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Is the study of flow properties of material



The resistance of a fluid to flow when it is subjected to stress


It is important to understand rheology properties of material because they affect

It is important to understand the rheological properties of materials because they affect the following:

Efficiency of mixing
Flow through pipes
Ease of packaging into and removal from containers
Physical stability of preparation
Rate of drug absorption
Spreading and adherence of preparation to skin



Shear stress
Shear rate


Stress = F/A
Rate = dv/dr
dv= difference of velocity between two planes of liquid
dr= distance between two planes of liquid

Viscosity = stress / rate


Rate unit



Stress unit



Newtonian fluid
Properties and formula

F/A = n dv/dr

n = coefficient of viscosity
Shear rate is directly proportional to shear stress

The flow curve / rheogram
Shows a straight line passing thru origin

Newtonian fluid have Constant viscosity


Rheogram axis

Stress (y) against rate (x)
n= Gradient = viscosity

Rate (y) against stress (x)
n= 1 / gradient

n = dynamic viscosity


Example of Newtonian fluid

Organic solvent
True solution
DILUTE suspension and DILUTE emulsion


Non Newtonian fluid types and meaning

Do not follow Newtonian flow

1) plastic
2) pseudoplastic
3) dilatant


Bingham flow and associated particle

Plastic flow

 The material behaves as an elastic solid at low shear stress
 A certain shear stress equivalent to the yield value must be exerted before appreciable flow begins
 At shear stress above yield value, the material resembles a Newtonian system
 Materials exhibiting plastic flow are shear thinning.

U= (F-f) / G

U= plastic viscosity
F= shear stress
f= yield value
G= shear rate

Plastic flow is associated with the presence of flocculated particles in a concentrated suspension.


Pseudoplastic and associated particles

Pseudoplastic materials show shear-thinning properties

 The material will flow as soon as a shear stress is applied.
 Its viscosity decreases with increasing rate of shear.
 It is often noted that the flow curve tends towards linearity at higher shear stress
 The viscosity of a pseudoplastic material is best represented by the entire flow curve.

F^N = n'G

F= shear stress
N = index of pseudoplasticity (N>1)
n' = viscosity coefficient
G= shear rate

Log G = NlogF - log n'

 Pseudoplastic flow is associated with polymers in solution.

E.g. Aq dispersion of hyrdrocolloid such as tragacanth, alginates, methylcellulose and synthetic materials such as PVP (polyvinylpyrrolidone)


Dilatant material and associated particles

 Dilatant materials show shear-thickening properties
 The material will flow as soon as a shear stress is applied
 Its viscosity increases with increasing shear stress

Dilatant flow is associated with high concentration of deflocculated particles
Eg suspension with high concentration (>50%) of small deflocculated particles

Dilatant flow properties pose a problem in production.

F^N = n' G
N = <1


Explain shear thickening

Under zero shear the particles are closely pack and interparticulate voids are at a minimum, which the vehicle is sufficient to fill and at low Shear rate such as those created during pouring.

AS flow rate increases the particles become displaced from the uniform distribution and the clumps that are produced results in the creation of a larger void into which the vehicle drains, so that the resistance to flow is increase and viscosity rises.

The effect is progressive with increased shear rate until eventually the material may appear paste-like as flow ceases.

Removal of shear stress results in the reestablishment of the fluid nature


When a non Newtonian fluid is sheared, structural changes will occur in the system, resulting in changes in viscosity of the fluid.

The degree of change is dependent on

 When a non-Newtonian fluid is sheared, structural changes will occur in the system, resulting in changes in viscosity of the fluid.
 The degree of changes is dependent on :
1) Rate of shear
2) Duration of shear
3) Frequency of shear

 The structural changes may be reversible or irreversible


Why thixotropy occurs

When non Newtonian material is subjected to shear, structural changes occur and the viscosity changes.

Once the shear stress is removed, even if the breakdown of structure is reversible, it may not return to its original condition instantly (rheological ground state).

Thus When material subjected to increasing shear rate and then decreased to zero, the down curve will be displaced wrt the up curve and a hysteresis loop will be included.

The area of the loop may be used as an index of the degree of breakdown. (Extent of break down)


Up curve and down curve

Up curve is obtain from flow curve by increasing shear rate or stress

Down curve is from decreasing rate or stress


Characteristics of thixotropy

Shear thinning ( increase stress = viscosity decrease)

Slow recovery of the apparent viscosity on standing of the system. ( up and down curve is not superimposable)


Why thixotropy occur at molecular level

 Thixotropic systems are usually composed of asymmetrical particles or macromolecules that are capsule interacting by numerous secondary bond.

At rest, they produce a loose three-dimensional structure, so that the material is gel-like when unsheared.

On shearing, they become aligned and flow as the energy imparted during shearing disrupts the secondary bond thus viscosity decreased (sol-gel transformation)

Upon removal of shear stress, the system starts to reform (not immediate)

The recovery time may be reduced by applying a gentle rolling or rocking motion which helps in the reformation of the network (rheopexy) as this increases the rate of collision of particles allowing bond formation.

 Thixotropy is a desirable property in pharmaceutical suspensions and emulsions


Dynamic viscosity

Dyne. cm^-2. S

SI = Pa.S

Alternative: poise (P)
Centipoise cP
1cP = 1 mPa. S


Kinematic visosity unit

Cm^2. S^-1

SI: m^2. S^-1

Alternative: stoke (St)
Centistoke (cSt)
1cSt = 1mm^2. S^-1


Absolute viscosity (applies to Newtonian fluid only)?

Dyne. Cm^-2. S

SI: Pa. S

Alternative: poise


Apparent viscosity (non Newtonian fluid)

Dyne. Cm^-2. S

SI: Pa. S

Alternative: poise


Determination of rheological properties and the equipment required

 Proper choice of instrumental method is essential for meaningful assessment of rheological properties of fluids

Newtonian fluids
 Shear rate is directly proportional with shear stress
 A single point determination using a certain shear rate or stress is theoretically adequate.
"one point" instruments that operate at a single shear rate can be used.

E.g. Capillary viscometers.

Non-Newtonian fluids
 Shear rate is not directly proportional with shear stress
 “Multiple point” instruments that operate at a variety of shear rates are required to obtain a
complete rheogram
E.g. rotational viscometers


Types of capillaries viscometer

U tube viscometer
Suspended level viscometer


Types of rotational viscometer

Concentric cylinder viscometer
Cone and plate viscometer


Types of efflux viscometer

Redwood viscometer
Flow cups


Capillary viscometer eqn

n1/n2 = t1p1/ t2p2

P = density
T = time
n = dynamic viscosity

V = n / p

V = kinematic viscosity.

V1/v2= t1/t2


Capillary bore size for Ostwald viscometer

And requirement

U tube

Size A-H
H = biggest therefore faster flow time.

The appropriate size should be selected such that a flow time of at least 300s for Size A and at least 200s for all the other sizes obtained.


Ubbelohde viscometer

Suspended level
No need to fill viscometer with a precise volume.

9sizes (1, 1A, 2 , 2A, 3, 3A, 4, 4A, 5)
Increasing bore size.

The appropriate one should be selected such that a flow time of at least 300 s for size 1 and at least 200 s for all the other sizes is obtained