Pharmaceutics II - Rheology
1.
2.
Definitions
Importance of Viscosity in Pharmacy
2.1
Liquids
2.2
Semi-Solids
2.3
Processing
3.
Measurement of Rheologic Properties
3.1
Capillary Viscometer
3.2
Cup and Bob/Disk Viscometer
3.3
Cone and Plate Viscometer
4.
Newtonian Systems
4.1
Newton’s Law of Flow
4.2
Fluid Flow and Reynolds Apparatus
4.3
Boundary Layers
5.
Non-Newtonian Systems
5.1
Plastic or Bingham Bodies
5.2
Pseudo-plastic Flow
5.3
Dilatant Flow
6.
Thixotrophy
6.1
Description
6.2
Measurement of Thixotropy
6.3
Rheopexy
6.4
Thixotropy in Formulation
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Pharmaceutics II - Rheology
7.
FLUID FLOW
7.1 Boundary Layers
7.2 Reynold’s Apparatus
8.
Determination of Rheologic Properties
8.1 Why measure viscosity?
9.
Applications of Rheology to Pharmacy
Course Outcomes:
1.
2.
3.
Describe the importance of rheology in the formulation, manufacture, stability and quality
assurance of pharmaceutical dosage forms.
Describe the rheological properties of Newtonian, non-Newtonian and thixoptropic systems
and to ascribe these characteristics to various pharmaceutical systems.
Describe methods of determining the viscosity of pharmaceutical formulations.
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Pharmaceutics II - Rheology
•
Texts
Physical Pharmacy, 4th Edition, Alfred Martin, Chapter 17, Rheology.
Pharmaceutics – The Science of Dosage Form Design, 2nd Edition, ME
Aulton, Chapter 4, Rheology.
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Pharmaceutics II - Rheology
1.
DEFINITIONS

Rheology is the science concerned with the deformation of matter
under the influence of a stress.

Viscosity is an expression of the resistance of a fluid to flow, the higher
the viscosity, the greater the resistance.

When stress is applied, it causes strain in the system which leads to
deformations which can be either:
•
elastic and spontaneously reversible
•
permanently irreversible
•
viscoelastic
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2. IMPORTANCE OF VISCOSITY IN PHARMACY
2.1 Fluids





Mixing
Particle size reduction of disperse systems with shear (e.g. creams)
Passage through orifices
Fluid transfer
Physical stability of disperse systems
2.2 Semi-Solids





Emulsions, pastes, suppositories and tablet coatings – semi-solid entities
which can flow or deform.
Spreading and adherence on skin
Removal from jars or extrusion from tubes
Capacity of solids to mix with immiscible liquids
Release of the drug from the base
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2.3 Processing


Production capacity and power requirements of equipment
Manufacturing equipment fitted with strain gauges to permit monitoring
of torque measurements

Units of viscosity – centipoise (η) – coefficient of viscosity - complex unit
1 centipoise = 1 mPa-s. (1 millipascal*s).
1 Pa = (kg.m/s²)/m² = kg/m.s² = N/m²
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3. MEASUREMENT OF RHEOLOGICAL PROPERTIES
3.1 Capillary (Ostwald) viscometer
•
The viscosity of a Newtonian liquid determined by
•
Ostwald viscometer.
Reference is usually water (at 25°C – ρ = 0.997g/cm3, η = 0.8904
centipoise)
•
The absolute viscosity of the unknown liquid η1 :
η1 = ρ1 t1
η2 ρ2 t2
•
η1 and η2 = viscosities of unknown and standard liquids
ρ1 and ρ2 = densities of unknown and standard liquids
t1 and t2 = respective flow times in seconds
Assuming a linear relationship
This equation is based on Poiseuille's law for a liquid flowing
through a capillary tube.
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3.2
Cup and Bob/Disk Viscometer
•
A cylindrical bob or flat circular disk
•
Sample shear
•
Variable rate of shear (revs/min) - Shearing stress is
read on the indicator scale.
•
Quick and easy to use but:
- The rate of shear is not constant across the
diameter
of the disk – average value - interpretation
- Requires a relatively large volume of sample (e.g.
100ml +)
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dv
dx ?
8
Brookfield Viscometer with RV Spindle
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Brookfield Viscometer with RV Spindle
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Range of RV Viscometer Spindles (RV1 to RV7)
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Range of HA Viscometer Spindles (HA1 to HA7)
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Range of T Viscometer Spindles (T-A to T-F)
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3.3
Cone and plate viscometer
•
- A flat, circular plate
- A wide-angled cone placed centrally above.
- The tip of the cone just touches the plate.
•
- Place sample at the centre of the plate.
- Raise plate into position under the cone.
•
- Cone is driven by a variable-speed motor .
- Sample is sheared in the narrow gap between the
stationary plate and the rotating cone.
•
- The rate of shear (revs/min) is increased and decreased
by a selector dial and
- The viscous traction or torque (shearing stress)
produced on the cone is read on the indicator scale.
•
- Important advantages of this viscometer:
- The rate of shear is constant throughout the entire sample .
- Only a small sample volume of 0.1 to 0.2 ml is required.
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4. NEWTONIAN SYSTEMS
4.1 Newton's law of flow (dynamic viscosity)
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•
A velocity gradient exists and this will be equal to
the velocity of the upper layer (m/s)
divided by the height of the cube (m)
•
•
•
dv
dx
rate of flow or
velocity gradient,
the rate of shear (s-1).
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•
Rate of shear = dv/dx (s-1)
•
The applied stress of force per unit area (F/A) required to bring
about flow is called the shear stress (S) and has units of N/m2.
•
Increased viscosity = increased shear force or shear stress required
to produce a certain rate of shear
A certain shear stress with produce a certain rate of shear
•
Rate of shear should be directly proportional to the shearing stress.
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•
F
A
α dv
dx
Rate of shear directly proportional to
the shearing stress.
F
A
=
Replace proportionality sign with a constant k .
k . dv
dx
•
F/A = η ● dv/dx
•
if F/A = Sthen
•
S = η dv/dx
•
dv/dx = 1/ η . S
y = m. X
where k = η = coefficient of viscosity
Newton's equation
+
or rearranged
C
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•
Newtonian fluids exhibit the least complex flow patterns e.g. true
solutions and water.
Viscosity here is a true constant unaffected by rate of shear
Only a single determination of viscosity at any rate of shear or any
shear stress is required to fully characterise the rheological
properties
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Pharmaceutics II - Rheology
Viscosity Diagram for a Newtonian Fluid
dv/dx = 1/ η . S
dv/dx
y = m.
x + c (c=0)
(rate
of
shear
s-1)
Unit for η
the poise
(complex
unit)
Gradient = 1/η
(1/coefficient of viscosity)
S (Nm-2 )
(F/A)
•
•
Viscosity is constant – unaffected by rate of shear – linear so 1/η (gradient) can be determined at any rate of sheer.
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Pharmaceutics II - Rheology
4.2 Measuring Viscosity of Newtonian systems
•
Rate of shear is proportional to shearing stress
•
Can us instruments that operate at a single rate of shear.
•
Provide a single point on the rheogram.
•
Extrapolation of a
line through this point to the
origin will result in the complete
rheogram.
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VISCOSITIES OF SOME FLUIDS OF PHARMACEUTICAL INTEREST
_______________________________
Fluid
Dynamic viscosity at 20°C (mPa s)
Chloroform
0.58
Water
1.002
Ethanol
1.20
Glyceryl trinitrate
36.0
Olive oil
84.0
Castor oil
986.0
Glycerol
1490
_______________________________
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5.
NON-NEWTONIAN SYSTEMS
Most pharmaceutical fluids do not follow Newton's equation:
- because the viscosity of fluid varies with the rate of shear.
-
therefore a single determination of viscosity at any one rate of shear
cannot yield the entire rheological profile.
-
i.
ii.
iii.
Plastic or Bingham flow
Pseudoplastic flow
Dilatant flow
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Pharmaceutics II - Rheology
Rheograms for Newtonian and Non-Newtonian Flow
Physical Pharmacy p.522
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Pharmaceutics II - Rheology
5.1
Plastic or Bingham flow
•
•
The rheogram does not pass through the origin.
Intersects with the shear stress (x) axis .
(or will if the straight part of the curve is extrapolated to the axis)
X - intercept is usually referred to as the yield value.
•
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Pharmaceutics II - Rheology
•
A Bingham body does not begin to flow until a shearing stress,
corresponding to the yield value, is exceeded.
•
If stress is less than the yield value, the system behaves like a solid
and exerts elastic deformations that are reversible.
•
The quantitative behaviour of these bodies is best described by the
Bingham Equation where fB is the Bingham yield value:
Newtonian
S = η . dv/dx
η=
S .
dv/dx
Non-Newtonian η pl = S - fB
dv/dx
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Pharmaceutics II - Rheology
•
In practice, deformation and flow usually occurs at a lower shear stress
value and this accounts for the curved portion of the curve.
•
The viscosity decreases initially and then remains constant.
•
In a highly flocculated system, there is interaction between flocs which
results in a structured system and plastic flow is associated with these
systems e.g highly flocculated suspensions.
•
The yield value is present because of the contacts between adjacent
particles (caused by van der Waals forces which may be capable of
withstanding weak stresses) which must be broken down before flow
can occur.
•
Consequently, the yield value is an indication of the degree of
flocculation; the more flocculated the suspension, the higher will be the
yield value.
•
This type of behaviour is also exhibited by creams and ointments.
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Pharmaceutics II - Rheology
5.2
Pseudoplastic flow
•
Many pharmaceutical products exhibit pseudoplastic flow
include natural and synthetic gums
e.g. liquid dispersions of tragacanth,
sodium alginate, methylcellulose,
sodium carboxymethylcellulose,.
•
As a general rule:
Pseudoplastic flow is exhibited by
polymers in solution
Plastic systems are composed of
flocculated particles.
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Pharmaceutics II - Rheology
•
The curve commences at the origin and there is no yield value.
•
No part of the curve is linear,
so viscosity cannot be expressed
by any single value.
•
The apparent viscosity may be
obtained at any rate of shear from
the slope of the tangent to the
curve at the specified point.
•
The viscosity decreases with an
increasing rate of shear
(shear-thinning systems).
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Pharmaceutics II - Rheology
•
Pseudoplastic flow cannot be satisfactorily expressed by
fundamental equations.
•
The following empirical equation correlates most closely with
experimentally observed flow not involving stress over vast ranges:
Sn = η1 dv
dx
n>1;
the term η' is a viscosity coefficient.
•
The exponent n rises as the flow
becomes increasingly non-Newtonian.
•
When n = 1, this equation reverts to
the classic Newton equation and the
flow is Newtonian.
Dr M. Skinner
1/η = gradient
(changes with S)
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Pharmaceutics II - Rheology
At the Particulate level:
•
The curved rheogram for pseudoplastic materials results from a
shearing action on the long-chain molecules which become
entangled and associated with immobilized solvent.
•
As the shearing stress is increased, the randomly arranged particles
tend to become disentangled and align their long axes in the
direction of flow.
•
This orientation reduces the internal resistance of the material and
offers less resistance to flow. Some of the entrapped water will also
be released.
•
Both of these account for the lower viscosity. Once stress is
removed, the structures reform spontaneously.
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Pharmaceutics II - Rheology
5.3
Dilatant flow
•
Dilatant flow - usually suspensions containing a high concentration
(>50%) of small, deflocculated particles.
•
Exhibit an increase in resistance to flow with increasing rates of shear.
•
Systems increase in volume when
sheared - termed dilatant.
•
The reverse of pseudoplastic systems.
•
Pseudoplastic systems –
shear-thinning systems,
Dilatant materials shear-thickening systems.
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Pharmaceutics II - Rheology
•
The same equation can be used to describe dilatancy in quantitative
terms:
Sn = η1 dv
dx
n<1
•
n is always less than 1
•
Decreases as the degree of
dilatancy increases.
•
As n approaches 1, the system
becomes increasingly Newtonian
in behaviour.
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Pharmaceutics II - Rheology
At the particulate level:
•
At rest:
- particles closely packed
- voids at a minimum.
•
Vehicle:
- sufficient to fill this volume
- allows the particles to move relative to one another at low rates of
shear.
•
Can pour a dilatant suspension from a bottle without shaking as it is
relatively fluid without shear stress applied.
•
If the shear stress is increased by shaking, the bulk expands or dilates as
the particles move quickly past each other and take an open form of
packing.
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Pharmaceutics II - Rheology
•
Such an arrangement results in a significant increase in the void
volume, with the vehicle now being insufficient to fill the voids
between the particles.
•
The resistance to flow increases since the particles are no longer
completely wetted or lubricated by the vehicle and eventually the
suspension will set up as a firm paste.
•
Caution must be taken in processing dilatant materials.
- Usually, the processing of dispersions containing solid particles is
facilitated by the use of high speed mixers, blenders or mills.
-
Dilatant materials may solidify under these conditions of high
shear, thereby overloading and damaging the processing
equipment.
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Pharmaceutics II - Rheology
6. THIXOTROPY
6.1 Description
•
So far for Newtonian and non-Newtonian behaviour:
- observed behaviour when the rate of shear was progressively
increased and plotted against the resultant shear stress.
•
Assumed that if the rate of shear was reduced, the down-curve would
be identical with and superimposed on the up-curve.
•
This is so with
•
For most non-Newtonian systems:
The flowing elements, whether particles or macromolecules, may
not adapt immediately to the new shearing conditions.
When subjected to a particular shear rate, the shear stress and
consequently the viscosity, will decrease with time.
Therefore the down-curve can be displaced with regard to the upcurve.
-
Newtonian systems
some non-Newtonian materials.
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Pharmaceutics II - Rheology
•
Thixotropic systems usually contain asymmetric particles and
through numerous points of contact, these particles set up a loose 3D network throughout the sample.
•
At rest, this structure confers some degree of rigidity on the system,
and it resembles a gel.
•
As shear is applied and flow starts, this structure begins to break
down as the points of contact are disrupted and the particles
become aligned in the general direction of flow.
•
The material undergoes a gel to sol transformation and exhibits
shear thinning.
•
Upon removal of the stress, the structure starts to reform. This is
not instantaneous, but is a progressive restoration of consistency as
the asymmetric particles come into contact with each other by
undergoing random Brownian movement.
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Pharmaceutics II - Rheology
•
Shear-thinning systems (plastic and pseudoplastic)
- down-curve is frequently displaced to the left of the up-curve
- rheogram exhibits a hysteresis loop.
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Pharmaceutics II - Rheology
•
i.e. the material has a lower consistency at any one rate of shear on
the down-curve than it had on the up-curve.
•
Indicates a breakdown of structure that does not reform immediately
when the stress is removed.
•
•
This phenomenon is known as thixotropy and may be defined as:
“An isothermal and comparatively slow recovery, on standing of a
material whose consistency is lost through shearing".
•
According to this definition, thixotropy can only be applied to shearthinning systems.
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Pharmaceutics II - Rheology
•
The rheograms obtained with thixotropic materials are:
- highly dependent on the rate at which shear is increased or
decreased
- the length of time a sample is subjected to any one rate of shear.
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Pharmaceutics II - Rheology
6.2 Measurement of thixotropy
•
Main characteristic of a thixotropic system is the hysteresis loop.
•
The area of hysteresis has been proposed as a measure of thixotropic
breakdown.
•
Two approaches:
- determine the structural breakdown with time at a constant rate of shear.
- determine the structural breakdown due to increasing shear rate.
•
Limitations:
- Does not taken into account the shape of the up- and down-curves. So
- Two different materials may produce loops of similar area but which have
completely different shapes representing totally different flow behaviour.
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Pharmaceutics II - Rheology
•
Rheogram of white soft paraffin
•
This is typical of a loop obtained with
some samples of white soft paraffin
where the up-curve exhibits a
number of bulges.
•
Lower shear rates
- the bulges are thought to be
associated with the initial loss of
3-D structure.
•
Higher shear rates
- the smoother deviations here are
associated with molecular
reorientation.
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Pharmaceutics II - Rheology
6.3
Rheopexy
•
This is a characteristic exhibited by some thixotropic systems.
•
A phenomenon where a sol forms a gel more readily when gently
shaken than when allowed to form the gel while the material is kept
at rest.
•
The rocking motion provides a mild turbulence which aids in
returning de-randomised particles to a random orientation.
•
The gel is the equilibrium form.
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6.4
Thixotropy in formulation
•
Thixotropy is a desirable property in liquid pharmaceutical systems
that ideally should have:
•
•
A high consistency in the container yet pour or spread easily.
e.g.
a well formulated suspension will not settle out readily in
the container
will become fluid on shaking and will remain so long enough
for a dose to be dispensed.
will regain consistency rapidly enough so as to maintain the
particles in a suspended state.
•
Also desirable with emulsions, lotions, creams, ointments and
parenteral suspensions to be used for intramuscular depot therapy.
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Pharmaceutics II - Rheology
6.5 Measuring Viscosity of Non-Newtonian systems
•
The instrument used must be able to operate at a variety of rates of
shear to obtain the complete rheogram.
•
The use of a one-point
instrument, even in
quality control in
industry, is erroneous
if the system is
non-Newtonian as the
flow properties could
vary significantly, but will
appear to be unchanged.
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Pharmaceutics II - Rheology
7 FLUID FLOW
7.1 Boundary Layers
Consider flow between two surfaces.
•
The rate of flow over an even surface will be dependent upon the
distance from the surface.
•
The velocity will be almost zero at the surface and increases
towards the middle where it becomes constant.
•
The region over which differences in velocity occur is called the
boundary layer.
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Pharmaceutics II - Rheology
•
Depth of the boundary layer is dependent
i.
ii.
viscosity of the fluid
rate of flow in the bulk fluid.
directly proportional
indirectly proportional
•
High viscosity and low flow rate will result in a thick boundary layer.
•
Boundary layers can never be eliminated entirely and represent an
important barrier to mass (and heat) transfer.
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Pharmaceutics II - Rheology
Streamline flow The 2 boundary layers meet at the centre of the tube,
resulting in a parabolic distribution.
Turbulent flow
There is movement at right angles to the direction of flow
promotes mixing
fluid layers tend to move at a more similar velocity
results in a rounded velocity profile.
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7.2 Reynolds’ Apparatus
Consider the flow of fluid through the system below.
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•
Low Velocity
Dye thread
Streamlined or Laminar Flow
•
Critical Velocity
•
High Velocity
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•
Reynolds found flow was affected by 4 factors
i. Density ( )
ii. Velocity (v)
iii. Diameter of pipe (d)
iv. Viscosity ( )
Re   vd / 
•
•
All measurable so can calculate Re.
If Re < 2000
streamline flow will occur
If Re > 4000
turbulent flow will occur
Distance Travelled after specific time
Re > 4000 (Turbulent)
High density
High velocity
High pipe dia.
Low viscosity
Re < 4000 (Streamlined)
Lower density
Lower velocity
Lower pipe dia.
Higher viscosity
Direction of Flow
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Ideal
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Pharmaceutics II - Rheology
Re   vd / 
•
If Re = 2000 to 4000 flow depends on nature of surface
- smooth, straight pipe - streamline flow at Re >> 2000
-rough, bends, joints and fittings – turbulent flow Re << 4000.
•
Important in fluid transfer during manufacturing processes e.g. piped
water and steam, filling processes, mixing processes.
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8. DETERMINATION OF RHEOLOGIC PROPERTIES
8.1 Why measure viscosity?
-Formulation development
Quantities of ingredients
Grades of ingredients
Formulation requirements
Production Methods - mixing rate
- temperature
Setting limits for production
- Production
Quality Assurance / Batch-to-batch
uniformity
? Production methods - variability
? Adjustments to formulation - thicken
? Quality of ingredients – natural
products vary
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•
Other rheologic properties:
tackiness or stickiness
"body”
"slip“
"spreadability"
•
Are difficult to measure by means of a conventional apparatus and
do not have precise meanings.
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8.2 Pharmaceutical Considerations and Applications
•
Problems in establishing meaningful shear rates
Viscosity requirements often emperical, however, researchers have
attempted to establish shear rates relating to the use of pharmaceuticals
e.g.
- topical application - 120 sec-1
- nasal spray in a plastic squeeze bottle - 1000 sec-1
- pouring from a bottle - below 100 sec-1.
•
However, think about the shear rate resulting from rubbing a cream into
the skin. This can range from 100 to 10 000 sec-1 depending on the
degree of rubbing. The shear rate for individual use by a process
therefore varies greatly.
•
Another example is squeezing a product from a collapsible container the shear rate depends on the squeezing force that the subject can exert
easily.
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Pharmaceutics II - Rheology
•
Visual perception
The importance of viscosity in visual perception must be considered
e.g.
cream to hold its shape in a jar
a lotion to pour
a toothpaste to retain its ribbon shape on a brush.
Here shear rate is determined by subjectively evaluating an
acceptable rate of deformation or flow under the constant stress of
gravity.
•
Ease of use
e.g. Toothpaste.
- After applying a rate of shear in squeezing the tube, the
toothpaste must flow onto the bristles.
- It must then recover its viscosity sufficiently to maintain its ribbon
shape on the brush.
- With shear, it must thin rapidly for ease in brushing.
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•
Topical preparations must meet certain criteria for:
Desirable pharmaceutical properties
feel, spreadability, colour, odour
Desirable pharmacological properties – drug release
•
Other psychologic and sensory characteristics e.g.
- Sensations in the mouth
- Between the fingers
- On the skin
are important considerations for manufacturers of cosmetic products
and dermatologic products.
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•
Cussler et al studied the texture of non-Newtonian liquids of widely
different rheologic properties applied to the skin.
Found that the consistency of the material could be accurately
assessed by a panel of untrained subjects by the use of only 3
attributes:
- thinness
- related to non-Newtonian viscous parameters
that could be measured with appropriate
instrumentation
- smoothness
- related to the coefficient of friction
- warmth
- complex concept that requires further study.
Only 1 of these can be reliably measured – the rest are largely
subjective.
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Pharmaceutics II - Rheology
•
It can therefore be seen why statement defining a suitable viscosity
for products are meaningless unless they are framed within a specific
judgement of use.
•
Product development
In product development it is vitally important that all trial formulations
be tested:
- against assumed stresses and shear rates likely to be experienced in
manufacturing, product movement, filling and use.
- These values must be calibrated, preferably with products
characteristically used and under the normal operating parameters
of that facility.
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