1. The document discusses various types of fluid flow including Newtonian and non-Newtonian systems. 2. It describes properties like viscosity and how they are measured using instruments like capillary viscometers, falling sphere viscometers, and rotational viscometers. 3. Non-Newtonian fluids exhibit time-dependent viscosity changes under stress like thixotropy, and can have plastic, pseudoplastic, or dilatant behaviors that alter viscosity with shear rates.

1. UNIT II

2. • Newtonian systems:
1. Law of flow
2. kinematic viscosity, effect of temperature,
• Non-Newtonian systems:
1. Plastic,Pseudoplastic, dilatant.
2. Thixotropy, Thixotropy in formulation
• Determination of viscosity:
1. Capillary, falling Sphere
2. Rotational viscometers.
• Deformation of solids: Plastic and elastic deformation, Heckel equation,
Stress, Strain,Elastic Modulus

3. • Defination: Bingham and crawford
Rheo - To flow
Logos - Science
ology - To study of

4. 1.Elastic deformation-
a.Spontaneous
b.Reversible.
2.Plasic deformation-
a.Permanant
b.Irreversible

9. Newtonian Fluids
• Viscosity of newtonian fluid remains constant while viscosity of non-
newtanian changes according to apllied shear force.
• Stress verses shear rate is linear and passing throught the origin and
proportionality constant is called as viscosity.
• E.g.Newtonian fluids-Water ,dil.solution,dil.suspension
• E.g. Non-newtaoian fluids-Ointment ,gel,colloidal dispersion,emulsion

10. Plane second Original Plane

11. • Velocity difference , dv; between two planes of liquid seeperated by
an infinitesimal distance dr,
is velocity gradient or rate of shear = dv/dr
• Force per unit area F’/A requre to bring about flow
is called as shearing stress F
• Newton says that’’ The higher the viscosity of liquid more the
shearing stress require to produce a certain rate of shear.’’
• Thus shearing stress is proprotional to rate of shear,
• F’/A ɶ dv/dr
F’/A = η dv/dr
• where the η is known as proportionality constant /coefficient of
viscosity/viscosity/dynamic viscocity.

12. • Viscosity :
Measure of the resistance to a fluid to deformation under shear stress.
Its a fluids internal resistance to flow and may be thought of as a
mesure of fluid friction.
• Unit:
Poise (Jean Louis maries poiseuille)
Define as the shearing force required to maintain a relative velocity of
1 cm / sec between two parallel planes,1 cm2 in area and 1 cm apart.
Centipoisee (cp ) 1 cp = 0.01 poise.
1 poise =100 centipoise =1 dyne sec cm -2 = 1gcm-1sec -1

13. • Slope of plot equal to the reciprocoal of viscosity, and is referred as
fluidity.
• $=1 /
$= Fluidity
η=Viscosity
η

14. • Kinematic viscosity
• Relative viscosity
• Specific viscosity
• Reducedd viscosity (of polymer)
• Intrensic viscosity(of polymer)

15. • Kinematic viscosity
Absolute viscosity divided by the its density at deffinite temperature.
Kinematic viscosity= η/ρ
• Relative viscosity
Its a ratio of viscosity of viscosity of solutio to the solvent.
Relative viscosity = η/ηs
• Specific viscosity
Its relative increse in viscosity of dipersion over that of the solvent.
Specific viscosity= η- ηs / ηs
Reduce visccosity (of polymer)
Its ratio of specific viscosity to the mass canc.of the polymer.
Reduce visccosity = ηsp/c
• Intrensic viscosity(of a polymer)
Limiting value of the reduced visccosity or the intrensic viscosity at deinite dilution of polymere.

16. • Viscosity of liquid generlly increase with temperature and that of gas is decreses.
η=AeEv/RT
η = Viscosity
A = Constant depending upon mol.wt.and molar volume of liquid
Ev = Activation enegry
R = Gas constant
T = Tempertaure

17. • Flow of material such as colloidal suspension,emulsionand ointment etc.does not
follow the simple newtonian flow thus these material are know as Non-newtonian
fluids.
The fluids shows the following characteristic flow
• 1.Plastic flow
• 2.Pseudo-plastic flow
• 3.Dialtant flow
• 4.Thixotrophy
• 5.Anti thixotropic or negative thixotropic
• 6.Negative rhopexy

18. • Plastic flow fluid graph does not passs throught origin.
• It intersect the shearing stress axis at point FI .
• The extrapolation of staright line to the X axis is touches at point FB and it is a yeild value.

19. • Bingham Bodies/Plastic Material:
• Bingham yeild value-FB-Actual flow
begin.
• The slope of the rheogram is termed mobility analogues to fluidity in newtonian systems
and its reiprocal is known as plastic viscosity (U)
• (F-FB )
U = ------------
G
• U define as shearing stress in excess of the yeild value , required to induce a unit rate of
shear G.
• E.g Zinc oxide in mineral oil serves as a simple e.g of bingham body.

22. • Non -Linear Curve
• Passing through origin.
• The rate of shear G, doses not icreases linearly with the shearing stress,F.
• Example:Tragacanth,gelatin,carboxy methylcellulose and other water soluble
mucilage and gum.

23. • Thus viscosity does not remains constant at all point thus system is known as
shear thining system.
• Fig.4.7 shows effect of rate of shear on the viscosity of pseudoplastic materials.
• Exponential equation is given by, F N = η’ G
• More the N value greater the Pseudoplasticity characters.(N greaterr than 1)

25. • Dialatancy is phenomenon in which the material exhibits an increase in resistance to
flow with increase rate of shear.
• The material returns to a state of fluidity when the sheaar is removed or the agitation is
stoped.The phenomenon is called as shear rate shickening .
• Fig.4.10 shows effect of raate of shear on the viscosity of dialatant system.
F N = η’ G
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27. • Example
1. 50% by weight of potassium silicate or fine starch powder with cold water to
whcih a deflocculaing agent may be added if necessary .
2. Titanium dioxide suspension.

28. • The non newtonian fluids like plastic ,pseudoplastic and dialatant are shows time
dependent change in the viscosity at varing shear stresses.
• This behaviour known as thixotrophy.
• Thixotrophy in plastic and pseudoplastic system:
In both type of system the viscosity is decresases upon application of shearing stress,at
given temperature.
On removal of stress it regain viscosity but after some time lag,is term as thixotrophy.
It describe as a reversible isotherm trnasformation from gel to sol.
Application of shear stress Removal of shear stress
Gel -----------------------------------> Sol----------------------------------> Gel

30. Thixotrophy in dilatant system:
• In the dialatant system with increasing shearing stress an apperant viscosity is also
increases at a give temperature.Thus system known as shear thickening system.
• On removal of shear stress ,viscosity again decreases after a lag time.This
phenomenon is known as thixotrophy in dialatant system
• Describe as reversible isothermal transformation form sol to gel.
Application of shear stress Removal of shear stress
Sol -------------------------- > Gel -----------------------------------> Sol

32. Irreversible thixotrophy:
On application of shearing stress breckdown of structure is therewith in the system
,which does not reform on removl of shearing stress ,or lag time is to long that from a
practical point of view the effect is irreversible.
Rheopexy:
The process of reformation of gel structure after it has been deformed can be
accelerated by applying gentle and regular movement(rolling and rocking motion).
Rolling and rocking
Sol----------------------------------->Gel
Anti-Rheopexy:
Reformation of sol state from gel state is aided by the gentle rolling or rocking
motion.
Rolling and rocking
Gel----------------------------------->Sol

33. Antithixotrophy or Negative thixotrophy:
In this there is an increase in consistancy ratherr than decrease in consistancy.
In plastic and pseudoplastic system ,viscosity first decreses after applying a shear
stress,and regain its viscosity afeter removal of stress but dowun word curve has more
viscosity than the upword curve.
Ex.Magnesium magma.
When magnesium magma is expose to increasing shear stress, the viscosity is gradually
increases.
The magma continously thickenedd at decreasing rate of shear and finally reaches a
equilibrium state (sol) ,where further cycles of increase and decrease shear rate no longer
increase consistancy of material.

34. • Anti thioxtrophy is different from dialatancy.
• Dialatncy is observe at deffloculated and ordinary conatin greater than 50 %
by volume of solid disperse phase.
• Anti thixotrophy have low solid content (1-10%) and are flocculatedd.

35. A.Capillary instrument.
1.Ostwald viscometer
2.Ubbelohde suspended level viscometer
B.Falling and rising body apparatus
1.Falling sphere viscometer
2.Rising sphere viscometer
C.Rotational viscometer.
1.Cup and bob viscometer a.Couette type b. Searle type e.g Stormer viscometer
2.Cone and plate

37. • Modified form of ostwald’s viscometer.
• Third arm is attached to the bulb below the capillary part of
the right arm as shown in fig.Liquid is introduced into the
viscometerr through the left arm in quantity sufficient to fill
the bulb in the left arm.
• The viscometer is fixedd verically in thermostated bath and
allowed to attain the required temperature.
• The sample volume is adjusted and the liquid is sucked or
blown into the middle arm until the menisus is just above
the mark B.
• The suction or pressure is released and the time taken for
the bottom of the meniscus to fall from B to C is noted.
• As liquid below the capillary tube is ventilateed down by
the third arm,the volume in the middle arm ramains
constant.

38. • Principle based upon stokes law which state that when body falls from viscous
medium,it experiences resistance or viscous drag which oppose the motion of the
body.At intial stage due to gravity it experiences the acceleration but soon this
acceleration is balancedd by the viscous drag and body falls with uniform terminal
viscosity.
(p s - p 0)g
V d2 = ------------------------
18 η
Where,
V- sedimentation velocity ps-desity of disperse phase
p0-density of disperse medium η-viscosity of disperse medium
g- accelration due to gravity d -diameter of particle

39. :

40. • In-this 1.9 cm diameter stainless steel sphere is connected to strain gauge via a
platinum-rhodium wire .
• It is lifted throught the material under the test at a slow rate by a motor driverr arm.
• The shearing stress caused by the strain in the gel structure is recorded
contineously.
• Stoke equation similar to that used for falling sphere instrument.

41. It consist of two coaxial cylinder of different diameters.In to
the outer cylinder the inner cylindr (bob)is place cenrtally.
The sample is place in between two cylinder.
Then the rotation is provided to the any one of the cylinder
and then the torque set up is there.
The torque set up in the bob is measured in terms of angular
deflection Q of a pointer that moves on a scale.
Depending upon rotaion provide to which cylinder they are
classify into two group
a.Couette type viscometer
b.Searle type viscometer

42. In this type of instrument,the cup is rotated and the
viscous drag on the bob produced by the liquid
results in a torque which is proportional to the
viscosity of the liquid.
E.g.Mac michael viscometer.

43. • In this type of instrument,the bob is
rotatedd while the cup is held stationary.
• E.g Stormer viscometer
Brookfield viscometer

44. • Viscometer in which the bob rotates and the cup is stationary.The instrument can be
used to attain fundamental rheological propertied such s yield value,plastic viscosity and
the thixotropic index.
• In operation,the test system is placed in the space between the cup and the bob and
allowed to reach temperature equilibrium.A weight is placed on the hanger and the time
for the bob to rotate a specific number of times is recorded.This data is then converted
to rpm.The weights are increased gradually and the whole procedure is repeated.
• In this way,a rheogram is obtained by plotting rpm vs weight added.by thw use
appropriate constants,the rpm value can be coverted to actal rates of shear in sec -1
• Similarly , the weights added can be transposed into the units of shear stress,namely
dyne cm -2.
• The viscoty of the material may be calculated using the following eqation:
η = Kv w / v
Where. W is the weight inn grams v i is the rpm generated due to w
Kv is an intrument constant which can be determine by analysing an oil of known viscosity using the instrument.

45. Fig:Stromer vicometer.

46. Consist of flat circular plate with a wide angle cone placed centrally above it.
During operation ,the sample is placed at the centre of the plate ,which is then raidsed into
position under the cone.The cone is driven by a variable speed motor and the sample is
sheared in the narrow gap betwen the stationary plate and the rotating cone.
The rate of shear in revolution per min.is increased and decreased and the torque producd
on the cone is measured.
A plot of rpm or rate of shear versus scale reading or shearing stress may thus be
constructed in an ordinary manner.The ferranti-shirley viscometer is an example of a
rotational cone and plate viscometer.
The viscosity in poise of a newtonian liquid measured in the cone-plate viscometer is
calculated by the of the eqation:
h = C T / v
Where, C is an instrument constant ,
T is the torque reading
v is the speed of the cone in revolution per min

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