Lecture 9: Material Properties – Fluids

Question 1

What is a non-linear Newtonian fluid?

Answer 1

non-linear relationship between how fluid is pushed around and how quickly it can be made to move

Question 2

What is a Newtonian fluid?

Answer 2

linear relationship between shear stress and shear strain rate

Question 3

What is an inviscid fluid?

Answer 3

no viscosity – theses are hypothetical fluids

Question 4

How are liquids vs. gases distinguished?

Answer 4

are molecules attracted to each other strongly or not

• liquids: cohesion between molecules – tension
• gases: molecules have no affinity for other gas molecules – no tension

Question 5

What is shear stress (𝜏)?

Answer 5

occurs when a force is applied parallel to the surface of an object

Question 6

What is shear modulus (G)?

Answer 6

the stiffness of a solid experiencing shear

Question 7

What is Young’s modulus of elasticity (E)?

Answer 7

the stiffness of a solid under tension/compression

Question 8

What happens to displacement (Δx) and h when shear stress (𝜏) is constant?

Answer 8

doubling h will also double Δx

∴ shear strain (ie. tan(θ) and Δx/h ratio) remains the same

Question 9

How do solids respond to shear stress?

Answer 9

by deforming

Question 10

How do fluids respond to shear stress?

Answer 10

by moving

Question 11

What is a viscometer?

Answer 11

devices that measure the force required to shear a fluid between a rotating inner cup and stationary outer wall

• fluid fills a very thin gap between inner and outer wall (distance d = thickness of fluid)
• fluid in direct contact with walls doesn’t slip
• when a motor makes the inner cup rotate, a force (shear stress) is applied to the fluid across the inner cups’ surface, and the fluid is dragged into motion

Question 12

In a viscometer, how does a fluid’s stickiness impact the flow of adjacent fluids?

Answer 12

in viscometers, layers of fluid slide past each other, as the fluid attached to the moving plate drags the fluid below it into motion

as shear stress is continuously applied, forces are being transmitted from the fluid in contact with the moving plate to the other adjacent fluids by the fluid’s stickiness
- if all fluids have equal amounts of stickiness – each bit of fluid (each arrow) is transmitting drag to the next with the amount of shear stress
- if one bit of fluid is more sticky – the adjacent bit of fluid would move closer to its own velocity
- if one bit of fluid has no stickiness – this bit of fluid would slide over another layer of fluid without causing that layer to move

Question 13

What is shear strain rate?

Answer 13

rate at which fluids experiencing shear stress moves/deforms

velocity gradient (Δv/d) – this is linear

Question 14

For how long do fluids deform?

Answer 14

only for as long as the shear stress is applied

Question 15

How does shear stress impact the shear strain rate?

Answer 15

greater shear stress = larger velocity gradient ∴ larger shear strain rate

Question 16

What is viscosity?

Answer 16

proportionality factor that expresses the relationship between how much force/area is applied vs. how steep the velocity gradient in the fluid is

Question 17

What is the slope of a shear stress / shear strain rate curve?

Answer 17

dynamic viscosity

Question 18

What is a high viscosity fluid?

Answer 18

high shear stress results in low shear strain rate

Question 19

What is a low viscosity fluid?

Answer 19

low shear stress results in high shear strain rate

Question 20

How is a fluid’s resistance to flow related to its viscosity?

Answer 20

resistance is a measure of the internal friction of a fluid’s molecules as they flow past one another

Question 21

Non-Newtonian Fluid Types

What is bingham plastic?

Answer 21

flows once stress exceeds yield stress

Question 22

Non-Newtonian Fluid Types

What is shear thinning?

Question 23

Non-Newtonian Fluid Types

What is shear thickening?

Answer 23

becomes more viscous

Question 24

How does shear thinning in blood occur?

Answer 24

occurs due to the way blood cells aggregate

• at low rates of shear, red blood cells clump together to form chances called rouleaux
• as shear rate increases, the blood cells separate, reducing the viscosity of the blood

Question 25

What are viscoelastic materials?

Answer 25

materials that display both viscous properties (can flow like fluids) and elastic properties (like solids)

Question 26

What happens if stress is held constant on a viscoelastic material?

Answer 26

strain increases with time – ie. material will flow stretch/creep over time

Question 27

What happens if strain is held constant on a viscoelastic material?

Answer 27

stress decreases with time (relaxation)

Question 28

What does the effective stiffness of a viscoelastic material depend on?

Answer 28

the rate of application of stress

Question 29

What do solids resist?

Answer 29

strain

Question 30

What do fluids resist?

Answer 30

rate of change of length

Question 31

Elastic Materials

What happens to stress if you increase the strain on a spring (ie. by stretching it out)?

Answer 31

stress will increase in direct proportion to the applied strain

Question 32

Viscous Materials

What happens to stress if you increase the strain on a dashpot?

Answer 32

• initially, viscosity of the liquid within initially resists the movement of the piston and therefore stress increases
• over time, fluid flows around the piston, causing an increase in the length of the dashpot and a decrease in stress

Question 33

Viscoelastic Materials

What happens to stress if you increase the strain on a spring and dashpot?

Answer 33

• stress increases as spring extends
• stress decreases as spring contracts, and dashpot extends slowly over time
• system remains at the strained length

Question 34

How is harmonic analysis of materials done?

Answer 34

sine wave strain (ɛ) input – machine lever oscillates up and down, changing the length of the sample

Question 35

How can you analyze the phase differences between two sine waves?

Answer 35

using Lissajous curve

• plot intensity (height) of the two sine waves at each time point as x/y coordinates
• depending on the phase shift between two waves, this will produce either a line, circle, or ellipse

Question 36

Harmonic Analysis – Elastic Materials

What do the stress and strain waves look like?

Answer 36

(elastic/Hookean solid)

both stress and strain are in phase

• described by Young’s modulus of elasticity E = 𝜎/ɛ
• stress and strain maximum and minimum are the same (in phase)

Question 37

Harmonic Analysis – Viscous Materials

What do the stress and strain waves look like?

Answer 37

(Newtonian fluid)

stress and strain are 90º out of phase

• described by the sample’s dynamic viscosity (𝜇)
• maximum stress precedes maximum strain
• maximum and minimum strain at the top and bottom of the machine’s lever stroke

Question 38

Harmonic Analysis – Viscoelastic Materials

What do the stress and strain waves look like?

Answer 38

stress and strain are somewhere between 0° (in phase) and 90° out of phase

• stress is maximum at some intermediate point
• maximum stress precedes maximum strain