Rheology

Dr. Sagar N Firke
Dept. of Pharmaceutics
Nanded Pharmacy College, Nanded

 Introduction
 Definition
 Importance
 Newton's laws
 Types of flow
 Viscosity
 Measurements of viscosity
 Thixotropy
 Pharmaceutical applications

 Definition: “Rheology, defines as science of flow of
fluids and deformation of solids under the stress”
‘rheo’ – to flow
‘logos’– science
 Study of flow properties of liquids is important for
simple liquids, gels, ointments, creams, and pastes
etc.
 These systems change their flow behavior when
exposed to different stress conditions.

Manufacturing of Dosage Forms
 Formulation of medicinal and cosmetic creams, pastes
and lotions.
 Formulation of emulsions, suspensions, suppositories,
and tablet coating.
Handling of Dosage Forms
 Fluidity of solutions for injection (Syringability).
 In mixing and flow of materials, their packaging into the
containers.
 Pouring from the bottle.
 Extrusion of a paste from a tube.

 Flow of liquids’ can be expressed by viscosity
 Viscosity is an index of resistance to flow of fluid.
 Newtonian Systems
 Consider ‘block’ of a liquid consist of layers of liquid
molecules arranged one above another and each layer is
separated by distance ‘dr’
 When the shear stress is applied to the upper layer, it
moves with a certain velocity ‘dv’
 Movement of the upper layer will induces the movement in
subsequent layers.

Fig 01: Representation of shearing force required to produce velocity
gradient between parallel planes of the block

 Velocity difference ‘dv’ between two planes of liquid
separated by infinite distance ‘dr’ is the called velocity
gradient or rate of shear, dv/dr.( Denoted by G)
 Force per unit are required to produce shear rate is
called as shear stress, F’/A.( Denoted by F)
 Higher the viscosity of liquid greater the shear stress
required to produce certain rate of shear.
Sr No Liquid Viscosity cp
01 Castor Oil 1000
02 Ethyl Alcohol 1.19
03 Water 1.0019
Table 01: Absolute viscosities of Newtonian liquids at 20O C

F’/A = η dv/dr OR
F = η G
η= F/G
Where, η = Coefficient of Viscosity ( Simple Viscosity)
Fig 02: Representation of Flow Curve of Newtonian Fluids

 The Unit of Viscosity is Poise, “which is force required to
produce velocity of 1cm /sec between two planes each of
1cm2 and separated by distance by 1cm ”
More convenient unit we use is Centipoise (cp)
1 cp =0.01 Poise
Reciprocal of viscosity is called as fluidity Ø =1/ η

 Kinematic Viscosity = η/ρ ( Centistocke)
 Relative Viscosity , ηr = η/ ηo
 Specific Viscosity, η= η- ηo / ηo
 Factors Influencing Viscosity
 Intrinsic factors: Molecular size, molecular weight,
intermolecular forces.
 Extrinsic factors: Pressure, Temperature
η = Ae Ev/RT

 “The systems which does not obey Newton’s equation of flow
called as Non-Newtonian systems/flow”
 When Non-Newtonian materials are analyzed in rotational
viscometers & results are plotted different consistency curves are
obtained.
These are,
1. Plastic Flow
2. Pseudoplastic Flow
3. Dilatant Flow
Examples: Butter, gums tragacanth, suspensions etc.

 Plastic flow:
 These substances initially behaves like elastic body and fails
to flow upon stress is exerted.
 Further increase in shear stress leads to nonlinear increase in
rate of shear which progressively get linearised.
Fig03: Mechanistic explanation of behaviour of plastic flow
U= plastic viscosity
F= shear stress
f = Yield value
G= rate of shear stress

 Pseudoplastic Flow
 As shear stress increases progressively, shear rate also
increases, but trend is not linear.
 Therefore the viscosity of Pseudoplastic system cannot be
expressed by a single value.
 Examples: Tragacanth in water, Sod.CMC in water etc.
Fig04: Mechanistic explanation of behaviour of Pseudoplastic flow

 Under normal condition the long chain molecules of
polymers are randomly arranged in dispersion.
 On applying a shear stress, these molecules begins to arrange
their long axes in direction of force applied.
 This stress induced orientation reduces the internal resistance
of the material.
 Thus the effective concentration and size of molecules
decreases.
Fig 05: Mechanism of Pseudoplastic behaviour

 Dilatant Flow
 The system exhibit increase in resistance to flow with
increasing shear stress.
 Upon shearing such systems increase their volume and
hence called as ‘Dilatant’ or ‘Shear thickening’ system.
 Examples: Suspension containing high solid contents
(> 50%), suspension of starch in water.
Fig 07: Mechanism of Dilatant behaviour
Fig 06: Consistency Curve of Dilatant system

Viscometers
Single Point
Ostwald Viscometer,
Falling Sphere viscometer
Newtonian Fluids
Multipoint
Cup & Bob viscometer,
Cone & plate viscometer
Non-Newtonian Fluids

 Capillary Viscometer
 When liquid flow by gravity , the time required to for the liquid
to pass between two marks (A & B) through vertical capillary is
determined.
 The viscosity can be determined by
η1 = ρ1 t1/ ρ2 t2 x η2
Where, ρ1 = density of unknown liquid
ρ2 = density of known liquid
t1= time of flow of unknown liquid
t2= time of flow of known liquid

 Above equation is derived from Pioseulle’s Equation
Where, η = Viscosity of the liquid, Poise
p= Pressure head in the capillary, dy/cm2
r= radius of the capillary
T= time of the flow, sec
L= length of the capillary, cm
V= volume of the liquid flowing through capillary, ml
Fig 08: Ostwald Viscometer

 Ordinarily, the viscosity of a liquid is determined with
respect to that of water.
 Let t1 and t2 be the times of flow of a fixed volume (V)
of the two liquids through the same capillary.
 The expression for relative viscosity ( η1 / η2 ) can be
derived from equation given below.
Since the pressure-head is proportional to density (d) of the
liquid, hence equation may :

 The Apparatus consist of glass tube positioned vertically.
 A constant temperature jacket for water circulation
around glass tube.
 The test liquid is placed in the glass chamber.
 A glass or steel ball is dropped into the liquid & allow it
to reach equilibrium with temperature of jacket.
 The tube with the jacket is then inverted which place the
ball at the top.
 The time taken for the ball to fall between two marks
(A & B) is accurately measured.

Fig 09: Falling Sphere Viscometer
η1 = t ( Sb –Sf) B
t= Time interval in second
Sb= Specific gravity of ball & fluid
B = Ball constant value supplied by manufacturer

 This viscometer belongs to category of rotational viscometer.
 In this sample is sheared in the space between outer wall of the bob
and inner wall of the cup.
 Principle: The sample is placed in the cup & the bob is placed in the
cup up to an appropriate height.
 The sample is accommodate between the gap of cup & bob.
 Either Cup or bob is allowed to rotate& the torque resulting from the
viscous drag is measured by sensor.
 A weight is placed on the hanger and time taken for the bob to rotate
100 times is recorded.
 The data is then converted to RPM, this value represents rate of shear
at one point.

 The number of revolutions (RPM) and torque represents the rate
of shear and shearing stress respectively1
η = kv
w/ v
W = Weight placed on hanger, shearing stress
V = RPM, shear rate
Kv = constant for the instrument

Fig 10: Cup & Bob Viscometer

 The sample is placed at the centre of the plate.
 The cone is driven by variable speed motor and sample is
sheared in the narrow gap between the stationary plate and
rotating cone.
 The viscosity is estimated by the equation.

Η = C T/v
Where,
C = Instrument Constant
T= Torque reading
V= is speed of the cone (rpm) Fig 11: Cone & Plate Viscometer

 Thixotropy: “is defined as an isothermal and comparatively slow
recovery , on standing of material, of which consistency lost
through shearing”.
 It can be observed by constructing consistency curves.
 The rate of shear is progressively increased , and corresponding
stress is measured using a suitable instrument.
 When these results are plotted, the up curve ‘ab’ is obtained.
 From desired maximum ‘b’ if the rate of shear decreases gradually
, the down curve ‘bc’ is obtained.
 In Non-Newtonian fluid the down curve is frequently displaced to
the left of up curve.

The curve shows that the material has low consistency at any point on the
down curve compared to that of up curve.
At rest Multi point contacts Gel State
( On storage) ( High Consistency)
On shear Contacts break down
(equilibrium) (Low Viscosity) Sol State
Set Aside Contact established due Gel State
(Removal of stress) to motion
* Particle-particle interactions in thixotropic material. Gel-Sol-Gel
Transformation*
Fig 12: Thixotropic behaviour of Plastic & Pseudoplastic material

 Bulges
 Concentrated aqueous magma (gel) of bentonite (10 to 15 %
w/v) produces hysteresis loop with bulge in the up curve.
 The crystalline plates of bentonite forms “a house of card” like
structure that causes the swelling of magmas.
Fig 13: Hysteresis loop formation in Rheogram

 Spurs
 Procain Penicillin gel produces a Rheogram where bulged curve may
develop into a spur like protrusion.
 The structural breakdown is indicated by high spur value represents
sharp point of structural breakdown.
Fig 14: Bulged curve formation in Rheogram

 Applications
 The greater the Thixotropy higher is the physical stability of the
suspension.
 Thixotropy is applicable in development of depot preparation.
References:
1. Textbook of Physical Pharmaceutics, by CVS Subrahmanyam.
2. Martins Physical Pharmaceutics & Pharmaceutical Sciences.

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