Rheological Properties Flashcards
What are the 3 types of deformation in polymers?
Simple shear - Occurs during processing of polymer melts
Elongation flow - Important in film formation, fibre pulling, blow moulding and vacuum forming
Bulk deformation - Important in injection moulding where liquid flow is generated by hydrostatic pressures
What is a Bingham plastic?
Do not deform below a certain yield stress. Above that, they show Newtonian behaviour. t = t0 + ny
Eg. Plasticine, clay slurries
What is a dilatant material?
Increase in shear viscosity with increasing shear rate (shear thickening)
Eg. Whipped cream lol
What is a pseudo plastic?
Decreasing shear viscosity with increasing shear rate (shear thinning)
Eg. Most polymer melts
Describe a stress strain graph for Bingham, pseudo plastic, dilatant and Newtonian.
Bingham is a straight gradient starting from a certain yield stress
Newtonian is a straight gradient starting from zero
Dilatant is increasing stress more steeply as strain increases - upwards curve
Pseudo plastic is increasing stress as strain increases but gradient decreases - levelling off curve
What is the actual flow of polymers like at increasing shear rates?
Polymers are entangled like spaghetti.
When sheared, they start to disentangle and align which makes the viscosity drop. The degree of disentaglement depends on shear rate.
At high shear rates, polymer will fully align so viscosity will be independent of shear rate - will be Newtonian
At very low shear rates, entanglement doesn’t impede the shear flow so same applied
At infinite slow shear, we have the zero shear rate viscosity n0
Between these regions, power law model applies
What does a graph of log apparent viscosity against log shear rate look like?
Newtonian region at low and high shear rates which are flat as in those regions, viscosity is independent of shear rate
Middle is a slope between the two Newtonian regions (flat slope area is the power law region)
What is the power law model in normal and logarithmic form?
Shear stress = K(T) (shear strain rate dy/dt)^n
Log (stress) = log (K) + n log (dy/dt)
What should a log log plot of shear stress v strain look like for a pseudo plastic?
Straight line
In the power law equation, what will n be is Newtonian, thinning or thickening?
Newtonian - n=1
Thinning - n<1
Thickening - n>1
What is apparent viscosity?
Shear stress / shear rate
For Newtonian, viscosity isn’t dependent on shear rate so apparent viscosity is constant.
What is the yield stress needed for a Bingham plastic to start showing normal flow behaviour?
Critical yield stress
When do you use the Bingham and Herschel-Bulkley model?
Bingham is for Bingham fluids with a constant viscosity above the critical yield stress
Herschel-Bulkley is for a shear thinning behaviour of a plastic fluid
What are the factors affecting melt viscosity?
Temperature
Molecular Weight - lower are Newtonian, higher are more entangled
MWD
Branching - more branching disrupts entanglement so lower viscosity
Fillers - adding fillers increases melt viscosity and decreases die swell
Blends
What is the viscosity equations for compatible and incompatible polymer blends?
Compatible: n = V1n1 + V2n2
Incompatible: 1/n = V1/n1 + V2/n2
V = volume fraction
n = viscosity
When do we use the WLF equation?
When necessary to estimate how a change of temp affects the viscosity of a polymer - ng should be calculated with existing conditions then use that to work out new viscosity in same equation with new temps
In capillary rheometry equations, what are R, P, L and Q?
R - radius of capillary
P - pressure
L - length of capillary
Q - volumetric output
What is Bagley correction and why is it applied?
In capillary rheometry, pressure is measured above the die.
In reality, there is an additional pressure drop at the entrance of the die where the material goes from a wide reservoir to a narrow capillary.
It is possible to correct this and estimate true pressure drop using Bagley correction.
Bagley correction gives a true shear stress and viscosity - true viscosity is a property of the material so wont change under different testing conditions
Why is Bagley correction recommended when using data for design, simulation and studies?
It gives a true value of viscosity and shear stress - this is a property of the material and wont change across instruments
Apparent viscosity can only be compared with samples tested in same instrument and die - usually used for quality control
What is required to calculate Bagley correction?
At least two sets of data obtained with the same:
- sample
- temperature
- barrel
- capillary dia and diff lengths
What would you do to the wall stress equation for capillary with Bagley correction?
Change L to Leffective which is L + eR
Graphically, how is Bagley correction factor found?
Distance from 0 to where the data sets cross the x axis on a pressure drop vs. L/R graph
When do we use the Rabinowitsch correction factor and what does it look like?
To factor in the pseudo plastic nature of the melt which means the velocity profile in the die is more plug like than parabolic.
Equation starting with y true
When should you use the Rabinowitsch correction factor?
Factor wont affect comparability of data I of you are trying to compare
Factor only needs to be used where data is used as fundamental data, in practicality, the error difference is fine for quality control
What is Melt Flow Index?
Simplified version of capillary flow experiment
Polymer is heated in a barrel and extruded through a standard die with a standard weight.
The weight in grams extruded after 10 minutes is the Melt Flow Index (MFI)
How is melt elasticity shown when extruded through a die?
When the melt is deformed through the die, the chains become orientated in the direction of flow. When the melt exits the die, the stress is removed and the chains relax causing some elastic recovery (die swell). Not fully recovered though because of some viscous element which causes chain slippage.
The polymer will remember the large cross section in the barrel and tries to return to it by swelling.
What affects die swell?
Increasing output rate increases the die swell.
Low temperatures increase the die swell.
Higher molecular weights increase the die swell.
Increasing the melt viscosity increases the die swell.
Increasing the difference between reservoir diameter and die damaged increases the die swell.
Decreasing the value of L/D increases the die swell (less time to forget the original chain state)
What change in velocity profile happens at the exit of a die?
Goes from a parabolic to a plug
Why must die swell be considered in design?
If you want a certain extrudate thickness, you need to calculate how much it is going to swell.
What is melt fracture and when does it occur?
Occurs during high capillary flow rates - melt is elongated under too high a stress
Extrudate becomes irregular and distorted when applied stress exceeds tensile stress of the melt.
How does die entrance angle affect melt fracture?
Increasing the die entrance angle to make it more sloped, increases the stress that can be applied before melt fracture.
If the entrance is flat (90*), then melt fracture happens at much lower stresses than if you slope the entrance.
What factors reduce melt fracture?
Increasing the angle of die entrance
Decrease the flow output rate
Increase the temperature (less viscosity so higher critical shear rate)
Local heating of die during extrusion
Decrease molecular weight of polymer
What is a cone and plate rheometer?
Polymer is placed between a heated cone and plate. Apex of cone is in contact with stationary plate and polymer fills gap. Angle of cone is usually small like 5*. Cone is rotated and Torque is measured over a range of rotational rates (w). Either constant speed or constant torque can be used.
Torque = 2/3 * pi * R^3 * shear stress
What are the pros and cons of a cone and plate rheometer?
Pros:
Flow conditions are precisely defined
Shear rate is nearly the same everywhere in the fluid as the gap angle is small
Cons:
Shear rate range is limited
At high shear rates, flow pattern breaks up at free boundary making non-steady state conditions
Shear strain rates are limited
What is a concentric cylinder viscometer?
Sample is sheared between two heated concentric cylinders, one of which is rotating at constant speed. Torque is measured over a range of speeds so viscosity and strain rates can be calculated.
Y = 2piR*N / H
n = TH/4pi2R3LN
N = revolution rate
Apparatus is limited to relatively low strain rates.
What is the Weissenberg effect?
Phenomenon when placing a spinning rod into a polymer.
Instead of being thrown outward, entanglements cause polymer chains to be drawn towards the rod.
Strain tensor of the turning motion produces a non-zero difference between the normal components of the resulting stress tensor so there is a force up or down.
