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EG-M01 Complex Fluid > Final day revision > Flashcards

Final day revision Flashcards

1
Q

Concentric cylinder assumptions

A
  • laminar flow
  • incompressible fluid
  • no radial flow
  • no axial flow
  • no slip at the surface of the cylinder
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2
Q

‘Interesting features’ of the Bingham concentric cylinder model

A

it is only valid where stress > yield stress

Searle mode : fluid closest to the bob is sheared but the fluid close to the cup is stationary

Couette mode : Fluid closest to the bob is sheared but the fluid close to the cup rotates with the cup. it does not experience flow.

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3
Q

Pipe flow assumptions

A
  • Laminar flow
  • Fully developed flow and steady flow
  • Incompressible fluid
  • Constant temperature
  • No pressure dependence on viscosity
  • no slip at the wall
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4
Q

Why is pipe roughness negligible for non-Newtonian fluids

A

Laminar sublayer tends to be thicker for non-Newtonian fluids, thus isolating the effect of wall roughness.

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5
Q

What is the yield stress

A

The minimum stress required to initiate flow

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6
Q

What are the two tests for yield stress

A
  • Dynamic test
  • Static test
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7
Q

Explain the dynamic test for yield stress

A

When the material is sheared with the application of progressively lower stress with associated reduction in flow

On the graph:

intercept A: the Bingham extrapolated yield stress

intercept B: the dynamic/lower yield stress

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8
Q

Explain the static test for yield stress

A

Application of stress to an undisturbed sample until flow is observed

intercept C: the static/upper yield stress

intercept B: the dynamic/lower yield stress

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9
Q

No-slip example

A

Fluid sheared within a concentric cylinder viscometer using Searle mode

Fluid closest to the bob surface moves at the same angular velocity as the bob meaning that the angular velocity between the two is 0.

Fluid closest to the cup is stationary meaning that the the angular velocity between the two is also 0.

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10
Q

What does it mean if slip occurs

A

The displacement of the surface doesn’t correlate with the imposed (and assumed) strain angle.

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11
Q

How do you probe slip?

A

Using the parallel plate system, conduct a series of stress controlled experiments with different physical gaps.

Slip velocity is independent of gap size, whereas the velocity difference across the sample varies as a function of stress and gap size.

apparent strain rate = V/h = (2*V_s)/h * strain rate

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12
Q

Sustainable operation

A
  • Waste volume reduction by dewatering and recycle water
  • Low solids concentration means Newtonian

easy pipeline transport but large environmental impact

  • increased solids concentration means non Newtonian (e.g shear thinning behaviour)

transport behaviours modified and improved environmental impact

  • Further increased concentration means yield stress material and increased viscosities

pipeline transport is a major concern but ideal environmental result. ‘dry’ stacking of concentrated waste solids instead of waste lakes

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13
Q

Spring general equation

A

stress = G * strain

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14
Q

Dashpot general equation

A

stress = viscosity * strain rate

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15
Q

Kelvin - Voigt general equation

A

stress = (G * strain) + (viscosity * strain rate)

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16
Q

What is the creep experiment

A

Apply constant stress and consider how the strain will change in time

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17
Q

How does the Kelvin Voigt model respond to the creep experiment

A
  1. Apply constant stress
  2. System will begin to move at a rate determined by the viscosity of the dashpot fluid
  3. A limiting deformation will be achieved which is determined by the spring stiffness.
  4. If the stress is removed, the system will slowly return to its original conformation because the spring will want to return to its original state.

The strains in the two elements are equal, and the stresses are additive.

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18
Q

What is the general equation for the Maxwell model

A

stress + relaxation time * stress rate = viscosity * strain rate

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19
Q

What is the relaxation time

A

a ratio of the viscosity coefficient to the spring stiffness coefficient

viscosity / G

20
Q

What is the step strain experiment

A

Apply a step strain, then consider how the stress will change in time.

21
Q

How does the Maxwell model respond to the step strain experiment

A
  1. Apply a step strain
  2. Spring will extend but the dashpot doesn’t have time to.
  3. Dashpot moves to relax the stress in the spring.
  4. Spring eventually returns to its original configuration.
  5. Memory of the overall initial configuration is lost.

Remember that the stresses in the two elements are equal, and the strains are additive.

22
Q

Explain the three step test.

A

Perform 3 tests on a material. Each uses a fresh sample.

If the materials structure is progressively broken down, then the time of the test influences the result.

1 - short duration test

2 - intermediate

3 - extended duration test

23
Q

Define the Deborah number

A

The ratio of the relaxation time to the process time.

De = Relaxation time / Process time

for De &laquo_space;1, the process time is much larger than the relaxation time and elastic effects will be minimal.

24
Q

How can the burgers model be represented

A
  • A two mode Maxwell model.

or

  • The Maxwell and Kelvin Voigt elements connected in series.
25
Q

How does the Burgers model respond to the creep/recovery thought experiment

A

1) Maxwell spring reacts first …. step strain

2) Voight element also begins to react
delayed approach to limiting strain

3) Dashpot also reacts….constant strain

4) stress removed

5) maxwell spring reacts first and returns to original configuration

6) Voight also begins to react…. delayed approach to original configuration

7) dashpot stops reacting

ensure to know the graph to go with these steps

26
Q

G* =

A

G* = G’ + iG’’

G* = complex modulus

G’ = storage modulus

G’’ = Loss modulus

G*[cos(pa) + i sin(pa)] = G’ + iG’’

27
Q

Longest relaxation time

A

cross section of the G’ and G’’ lines on graph.

longest relaxation time = 1 / (angular velocity)_c

28
Q

G’ and G’’ in the Kelvin Voigt model

A

G’ = G

G’’ = viscosity * angular velocity

29
Q

G’ and G’’ in the Maxwell model

A

G’ = (G * rt^2 * av^2)/(1+(rt^2 * av^2))

G’’ = (G * rt * av) / (1 + rt^2 *av^2)

30
Q

Why must an amplitude sweep be conducted first?

A

To define the linear viscoelastic range.

31
Q

Which equipment causes inertial effects?

A

CMT

32
Q

How can inertial effects be reduced?

A
  • Use a smaller gap
  • Use a lighter geometry
33
Q

What is a frequency sweep used for?

A

To study the behaviour over a range of time scales.

34
Q

If the raw phase angle > 90 then

A

the response is dominated by inertia

35
Q

What should you do to represent the Sisko model as the Bingham model?

A

set n = 0

then multiply through by the strain rate

36
Q

When is the Carreau model used

A

when there is zero shear viscosity which then transitions to a high shear viscosity via close to power law behaviour.

37
Q

What is the difference between the Cross model and the Carreau model?

A

The cross model has a less abrupt transition to shear thinning.

38
Q

What is the difference between the meter model and the cross model?

A

The meter model considers viscosity as a function of shear stress rather than as a function of shear rate.

39
Q

How do you convert the meter model to the Ellis model?

A

Set the infinite viscosity to 0.

Represents the first half of the meter model.

40
Q

Explain Searle mode for the concentric cylinder system

A

When torque is applied to the bob, and the angular velocity is measured at the bob

41
Q

Explain Couette mode for the concentric cylinder system

A

When angular velocity (rotation) is a applied at the cup, and the torque is measured at the bob.

42
Q

In the context of SAOS, what is the equation for stress (Hookean solid) + (Newtonian liquid)

A

Hookean solid:

stress = G * initial strain * sin(av * t)

Newtonian liquid:

stress = viscosity * av * strain_0 * sin(av * t +pi/2)

43
Q

How do you convert degrees to radians

A

pi/2 radians = 90 degrees

44
Q

what is on the axis of the velocity profile

A

x axis : u/umax

y axis: r/rmax

45
Q

What is on the axis of the Thixotropy - hysteresis graph

A

stress (y) vs strain rate (x)

46
Q

What is on the axis of the SAOS axis

A

(stress/strain) y axis

(time) x axis

EG-M01 Complex Fluid (2 decks)

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