches 1, the system becomes increasingly

=
η' G (6)
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:
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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.
Shearing stress
Sol structure
Breakdown of structure, flow starts, particles are
aligned and transform to sol (shear thinning)
Removal of 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 &
exhibits shear thinning.

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 of Viscometer
“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 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.
For newtonian liquids:
η
= t
) Sb – Sf ( B
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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 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 or
shearing stress may be plotted.
C is an instrumental
constant.
T is torque reading.
V is speed in revolution /
minute.
η =
CT/V
U= C
(T - T f ) / V
f = Tf x Cf
C f is constant
Plastic materials
Advantages :
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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:
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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.
Thixotropy suspension of
pencillin G
Ordinary 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:

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
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)



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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.