Medicine pharmacy health

1. Rheology

2. Outline
❑ Introduction
❑ Importance of Rheology
❑ Newtonian and Non-Newtonian Flow
❑ Flow characteristics of Newtonian Fluids
❑ Flow characteristics of Non-Newtonian materials
❑ Thixotropy
❑ Determination of viscosity
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3. Chapter Objectives
At the end of this lesson the students should be able to:
❑ Define rheology
❑ Understand Newton's law of flow
❑ Differentiate flow properties and corresponding rheogram
between Newtonian and Non-Newtonian materials
❑ Appreciate the fundamentals of determination of rheological
properties
❑ Recognize different factors affecting rheological properties of
materials
❑ Provide examples of fluid pharmaceutical products exhibiting
various rheological behaviors
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4. Introduction
❑ The term rheology (Greek words), rheo ‘to flow’ and logos
‘science or Study’.
➢ Hence simply rheology is the study of flow
❑ Rheology is defined as the science concerned with the flow
of matter under the influence of applied force or stress
❑ Redefined as the flow of fluids (liquids and gases) and the
deformation of solids in response to an applied force or
stress
➢ Deformation = change of matter in terms of shape and/or
volume
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5. Introduction…
The deformation of any pharmaceutical system can be
arbitrarily divided into two types:
❑ Elastic Deformation: it is a spontaneous and reversible
deformation
❑ Plastic deformation: it is a permanent or irreversible
deformation
➢ The plastic deformation: flow and exhibited by viscous bodies
➢ Great importance in any liquid dosage forms like suspensions,
solutions, emulsions etc
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6. Introduction…
❑ Ideal solids deform elastically
➢ hence the energy required for the deformation is fully
recovered when the stresses are removed
❑ Ideal fluids such as liquids and gases deform irreversibly (i.e.
they flow)
➢ hence the energy of deformation is dissipated within the fluid
(as heat form) and can’t be recovered simply by removing the
stresses
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7. Importance of rheology
❑ In liquid and semisolid DF:
➢ Pourability of liquid dosage forms
➢ Syringeability of injections
➢ Spreadability of creams and ointments
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❑ In mixing and flow of materials
❑ Packaging into containers
❑ Removal prior to use
❑ Acceptability to the patient
❑ Physical stability
❑ Biological availability
The product rheology
must be optimized: by
controlling the viscosity
of the product

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Rate of shear (G)
Shear stress (F)
Viscosity (ᶯ)
Three important rheological terms
Terms
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9. The force per unit area (F/A) needed to bring about flow is
known as the shearing stress, S
Shear stress (F or S) = F’/ A
The SI unit of: N . Sec/m2
Other unit F: dynes . Sec/cm2
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Shear stress (F)
Area
F’
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10. ❑ The phenomenon of viscosity is best understood by a
consideration of a hypothetical cube of fluid made up of
infinitely thin layers (laminae) which are able to slide over one
another like a pack of playing cards
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Rate of shear (G)
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Rate of shear (G)…
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12. ❑ When a tangential force (F) is applied to the uppermost
layer each subsequent layer will move at progressively
decreasing velocity
➢ This results in velocity gradient which is called shear rate (G),
❑ Hence rate of shear (dv/dx or G) is the difference in velocity
(dv) of two layers of a liquid separated by an infinitesimal
distance (dx).
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Rate of shear (G)…
Shear rate (G) = dv/ dx
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❑ The bottom layer is considered to be fixed in place b/c
➢ The adhesive force b/n the wall and the flowing layers
➢ Inter-molecular cohesive forces which is called viscosity

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Measure of the resistance of liquid
to deformation under shear stress
A fluid’s internal resistance to flow
and may be thought of as a measure
of fluid friction
The resistance offered when one part
of the liquid flows past another
Viscosity
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Viscosity

14. ❑ Newton recognized that: the higher the viscosity of a liquid,
the greater the F required to produce a certain G
❑ The F required for one layer of a liquid to slip past another
layer with a given G depends
➢ Directly on the viscosity of the liquid and on the areas of layers
exposed to each other and
➢ Inversely on the distance separating the two surfaces
❑ Viscosity fluid resists motion b/c its molecular makeup gives it a
lot of internal friction
❑ Inviscid fluid flows easily b/c its molecular makeup results in very
little friction when it is in motion.
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Newton law of flow
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1 poise is defined as the F required to produce a velocity difference of 1 cm/sec
b/n two parallel layers of liquids of 1cm2 area each separated by 1 cm distance
Newton law of flow…
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dr
dv
A
F

=
'
Shear
of
Rate
Stress
Shearing
G
F
dr
dv
A
F'
η =
=
=
Where  is a constant known as coefficient of viscosity/viscosity/
absolute viscosity, whose SI unit of measurement is N-s-m-2 Pa-s or
Kg (m-s)-1 – where 1 N-s-m-2 =1 Pa-s = 1 Kg (m-s)-1
❑ However the CGS system is commonly used: dynes-sec-cm-2
g(cm-s)-1 or poise: where 1dynes-s-cm-2 = 1 g(cm-s)-1 = 1 poise
NB: 1 N-sec-m-2 = 10 poise
Absolute viscosity
dr
dv
A
F

'
Thus, in Newtonian law G is  to the F

16. Classification of rheological systems
❑ Materials (particularly liquids and semisolids) are classified
into two general types depending on relation b/n F and G
(i.e. depending on their flow characteristics.)
➢ Newtonian systems
➢ Non-Newtonian systems
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17. Newtonian fluids
Newtonian liquids: are liquids that obey Newton’s law of flow
❑ The relation between F and G is linear
➢ i.e. regardless of the magnitude of the force (F) applied, the
viscosity (absolute viscosity) is constant:
❑ Newton’s equation for the flow of a liquid is
❑ Plot of shear stress Vs shear rate: the slope gives the
viscosity and The curve always passes through the origin
➢ The reciprocal of viscosity is called fluidity: 1/η = Slope
F = η * G
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18. Characteristics of Newtonian flow
❑ 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.
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19. Newtonian fluids…
❑ 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
Examples of Newtonian fluids include:
➢ Water , Air
➢ Glycerin and most mineral oil
➢ True solutions
➢ Very dilute suspension and emulsions
➢ Liquid paraffin
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20. Newtonian fluids: Kinematic Viscosity
❑ It is the preferred unit when the F and G of the fluid are
influenced by the density
❑ It is the absolute viscosity divided by the density of liquid at a
specified temperature
ρ
η
KV =
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❑ The SI unit of KV is m2/s however, the commonly used unit is
the CGS system known as Stoke (St) where:
1 St = 10-4 m2s-1 = 1 cm2s-1 =100 cSt = 100 mm2s-1
Eg. A 50% aqueous solution of glycerin has a viscosity of 54.4 cP
and density of 1.216 g/cc. What is the KV of the glycerin
solution?

21. ❑ This type of flow behavior is observed in liquids in which the
relationship between F and G is non-linear
❑ In other words, substances that fail to follow the
Newtonian equation of flow
❑ The viscosities of these fluids is not constant: vary with
shear rate
➢ Hence stating a single viscosity is misleading :
• Apparent viscosity
❑ Most liquids in pharmacy are non-Newtonian fluids
➢ Example: emulsions, creams, suspensions and ointments.
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Non-Newtonian fluids
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22. ❑ Based on the types of rheograms obtained, non-
Newtonian systems can be classified in to three classes:
➢ Plastic flow
➢ Pseudo-plastic flow
➢ Dilatant flow
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Non-Newtonian fluids…
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23. Plastic flow
❑ Describes a system in which no flow occurs until F reaches a
critical transition point called the yield value (f)
➢ Below yield value, the system acts like a solid (elastic body)
➢ In b/n 0 & f it shows non-linear relationship b/n F and G
➢ Above yield value the relationship becomes linear
❑ Application of F beyond yield value and removing it causes
permanent change in plastic materials
➢ Substances that exhibit plastic flow are called Bingham
bodies.
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24. Plastic flow…
The slope of the rheogram is
termed mobility, analogous to
fluidity in Newtonian systems
and its reciprocal is known as the
Plastic viscosity, U
G
f
F
U
−
=
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25. ❑ Extrapolations of the linear plot gives ‘x’ intersect: yield value
➢ This curve does not pass through the origin
➢ Intersects the shear stress axis at a particular point, yield value
➢ As the curve above yield value tends to be straight, the plastic flow
is similar to the Newtonian flow above yield value
❑ Examples:
– Flocculated suspensions
– Solid powder materials
– Topical ointments
– Pastes (tooth pastes)
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Plastic flow…
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26. Flocculated Suspension: Mechanism of Plastic Flow
❑ The yield value represents the stress required to break the inter-
particular contacts so that particles behave individually
❑ Thus it is indicative of the forces of flocculation
• increased by the increased concentration of the dispersed phase
Shear
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 Flocculated particles in a concentrated suspensions usually show
plastic flow.
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Plastic flow…
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❑ The yield value of creams and ointments is the force required to
spread the substance on the skin surface
❑ Yield value of powders is the minimum force to compress it into
tablet
❑ Powders with low yield value compressed at low force and are
generally used as binders.
Plastic flow…
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29. Pseudo-plastic Flow (shear-thinning)
❑ In shear-thinning system the viscosity decreases with an
increasing shear force
❑ F is inversely proportional to viscosity thus they referred as
shear thinning systems
➢ Increase in F, increases G due to decrease in viscosity
❑ Pseudo plastic flow is exhibited by polymer dispersions like:
➢ Tragacanth in water
➢ Sodium alginate in water
➢ Methyl cellulose in water
➢ Sodium carboxy methyl cellulose in water
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30. Pseudo-plastic Flow…
❑ The viscosity of a pseudo-plastic
substance decreases with
increasing G (shear-thinning
systems)
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A
B
A < B
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31. Why do Pseudo-plastic systems become thinner with force
❑ At rest, the linear polymers with in the solution become
coiled up in their globular form: gel state
❑ When shear stress is applied, the polymer chains untangle
❑ With increasing F or agitation, the polymers align them
selves in the direction of flow
❑ This decreases internal resistance which in turn decreases
viscosity.
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32. Pseudo-plastic Flow…
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Pseudo-plastic Flow…
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Pseudo-plastic Flow…
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34. ❑ Useful for suspensions
❑ High viscosity at rest prevents particle sedimentation and
aggregating: improve stability of suspensions
❑ Suspensions flow smoothly out of a bottle: easy to administer
correct doses to the patients
❑ Syringeability of suspensions: as suspensions pass through the
needle it undergoes high shear stress as A is very small
❑ So, easier to push through the needle so more comfortable for
the patients.
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Why is shear thinning useful?
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35. Dilatant Flow
❑ Increased viscosity with increased shear stress that is they
thicken when shaken hence shear thickening systems
❑ F is directly proportional with viscosity and Increase in F,
decreases G due to increase in viscosity
❑ This systems are called dilatant because they also increase in
volume with agitation
➢ Example: deflocculated suspensions (>50% of solids)
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A
B
A > B

36. ❑ At rest, the particles are closely packed with a minimum inter-
particle volume, or voids
❑ The vehicle is sufficient to fill this volume
❑ As the shear stress is increased, the bulk of the system expands
or dilates: the particles become open packed
❑ Increase in the inter-particle void volume then system becomes firm
structure
❑ Vehicle become insufficient to fill the increased voids
❑ The resistance to flow increases: This process is reversible
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Why does these systems dilate?
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Dilatant Flow…
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❑ Dilatant flow is problematic during manufacturing of the
dosage form as well as administering to the patients
❑ A dilatant system pushed through the barrel of an injection and
the needle will thicken with F, making it hard to push through
❑ Cause injury and pain to the patients
Is Dilatant Flow useful?
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39. Summary of flows
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40. Thixotropy
❑ When Newtonian systems are left to rest they will revert
back to their original form
❑ This reversal to the original state takes the same path as
they were under stress – the only change being the direction
➢ They have identical down and up wards curve
➢ Their viscosity is constant on the down and upward curve
❑ Similarly, non-Newtonian systems, when left to rest, slowly
revert back to their original state, however, they don’t have
identical downward curves
❑ This phenomenon is known as Thixotropy
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41. 27-Jul-22 41
❑ Thixotropy is the decrease in viscosity as a function of time
upon shearing, and recovery of original viscosity as a
function of time without shearing.
➢ It is a slow isothermal reversible conversion of gel to sol
❑ It is also defined as a progressive decrease in viscosity with
time for a constant applied shear stress, followed by a
gradual recovery when the stress is removed
❑ It is characteristics feature of psudo-platic flow usually
composed of asymmetric particles or macromolecules
➢ capable of produce a loose 3D structure interacting by
numerous secondary bonds
Thixotropy…
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42. ❑ When stress is applied the 3D structure is broken down turning
the gel into solution that gives viscosity.
❑ When the applied stress is removed, it takes longer for the 3D
structure to reform than it takes to break down
❑ Finally the material reform its original structure of state: Gel
Gel
Solution
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Thixotropy…
42

43. ❑ Rheogram of thixotropy materials depends on
➢ Applied shear rate or shearing force
➢ Kinematic history: the duration /time of shearing
➢ The previous history of the sample has significant effect on the
rheologic properties of a thixotropic system
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Rheogram of Thixotropy flow
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❑ Rheogram of thixotropy materials show a
hysteresis where, as the F is increased an
up-curve is obtained, on reducing the F
gradually, a down curve shifted to the left
side is obtain

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❑The area of hysteresis loop tells the time taken for the
product to settle down after the force is removed
❑The smaller the area, the shorter for the suspension to
settle down and form a gel
❑Example: high M.Wt products take longer time because
their hysteresis loop area is larger as compared to low
M.Wt products
The importance of hysteresis loop?
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45. ❑ It is useful for suspensions and creams;
➢ Thinspread up on application of F
➢ For pharmaceutical suspensions, it is desirable that on shaking
(high shear stress), the suspension should pour (or flow) easily
from its container and on standing, its viscosity rises to
prevent (or slow down) settling.
❑ For intramuscular depot injections
➢ High F in the needle: allows easy administration
➢ At rest in the muscle: viscous gel is formed which can release
the drug slowly over longer period of time
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When is Thixotropy useful?
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46. Anti/Negative thixotropic
❑ When dilatant system are recovered from the applied stress,
the curve is displaced to the right
❑ However, antithixotropic systems should not be confused with
dilatancy
❑ Antithixotropic systems have low solid content (1-10%) and
their equilibrium state is a solution.
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❑ Antithixotropy => increased collision
of dispersed particles => increased
interparticle bonding
❑ Resulting in small numbers of
relatively large floccules which at rest
break up and gradually return to their
original state.

47. Irreversible Thixotropy (shear destruction)
❑ For an irreversible thixotropy the application of stress
causes breakdown of structure within the system but
➢ The structure does not reform on removal of the F, or
➢ The time lag is so long that from a practical point of view the
effect is irreversible
❑ Example: gels produced from higher M.Wt polysaccharides and
yoghurt
➢ On application of high shear,
– The 3D structure of the polysaccharides is disrupted and
the original gel-like structure is never recovered
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48. Measurement of Viscosity
❑ Different viscometers are used to measure viscosity of different
fluids and semisolids
❑ Successful determination of viscosity depends on the choice of
the correct instrument
➢ For a Newtonian system;
• Instruments that operate at a single rate of shear such as
capillary viscometers can be used
➢ For non-Newtonian systems
• Multi-point instruments that can operate at different
rates of shear are required
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49. Ostwald Viscometer
❑ It is a type of capillary viscometer which is used to determine
the viscosity of Newtonian liquids
❑ This is a ‘U’ shaped tube with two bulbs and two marks (upper
and lower).
❑ The device is used to determine the time required for a liquid to
pass b/n two marks through a vertical capillary tube due to
gravity.
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❑ The time of flow of the liquid under test is
then compared with a liquid of known
viscosity (usually water)
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2
2
2
1
1
1 



t
t
=
ρ1= Density of unknown liquid t 1= Time of the unknown liquid

50. The time of flow between marks on an Ostwald viscometer using
water (ρ= 1) was 120 seconds at 20°C. The time for a liquid (ρ=
1.05) to flow through the same viscometer was 230 seconds.
What is the viscosity of the liquid?
(Viscosity of water is 1 centipoise at 20°C )
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Ostwald Visco...
Exercise

51. Falling Sphere Viscometer
❑ Consists of a ball, generally made of steel, that is allowed to fall
through a liquid filled cylindrical transparent tube having
graduation marks.
❑ The tube is filled with the liquid whose viscosity is to be
determined
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52. Falling Sphere Viscometer…
❑ The velocity of the falling ball is measured and viscosity is
calculated using stoke’s law
where d= diameter of the ball; ρ s and ρ l are density of the ball and
the liquid; g= Gravitational acceleration; and V= velocity of the ball
❑ As d2g/18 is constant, can be replaced by another constant ‘K'
Therefore, the equation will be
V
g
d l
s
18
)
(
2



−
=
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V
K l
s )
( 


−
=
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53. ❑ The basic RV test measures the torque required to maintain a
constant rotational speed of a cylindrical spindle while
submerged in test fluid at a constant temperature
❑ This torque is converted to a dynamic viscosity and displayed
automatically by the RV
❑ Viscosity is determined by measuring the resistance of a
spindle rotating in the sample.
❑ RV can be used for the accurate Measurement of Viscosity for
both Newtonian and non-Newtonian fluids
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Rotational Viscometer

54. Factors affecting rheological properties
Chemical factors
Extent of Hydration
❑ Molecules of hydrophilic polymer in solution are completely
surrounded by immobilized water molecules forming a
solvent layer
➢ Such hydration gives rise to an increased viscosity.
Impurities, Trace Ions and Electrolytes
❑ Chemical impurities are the major factors in changing the
viscosity of natural polymers
❑ At high conc. they compete for adsorbed water molecules
surrounding the polymer and dehydrate it. Hence,
➢ viscosity of the dispersion decreased and precipitation
occurs.
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55. Factors affecting rheological…
Physical factors
Temperature
❑ A temperature increase usually produces a rapid viscosity
decrease
❑ Prolonged heating may produce drastic decrease in viscosity
due to decomposition of the polymer, e.g., gelatin
Concentration
❑ In concentrated suspensions: a decrease in particle size or an
increase in the surface area of the solid phase produce an
increase in the viscosity of the system.
➢ This due to immobilization of the vehicle with an increase in
the fraction of the suspension volume occupied by the solid.
Shear stress/ shear rate and Shear time??
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Factors affecting rheological…
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