RHEOLOGY

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RHEOLOGY
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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.

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• 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.

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• 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.

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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
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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
  8 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.

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F'/A ? dv / dr (1)
Where ? is the viscosity . Equation (1)
is frequently written as ? 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.
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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/? (3)
• Kinematic viscosity is the absolute viscosity
  divided
• by the density of the liquid
• Kinematic viscosity ?/? (4)
• The units of kinematic viscosity are the stoke
  (s)
• the centistoke (cs).

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• 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.

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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.

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• 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 gt 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.
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• FN ?' 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 ?' G
• The term ?' is a viscosity coefficient.
• Following rearrangement, equation (6) may be
  written in the logarithmic form
• log G N log F - log ?'
  (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.

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Shearing stress
Coiling entanglement
Alignment disentanglement
Due to
Random Brownian motion in fluids
Shear stress applied to the fluid
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The curved rheogram for pseudoplastic materials
is due to shearing action on the long chain
molecules of materials such as linear polymers.
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. Therefore, the
viscosity diminishes as the shear is increased

• 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.

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• FN ?' 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 ?' is a
  viscosity coefficient.
• Following rearrangement, equation (6) may be
  written in the logarithmic form
• log G N log F - log ?'
  (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.

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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.

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• FN ?' G (6)
• N is always lt 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.

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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.
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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.
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Time-Dependent BehaviourThixotropy

• 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.

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• 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
  .

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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)
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• 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.

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• 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.

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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

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• 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

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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 B ( Sb Sf ) ? t

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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.

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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.

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

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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.

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• (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.

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(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

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)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.

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• (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.

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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.

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(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.

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(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.

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• 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.

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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.

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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.
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(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.

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(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

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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.