Rheology -II 24.pdf of physical pharmaceutics 2

Good you can refer it

1. RHEOLOGY -II
7/26/202
4

2. MEASUREMENT OF
VISCOSITY
27/26/202
4

3. DETERMINATION OF RHEOLOGIC (FLOW)
PROPERTIES
•Cup and bob
Eg:-Cone and plate
Principle
Viscosity det. at several
rates of shear to get
consistency curves
Application
Newtonian flow
Application
non -Newtonianflow
Selection of viscometer
Single point
viscometer
Eg;-Ostwald viscometer
Falling sphere viscometer
Principle
Stress α rate of shear
Equipment works at Single
rate of shear
Multi point
3

4. INSTRUMENTATION
“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.

5. SINGLE POINT VISCOMETERS
❑Ostwald viscometer (Capillary) The Ostwald viscometer
is used to determine the viscosity of Newtonian fluid.
❑Both dynamic and kinematic viscosities can be obtained.
❑ The viscosity of Newtonian fluid is determined by measuring
time required for the fluid to pass between two marks

6. OSTWALD VISCOMETER
7/26/202
4

7. •Principle: When a liquid flows by gravity, the time required for the
liquid to pass between two marks ( A & B) through the vertical
capillary tube.
•The time of flow of the liquid under test is compared with time
required for a liquid of known viscosity (Water).
•Therefore, the viscosity of unknown liquid (η
1) can be determined
by using following equation:

8. Where,
ρ
1 = density of unknown liquid
ρ
2 = density of known liquid
t1 = time of flow for unknown liquid t
2 = time
of flow for known liquid η
2
= viscosity of
known liquid
Eq. 1 is based on the Poiseuille’s law express the following relationship for the
flow of liquid through the capillary viscometer.
Where,
r = radius of inside capillary, t = time of flow,
Δ P = pressure head dyne/cm
2 ,
l = length of capillary cm, V = volume of liquid flowing, cm
3
η = П r
4 t Δ P / 8 l V
8

9. • For a given Ostwald viscometers, the r, V and l are combined into constant
(K),then eq. 2 can be written as
•In which, the pressure head ΔP ( shear stress) depends on the density of liquid
being measured, acceleration due to gravity (g) and difference in heights of
liquid arms of the viscometers.
• Acceleration of gravity is a constant, &
constant for all liquids.
the levels in capillary are kept
η = KtΔP

10. • If these constants are incorporate into the eq. 3 then, viscosity of
liquids may be expressed as:
On division of eq. 4 and 5 gives the eq .1,
which is given in the principle,
η1 = K’t
1 ρ
1
η2 = K’t2 ρ2
eq. 4
eq. 5

11. •Equation.6, may be used to determine the relative and
absolute viscosity of liquid.
•This viscometer, gives only mean value of viscosity because one value of
pressure head is possible.
•Ostwald not convenient for highly viscous ,because of difficulty in
filling viscous liquids and due to drainage errors.
•Suspended level viscometer is used for highly viscous fluid i.e.
Methyl cellulose dispersions
•Ostwald viscometer is used to determine the viscosity of a
Newtonian liquid. Both dynamic and kinematic viscosities can be
obtained.

12. PRACTICAL CONSIDERATIONS
R
e = VdǷ
dynamic viscosity
APPLICATIONS
1.Used for quality control purposes in the formulation
2. The study of flow of liquids through a capillary tube throw light upon
circulation of the blood

13. FALLING SPHERE VISCOMETERS
❖It is called as Hoeppler falling sphere viscometer.
Principle:
❖ A glass or steel ball is dropped into the liquid and allowed
to reach equilibrium with the temperature of the outer jacket
❖The rate at which the ball of particular density and diameter
function of viscosity of sample.
Construction:
❖Glass tube positioned vertically.
❖ Constant temperature jacket with provision for water
circulation is arranged around the glass tube

14. Working:
❑ A glass or steel ball is dropped into the liquid & allowed to reach
equilibrium with temperature of outer jacket.
❑ The tube with the jacket is then inverted which places the ball at the top of
the inner glass tube.
❑ The time taken for the ball to fall between two marks is measured, repeated
the process for several times to get concurrent results.
❑ For better results, a ball should be used such that ‘ t’ NLT 30 sec.
to fall between two marks.

15. Where,
t = time interval in sec. for ball to fall between two marks
S
b & S
f = Specific gravities of ball and fluid underexamination.
B = Constant for particular ball.
This instrument can be used in range of 0.5 to 200,000 poise.
η = t ( S
b – S
f ) B

16. INSTRUMENTATION
“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.

17. MULTI POINT VISCOMETERS
(ROTATIONAL)
Cup and Bob
•This is a multipoint viscometer and belongs to the
rotational viscometers.
category of
•The sample is placed in the cup and the bob is placed in the cup
up-to an appropriate height.
•The sample is accommodated between the gap of cup and bob.
•Cup or bob is made to rotate and the torque (shearing stress)
resulting from the viscous drag is measured by a spring or
sens
9o
/1/2r
023inthe drive of the bob. 17

18. ✓Couettetype viscometers: revolving cup type
❑Cup is rotated, the viscous drag on the bob due to sample causes to turn.
❑The torque is proportional to viscosity of sample.
Ex. MacMichael viscometer

19. ✓Searle type viscometers: Revolving bob type
Bob is rotated, the torque resulting from the viscous drag of the system
under examination is measured by spring or sensor in the drive to the
bobEx.Stormerviscometer,rotoviscometer cannotbeusedifviscosity
below20cp.-Brookfield–no.ofspindles/bobsofvariousgeometries-
pastesandsemisolid
Working:
❑ The test sample is place in space between cup and bob & allow to
reach temperature equilibrium.
❑ A weight is placed on hanger and record the timeto make 100
revolutions by bob, convert this data to rpm.Theweightisincreasedand
wholeprocedureisrepeated.

20. •This value represents the shear rate at one point of shearing stress.
•Same procedure is repeated by increasing weight.
•So then plotted the rheogram ,rpm Vs weights added.
• The rpm values can be converted to actual rates of shear and weights can be
converted into units of shear stress, dy/cm
2
by using appropriate constants.

21. Mathematical treatment: pseudoplastic flow
• For, rotational viscometers, the relationship can be expressed as,
η = K
v w/v
where
v, rpm generated by weight w, in gm
K
v is obtained by analyzing material of known viscosity in poise

22. PLUG FLOW
7/26/202
4
• One potential disadvantage of cup-and-bob viscometers is variable shear stress
across the sample between the bob and the cup.
• In contrast to Newtonian systems, the apparent viscosity of non-Newtonian
systems varies with shear stress.
• With plastic materials, the apparent viscosity below the yield value can be
regarded as infinite.
•Above the yield value, the system possesses a finite plastic viscosity.

23. • When the bob is made to rotate at relatively low rates of shear, the stress closer
to the rotating bob may be higher than the yield value.
•But the shear stress at the inner wall of the cup may be below the yield value.
• Material in this zone would therefore remain as a solid plug and the measured
viscosity would be in error.
• A major factor determining whether or not plug flow occurs is the gap
between the cup and the bob.
• The operator should always use the largest bob possible with a cup of a
definite circumference so as to reduce the gap and minimize the chances of
P
9/1
l
/2
u
023
g flow.
23

24. • In a system exhibiting plug flow in the viscometer, more and more of the
sample is sheared at a stress above the yield value as the speed of rotation of
the bob is increased.
• It is only when the shear stress at the wall of the cup exceeds the yield value,
however, that the system as a whole undergoes laminar, rather than plug, flow
and the correct plastic viscosity is obtained.
• The phenomenon of plug flow is important in the flow of pastes and
concentrated suspensions through an orifice (e.g., the extrusion of toothpaste
from a tube).
7/26/202
4

25. •High-shear conditions along the inner circumference of the tube aperture
cause a drop in consistency.
• This facilitates extrusion of the material in the core as a plug. This
phenomenon is, however, undesirable when attempting to obtain the
rheogram of a plastic system with a cup-and-bob viscometer.
•Cone-and-plate viscometers do not suffer from this drawback
7/26/202
4

26. ❑The phenomenon of plug flow can be minimized by
1.Using the largest bob possible in order to reduce the gap
2. Increasing the speed of rotation of the bob so that the stress at outer wall of
the cup is above the yield value and the system undergoes laminar flow.
7/26/202
4

27. CONE AND PLATE VISCOMETER
(ROTATIONAL VISCOMETER)
Example Ferranti Shirley
Principle:
❑ The sample is placed at the center of the plate, which
is then raised into a position under the cone.
❑ The cone is driven by a variable speed motor and
sample is sheared in the narrow gap between
stationary plate and rotating cone.
7/26/202
4

28. •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 (shearing stress)
may be plotted.
7/26/202
4

29. PHARMACEUTICALAPPLICATIONS
7/26/202
4
1.The viscosity of creams and lotions may affect the rate of absorption of the
products by the skin.
2.A greater release of active ingredients is generally possible from the softer,
less viscous bases.
3.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.

30. 4.The rate of absorption of an ordinary suspension differs from thixotropic
suspension.
7/26/202
4
5.Thixotropy is useful in the formulation of pharmaceutical suspensions and
emulsions. They must be poured easily from containers (low viscosity)

31. Viscosity for Newtonian system can be estimated by,
η = C.T/v eq.1
eq.2U = Cf.T – Tf / v
Yield value (f) = Cf × Tf
Tf = Torque at shearing stress axis (extrapolated from linear portion of the
curve)
f
C –instrumental constant
C = Instrument constant,
T = Torque reading
v = Speed of the cone (rpm)
Plastic viscosity determined by,
31

32. VISCOELASTICITY
7/26/202
4
•Viscoelasticity is the property of materials that exhibit both viscous and
elastic characteristics when undergoing deformation.
•Viscous materials, like honey, resist shear flow and strain linearly with
time when a stress is applied.
1.With cone-plate geometry the sample appears to ‘roll up’ and at high shear
rates and is ejected from the gap.
2.With concentric cylinder geometry, the sample will climb up the spindle of
the rotating inner cylinder (Weissenberg effect).