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# rheology class

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```									   In 1948, term Rheology was suggested by Bingham and Crawford,
and it describes branch of science which deals with deformation and
flow of mater.
Rhe/ology (Greek)

To flow        Science

   Viscosity (: it is an expression of resistance of fluid to flow, that
means with high resistance to flow the viscosity is high and vice
versa.
   Rheology affects in the following pharmaceutical issues
1. Mixing and preparation of dosage forms
2. Packaging in containers
3. Removal prior to use including pouring from bottle, extrusion
from tube, and passage through the needle
4. Physical stability
5. Patients acceptability
6. Biological availability (↔ absorption rate from GIT)

   Rheology of material is described by 3 parameters
A. Stress
B. Strain
C. Time

A. Shearing stress

    Block of liquid consist of parallel of
molecules like cards
    Representation of the shearing stress =
F/A= force per unit area required to
cause flow
    Shearing stress unit

System SI unit             Cgs system
Unit   Pascal, pa          Dynes/ cm2

Note that 1 pa = 10 dynes/ cm2

1
Exercise: 1 gm weight is hung from rubber band with cross sectional are
of 0.049 cm 2. Find the stress on the rubber band?

S = F/ A= weight X g (acceleration due to the gravity) / A

= [1 gm X 980.7 cm / sec 2] / 0.049 cm 2

= 1 x 10 4 dynes/ cm 2 = 1000 pa = 1 kpa                      Dynes = gm. cm/ sec 2

B. Strain

   Strain: deformation of a body in response to a stress
   Type of strain
A. Elongation and compression strain = Δ L Change in length / original length

B. Shear strain= rate of shear= velocity of gradient (liquid)

   Rate of shear

dv
V4
V3
dr
V2
V0
V1

o Bottom layer is stationary layer
o Each layer moves with velocity directly proportional to the distance
from stationary layer
o Velocity gradient = dv/ dr
= difference of velocity between two planes of liquid
distance

Unit of rate of shear is Sec –1

2
C. Time

   Time effects on the rheology of some materials (time dependent)
   Basically is the length of time that material subjected to stress
   It will be discussed fully in one the flowing lectures

Elasticity and viscosity

   Elasticity: it is the ability of material to restore to its original shape
upon releasing of stress
   Young’s Modulus defines the elasticity (E) as follows:

S, shearing stress              F/A          Pa or dynes/ cm2
E   =                                  =             =                      = Pa or dynes/ cm2
Elongation or compression         Δ L       No unit

Newton theory

   Newton establish the following relationship:
1. With higher viscosity, the greater was the force required to
cause liquid to flow.

                  Higher shearing stress

2. Shearing stress rate of shear
S or F  G

   Newton introduced as constant and the equation became
F  G
F=G               Viscosity = shearing stress / rate of shear
F/G
3
F/G      = [Dyne/ cm 2 ] / sec -1 = [(gm.cm/Sec 2)/ cm 2 ] / Sec -1

gm/Sec. cm

   Unite of viscosity

SI unit       Pascal-sec “ pa-sec”

Cgs unit      Poise “ p”

 Note that 1 pa-sec = 10 poise = 10 dyne. Sec/ cm
 Centipoises “ cp”= 0.01 poise

Fluidity

Fluidity = = 1/ the opposite of viscosity)

Example of viscosity of some liquid, at temperature 20 0C

Liquid      p)
Water            0.01
Ethanol          0.012
Benzene          0.0065
Glycerin         15
Caster oil       10.3

4
Viscosity expression

1. Kinematic viscosity: this expression is used in the U.S. Pharmacopoeia.
Kinematic viscosity is defined as absolute viscosity-divided by the
density of liquid at a definite temperature:

Kinematic viscosity = / 

Unit of the kinematic viscosity = [gm. Sec/ cm 2 ]/ [gm/cm3]
= cm 2 /sec (SI unit)
= m 2/ sec (Cgs system)

Usually it is expressed as Stoke “s” = 10 –4 m 2 / sec or as centistokes
“cs”= 10 –6 m 2/ sec.

2. Relative viscosity: r: it is defined as the ratio of the viscosity of the
solution to that of the solvent.

Relative viscosity = r o

It should be noted that relative viscosity has no unit.

3. Specific viscosity: this term is defined as the relative increase in viscosity
of the solution over that of solvent alone. Note that sp has no unit.

Specific viscosity= sp =  - o =  o]-1 = r –1

Specific viscosity can be used to determine the volume of a molecule in
solution based on the following equation

sp = [2.5 C. N.V]/ M          C = concentration
V= volume of the molecule
M = molecular mass

5
4. Reduced viscosity: (number viscosity) it is can be obtained through
dividing the specific viscosity by concentration.

Reduced viscosity= sp / C

5. Intrinsic viscosity: (limited viscosity number): when reduced viscosity is
determined at various concentration and results are plotted as shown in
the following figure, the resulting line can be extrapolated to c = 0 to
obtain the intercept ( the intercept is known as the intrinsic viscosity
and is given the symbol [ its unit = ml/ gm
Reduced viscosity sp/ C

 intrinsic viscosity

Concentration gm/ dl

The Intrinsic viscosity is an important quantity in polymer science for it is
used to obtain the average molecular weight of high polymer science.
Determination of the approximate molecular mass of polymer can be
obtained using “ Mark- Houwink equation”:

[M

[intrinsic viscosity

M= molecular weight

K and  = constant can be obtained at given
temperature for specific polymer-solvent
system


6
Temperature dependence and the theory of viscosity

 The viscosity of gases increases with temperature.
 The viscosity of liquids decreases with temperature, while the fluidity of
liquids increases with temperature.
 The relation between viscosity and temperature is found by Arrhenius
and can be expressed by the following equation “Arrhenius equation”

A e Ev/RT
viscosity
A= arrhenius factor, constant depend on
molecular weight and molar volume of
liquid
Ev= activation energy that required to initiate flow
between molecules
R= gas constant “1.987”

R
Ev/
pe =
TR
TR
+ A nl nl
+ A nl nl                               Slo
ln 

vE
vE

Intercept = ln A

1/T

 The explanation of effect of raising the temperature on lowering the
viscosity of liquids is that braking down the bonds between liquids
molecules happens with raising the temperature resulting in less resistant
to flow (↓ 
 An example of effect of temperature on the viscosity:

Temperature               20 o C         50 o C                 99 o C
Viscosity of water        0.01 p        0.0055 p               0.0028 p

7
Newtonian and Non-Newtonian systems

 Fluids have been classified into two types of systems that described
the viscosity behaviors of the fluids. This classification is based on the
obedience of the Newtonian’s law.

Newtonian fluids                                                     Newtonian fluids
 Doesn’t obey Newtonian’s law
                        Obey Newtonian’s law                                                      dependent on the rate of shear
                         F/G                                                                   Examples are suspensions and
                        Examples are water and milk                                               ointments
                        Linear relationship between shear                                        Dependant on time
stress and rate of shear                                                 Classified into
1- Plastic
2-Pseudo-plastic
Rate of shear, G
Shearing stress, F


e=                                                                 3-Dilatant
op                                          pe=
Sl                                          Slo

Rate of shear, G                              Shearing stress, F

 It is not dependant on arte of shear



Rate of shear

 It is not dependant on time



Time

 It is dependant on temperature

8
Non-Newtonian systems

Most of the pharmaceutical products are considered Non-Newtonian
systems. In the following sections those types will be discussed.

A- Plastic Flow

      It is called Bingham bodies, the following graph describes the
viscosity of plastic material:
Rate of shear

fB = yield value

Shearing stress

 As you noted that the line doesn’t pass through (0,0)
 Under the yield value substance behaves as a solid “ elastic material”.
Increase in F accompanied with no change in rate of shear. It doesn’t
flow until exceed this value (fB).
 U= plastic viscosity = [F- fB]/ G
 Above the yield value, fB, plastic system resembles Newtonian system
 U= plastic viscosity = 1/slope = 1/ 
 An example of plastic flow is flocculated particles in concentrated
suspension. As you see in the flowing graph, we need the yield value
(stress) to brake down the bond “ vander waals forces” between
suspended particles
F and G is still zero

Like Newtonian


Rate of shear, G
9
B-Pseudoplastic Flow

 It is called shear thinning fluids
 Examples of pharmaceutical products that exhibit psuedoplastic flow
are natural and synthetic gum (tragacanth, sodium alginate,
methylcellulose). Another examples are paint and shampoo.
 Psuedoplastic flow is exhibited by polymers in solution, in contrast to
plastic systems, which are composed of flocculated particles in
suspension.
 The following graph describes the flow behavior of pseudoplastic
material.
G

F

 No yield value, it starts to flow with beginning of applying the stress
 The curve is not linear in any part
 Viscosity can’t be expressed by single value, therefore, you can

1
G


slope of the tangent to
the specific curve at
F              specified point

 ↑ rate of shear = ↓





F
10
An explanation of psudoplastic flow behavior: (suspending agent like
gelatin)

A                                                 B

H2O            H2O
H2O
Shear
H2O                                                     H2O
H2O

H2O
H2O                                                               H2O

A- At rest the molecules (long chain molecules) lie in random
arrangement, intertwined and bound to the solvent molecules
resulting in high resistant (↑
B- Under shear the molecules align and squeeze out the bound
water molecules (associated water molecules). The viscosity of
the system consequently decreases proportional to the increase
in rate of shear.

C-Dilatant Flow

 The flow properties is inverse to that of pseudoplastic
 It is called shear thickening, the fluids exhibit an increase in
resistance to flow with increasing rates of shear.
 An Example of this type is suspension with high percentage of
dispersed solids (50%), like “ Ketchup” that is a high concentrated
starch suspension.
 The flow properties are illustrated in the following graphs:

11
increases with raising the shear

G                                   

F                                    G
 An explanation of dilatancy:

Increasing

Rate of shear

 Particles deflocculated                     Expansion, open packed (dilated)
 Close packed particles                       particles
 Volume of the voids is small                Increase inter-particle void volume
and the vehicle is sufficient               Insufficient vehicle to fill the increase
to wet the particle                          in voids
 Relatively low viscosity                    Increase in due to the particles no
longer wetted or lubricated by liquid

Note that with high rate of shear, the viscosity increases and this considers
disadvantageous in manufacturing. Dilatant materials may solidify under
high shear conditions, therefore, it could damage the processing equipment
(mill).

12
Time dependent behavior

 Newtonian systems are time independent. The viscosity of fluid will
not vary with shear rate and it is independent on the of length time
that the shear rate is applied. Also, replication of the same shear rate
will get the same viscosity.
 Non-newtonian systems are time dependent meaning that the viscosity
changing based on the length of the time that shear is applied and
history of the fluid.
 The following figures illustrate the effect of time on viscosity:

e
urv
w n-c                    Newtonian system: it is time independent
do                         meaning through out the up-curve and
G                                             down curve the viscosity is the same
rve           The curves are
-cu
up                  superimposed

F

Pseudo-plastic             Plastic                Dilatant

G

F

    Non-Newtonian system is time dependent
    In pseudo-plastic and plastic fluids the viscosity is lower in down
curve that up-curve
    In dilatant fluids the viscosity is higher in down curve than up-
curve
    Incase of plastic and pseudo-plastic fluids, after applying a
certain level of shear and removing this shear…particles don’t
reform immediately (meaning stay in low viscosity status due to
breakdown in the structure)

It is called Thixotrpy
13
Thixotropy                                 Rheopectic

 It means “ to change by touch”                      Viscosity increases with time
 Definition: it isothermal and comparatively slow    In dilatant fluids
recovery or standing of a material of a             It happens rarely
consistency lost through shearing
 Formally: applied for pseudoplastic
 Commonly: named for plastic and pseudoplastic
fluids

Thixotropy in formulation:


With shear                        1. Pour or spread easily
2. Accurate of dosing
3. In storage, lo settle (↑

↑                           ↓

 Desirable: in suspension, emulsions, lotions, creams and ointments
 Greater thixotropy: low rate of settling suspension
 Examples: 40-70% w/v procaine suspension in water

Measurement of Thixotropy:

 Quantitative measurement can be done in the following way:
1. Determine structure breakdown with time at constant shear
2. Determine structure breakdown due to raising in shear rate

14
A-Determine structure breakdown with time at constant shear

t2
 t1
d         c      b
1/U2

G                                   1/U1
e

a

F
 Shear rate after reaching point a, has been held constant for t1 and t2
 Viscosity = 1/slope
rate of breakdown                 = (U1-U2)/ ln (t2/t1)
   B=       with time and constant
shear rate

B-Determine structure breakdown due to raising in shear rate

1/U2

V2

V1
G
1/U1

F

       M= Thixotropic coefficient = (U1-U2)/ ln ( V2/V2)
       Measure the loss in shearing stress per unit in increase in shearing
rate. Unit is dyne. Sec/ cm 2
       V1 and V2 are the maximum rate of shear

15
Viscosity measurement

 Newtonian system  Rate of shear (G) directly proportional to shearing
stress (F)

 “one point” instrument can be operated at single rate
of shear

 Non-Newtonian system  “multipoint” instrument can be operated at a
variety of rates of shear and shearing stress

1. Capillary viscometer: = ostwald viscometer

Use for Newtonian systems

 Measure the time required for liquid to
pass between two marks and compare this
time to standard solution
 u/ s = (p 1 t1)/ (p2 t2)
 rel = u/ s
 t…time, p ..density, and …. viscosity
 1…unknown and 2… standard solution

Example: assume that time required for acetone to flow
between the two marks on the capillary viscometer is 45
sec , and for water the time was 100 Sec at 25 oC. The
density of acetone is 0.786 g/cm3 and that of water is
0.997 g/cm2 at 25 o C. the viscosity of water is 0.8904
centipoise at this temperature. Find the viscosity of
acetone at 25 oC.

u/ s = (p 1 t1)/ (p2 t2)

u/ 0.8904 = (0.786 x 45)/ (0.997 x 100)

u = 0.316 cp

16
2. Falling sphere viscometer:

 This type of viscometer uses for Newtonian systems
 Can measure wide range of viscosity “0.5-200,000 poise”
 Record the time interval that a specific ball falls between two
marks
 Viscosity can be calculated from

t (Sb- Sf) B

viscosity

t= time interval (Sec)

Sb= Specific gravity of ball

Sf= specific gravity of liquid

B= constant is provided by
manufacture for the balls

17

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