1. Rheology

4. Strain and Strain (Shear) Rate
a dimensionless quantity representing the relative deformation of a material
Normal Strain Shear Strain

5. Shear Stress is the intensity of force per unit area, acting tang

6. Simple Shear Flow

7. Fluid Viscosity Newtonian fluids Non-Newtonian fluids
viscosity is constant (Newtonian viscosity, )
Non-Newtonian fluids
shear-dependent viscosity (apparent viscosity, )

8. Viscosity: Introduction
The viscosity is measure of the “fluidity” of the fluid which is not captured simply by density or specific weight. A fluid can not resist a shear and under shear begins to flow. The shearing stress and shearing strain can be related with a relationship of the following form for common fluids such as water, air, oil, and gasoline:

9. Viscosity: Introduction
is the absolute viscosity or dynamics viscosity of the fluid, u is the velocity of the fluid and y is the vertical coordinate as shown in the schematic below:

10. Viscosity
Viscosity is a property of fluids that indicates resistance to flow. When a force is applied to a volume of material then a displacement (deformation) occurs. If two plates (area, A), separated by fluid distance apart, are moved (at velocity V by a force, F) relative to each other,
y = y-max
y = 0
= Coefficient Viscosity ( Pa s)
Newton's law states that the shear stress (the force divided by area parallel to the force, F/A) is proportional to the shear strain rate . The proportionality constant is known as the (dynamic) viscosity

11. In cgs unit , the unit of viscosity is expressed as poise
The unit of viscosity in the SI system of units is pascal-second (Pa s)
Shear stress
In cgs unit , the unit of viscosity is expressed as poise
1 poise = Pa s
Shear rate
1 cP = 1 m Pa s

12. Newtonian fluid
 =
 =

13. Newtonian
From
and
 =
 =
P =
  = 8v/D

14. Non-Newtonian Fluids

15. Flow Characteristic of Non-Newtonian Fluid
Fluids in which shear stress is not directly proportional to deformation rate are non-Newtonian flow: toothpaste and Lucite paint

17. (Casson Plastic)
(Bingham Plastic)

18. Viscosity changes with shear rate
Viscosity changes with shear rate. Apparent viscosity (a or ) is always defined by the relationship between shear stress and shear rate.

19. Model Fitting - Shear Stress vs. Shear Rate
Summary of Viscosity Models  h = g
Newtonian
Pseudoplastic
Dilatant
Bingham
Casson
Herschel-Bulkley  g n = K ( n
< 1 )  g n = K ( n
> 1 )   h g n = + y  1 2 1 2 h 1 2 g 1 2 =  + c   g = + K n y
or  = shear stress, º = shear rate, a or  = apparent viscosity
m or K or K'= consistency index, n or n'= flow behavior index

20. Herschel-Bulkley model (Herschel and Bulkley , 1926)
Values of coefficients in Herschel-Bulkley fluid model
Fluid m n 0
Typical examples
Herschel-Bulkley
>0
0<n<
Minced fish paste, raisin paste
Newtonian 1
Water,fruit juice, honey, milk, vegetable oil
Shear-thinning
(pseudoplastic)
0<n<1
Applesauce, banana puree, orange juice concentrate
Shear-thickening
1<n<
Some types of honey, 40 % raw corn starch solution
Bingham Plastic
Toothpaste, tomato paste

21. Non-Newtonian Fluid Behaviour
The flow curve (shear stress vs. shear rate) is either non-linear, or does pass through the origin, or both. Three classes can be distinguished.
(1) time-independent fluids
(2) time-dependent fluids
(3) visco-elastic fluids

22. Time-Independent Fluid Behaviour
Fluids for which the rate of shear at any point is determined only by the value of the shear stress at that point at that instant; these fluids are variously known as “time independent”, “purely viscous”, “inelastic”, or “Generalised Newtonian Fluids” (GNF).
1. Shear thinning or pseudoplastic fluids
2. Viscoplastic Fluid Behaviour
3. Shear-thickening or Dilatant Fluid Behaviour

23. Shear thinning or pseudoplastic fluids
Viscosity decrease with shear stress. Over a limited range of shear-rate (or stress) log (t) vs. log (g) is approximately a straight line of negative slope. Hence
 yx = m(gyx)n (*)
where m = fluid consistency coefficient
n = flow behaviour index
Eq. (*) is applicable with 0<n<1
Re-arrange Eq. (*) to obtain an expression for apparent viscosity
ma (= yx/gyx)

24. Pseudoplastics
Flow of pseudoplastics is consistent with the random coil model of polymer solutions and melts. At low stress, flow occurs by random coils moving past each other without coil deformation. At moderate stress, the coils are deformed and slip past each other more easily. At high stress, the coils are distorted as much as possible and offer low resistance to flow. Entanglements between chains and the reptation model also are consistent with the observed viscosity changes.

25. Why Shear Thinning occurs
Unsheared
Sheared
Aggregates break up
Anisotropic Particles align with the Flow Streamlines
In the same form as the cube used to define the other terms of stress and strain, we see a change in the molecules or particles/aggregates as shear is applied
the result is a lower energy dissipation, so the viscosity drops
when the sample is back at rest, then Brownian motion randomises the particles over time to rebuild the viscosity.
if the rebuild process is slow enough then the sample is said to be thixotropic [time dependant]
Random coil Polymers elongate and break
Courtesy: TA Instruments

26. Shear Thinning Behavior
Shear thinning behavior is often a result of:
Orientation of non-spherical particles in the direction of flow. An example of this phenomenon is the pumping of fiber slurries.
Orientation of polymer chains in the direction of flow and breaking of polymer chains during flow. An example is polymer melt extrusion
Deformation of spherical droplets to elliptical droplets in an emulsion. An industrial application where this phenomenon can occur is in the production of low fat margarine.
Breaking of particle aggregates in suspensions. An example would be stirring paint.
Courtesy: TA Instruments

27. 2. Viscoplastic Fluid Behaviour
Viscoplastic fluids behave as if they have a yield stress (0). Until  0 is exceeded they do not appear to flow. A Bingham plastic fluid has a constant plastic viscosity
for
Often the two model parameters 0B and mB are treated as curve fitting constants, even when there is no true yield stress.

28. or Dilatant Fluid Behaviour
3. Shear-thickening
or Dilatant Fluid Behaviour
yx = m(yx)n (*)
where m = fluid consistency coefficient
n = flow behaviour index
Eq. (*) is applicable with n>1.
Viscosity increases with shear stress.
Dilatant: shear thickening fluids that contain suspended solids. Solids can become close packed under shear.

29. Time-dependent Fluid Behaviour
More complex fluids for which the relation between shear stress and shear rate depends, in addition, on the duration of shearing and their kinematic history; they are called “time-dependent fluids”.
The response time of the material may be longer than response time of the measurement system, so the viscosity will change with time. Apparent viscosity depends not only on the rate of shear but on the “time for which fluid has been subject to shearing”.

30. Thixotropic : Material structure breaks down as shearing action continues : e.g. gelatin, cream, shortening, salad dressing.
Rheopectic : Structure build up as shearing continues (not common in food : e.g. highly concentrated starch solution over long periods of time
Thixotropic
Rheopectic
Shear stress
Shear rate

31. Rheological curves of Time - Independent and Time – Dependent Liquids_ _ + + A B C D E F G
Non - newtonian
Rheological curves of Time - Independent and Time – Dependent Liquids

32. Visco-elastic Fluid Behaviour
Substances exhibiting characteristics of both ideal fluids and elastic solids and showing partial elastic recovery, after deformation; these are characterised as “visco-elastic” fluids.
A true visco-elastic fluid gives time dependent behaviour.

33. Newtonian Pseoudoplastic Dilatant Common flow behaviours
Shear stress
Shear stress
Shear stress
Shear rate
Shear rate
Shear rate
Viscosity
Viscosity
Viscosity
Shear rate
Shear rate
Shear rate
Common flow behaviours

34. Examples
Newtonian flow occurs for simple fluids, such as water, petrol, and
vegetable oil.
The Non-Newtonian flow behaviour of many microstructured products can offer real advantages. For example, paint should be easy to spread, so it should have a low apparent viscosity at the high shear caused by the paintbrush. At the same time, the paint should stick to the wall after its brushed on, so it should have a high apparent viscosity after it is applied. Many cleaning fluids and furniture waxes should have similar properties.

35. Examples
The causes of Non-Newtonian flow depend on the colloid chemistry of the particular product. In the case of water-based latex paint, the shear-thinning is the result of the breakage of hydrogen bonds between the surfactants used to stabilise the latex. For many cleaners, the shear thinning behaviour results from disruptions of liquid crystals formed within the products. It is the forces produced by these chemistries that are responsible for the unusual and attractive properties of these microstructured products.

36. Newtonian Foods Examples: Water Milk Vegetable oils Fruit juices
Shear stress
Shear rate
Examples:
Water
Milk
Vegetable oils
Fruit juices
Sugar and salt solutions

37. Pseudoplastic (Shear thinning) Foods
Shear stress
Shear rate
Examples:
Applesauce
Banana puree
Orange juice concentrate
Oyster sauce
CMC solution

38. Dilatant (Shear thickening) Foods
Shear stress
Shear rate
Examples:
Liquid Chocolate
40% Corn starch solution

39. Bingham Plastic Foods Examples: Tooth paste Tomato paste Shear stress
Shear rate
Examples:
Tooth paste
Tomato paste

40. Measurement of Viscosity
Viscosity of a liquid can be measurement
Capillary Tube Viscosity
Rotational Viscometer

41. Viscosity: Measurements
A Capillary Tube Viscosimeter is one method of measuring the viscosity of the fluid.
Viscosity Varies from Fluid to Fluid and is dependent on temperature, thus temperature is measured as well.
Units of Viscosity are N·s/m2 or lb·s/ft2

42. Capillary Tube Viscometer

43. Newtonian
 =
 =

45. Capillary tube viscometer
Reference sample with known density and time will be used (at specified temperature).
Time and density of sample will be evaluated and then the viscosity can be determined.

46. Falling sphere method
This method can be used for assumption that falling is in Stoke region.
When the sphere is fell through the fluid, distance and time of falling will be measured (velocity).

47. Falling sphere method

48. Example
In a capilary flow experiment using buret, 30 ml of water was emptied in 10 s. A 40% sugar solution (specific gravity 1.179) having similar volume took 52.8 s for emptying. What was the viscosity of sugar solution?

49. Viscometers
In order to get meaningful (universal) values for the viscosity, we need to use geometries that give the viscosity as a scalar invariant of the shear stress or shear rate. Generalized Newtonian models are good for these steady flows: tubular, axial annular, tangential annular, helical annular, parallel plates, rotating disks and cone-and-plate flows. Capillary, Couette and cone-and-plate viscometers are common.

51. Rotational Viscometer

52. Non-newtonian fluid from  = 2r2L  =
 =
from
Integrate from r = Ro Ri and  = 0i

53. Non-newtonian fluid  or a º obtain
Linear : y = y-intercept + slope (x)

54. K and n
n = 0.25
K = 59.02
(shear thinning)

55. Apparent viscosity (Pa.s)
Example
The shear rate for a power law fluid without yield stress when using a single spindle viscometer is given by (4N/n). Determine the flow behavior index and consistency coefficient based on the following data:
Apparent viscosity (Pa.s)
RPM
5.0 6
1.5 60