Recent advances in Rheometry for process relevant material ...1 Barnes (2000) Handbook of Elementary...
Transcript of Recent advances in Rheometry for process relevant material ...1 Barnes (2000) Handbook of Elementary...
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Recent advances in Rheometry for process relevant material characterisation
Dr Dan Curtis
Complex Fluids Research Group Swansea University
IChemE Technical Event: Mixing
Port Talbot, South Wales 25th April 2017
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The next 40 minutes (ish)…..
The Very Basics: Mixing Low Viscosity Newtonian Fluids Complex Fluids Mixing Complex Fluids Traditional approaches for characterising Complex Fluids Small Amplitude Oscillatory Shear Fourier Transform Mechanical Spectroscopy Novel approaches for characterising Complex Fluids Optimal Fourier Rheometry / Optimally Windowed Chirps Superposition Rheometry Future projects …….
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Recent advances in Rheometry for process relevant material characterisation
The Very Basics: Mixing Low Viscosity Newtonian Fluids
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The very basics – Po = f(Re).
Chhabra & Richardson (2008), Non-Newtonian Flow and Applied Rheology: Engineering Applications. Elsevier 2008.
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The very basics – Po = f(Re).
Dimensional Analysis: P = f(μ, ρ, D, DT ,N, g, geometric dimensions)
𝑃
𝜌𝑁3𝐷5 = 𝑓𝜌𝑁𝐷2
𝜇,𝑁2𝐷
𝑔, 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑟𝑎𝑡𝑖𝑜𝑠
Power Number
Reynolds Number
Froude Number
Chhabra & Richardson (2008), Non-Newtonian Flow and Applied Rheology: Engineering Applications. Elsevier 2008.
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The very basics – Po = f(Re).
Chhabra & Richardson (2008), Non-Newtonian Flow and Applied Rheology: Engineering Applications. Elsevier 2008.
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The very basics – Po = f(Re).
Dimensional Analysis: P = f(μ, ρ, D, DT ,N, g, geometric dimensions)
𝑃
𝜌𝑁3𝐷5 = 𝑓𝜌𝑁𝐷2
𝝁,𝑁2𝐷
𝑔, 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑟𝑎𝑡𝑖𝑜𝑠
Viscosity
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The Very Basics – Measuring Viscosity.
𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 =𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠
𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛 𝑟𝑎𝑡𝑒
𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑠ℎ𝑒𝑎𝑟 𝑓𝑜𝑟𝑐𝑒
𝑎𝑟𝑒𝑎
𝜎 =𝐹
𝐴
𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛 𝑟𝑎𝑡𝑒 = 𝛿𝜃
𝛿𝑡≈𝛿𝑢
𝛿𝑦
i.e. the velocity gradient
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The Very Basics – Measuring Viscosity.
1 Barnes (2000) Handbook of Elementary Rheology, INNFM 2 Brookfield DV1 3 TA Instruments, AR-G2
U-tube Viscometer1
Flow Cup1
Basic Viscometer2
Rheometer3
£2k £30k – 80k £200 £100 - 150
NOTE: Other viscometers/rheometers are available
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The Very Basics – Measuring Viscosity.
1 Barnes (2000) Handbook of Elementary Rheology, INNFM 2 Brookfield DV1 3 TA Instruments, AR-G2
U-tube Viscometer1
Flow Cup1
Basic Viscometer2
Rheometer3
£2k £30k – 80k £200 £100 - 150
NOTE: Other viscometers/rheometers are available
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Recent advances in Rheometry for process relevant material characterisation
Complex Fluids
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What is a complex fluid anyway?
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What is a complex fluid anyway?
Non-Newtonian Fluid: Apparent viscosity depends on shear rate
Newtonian Fluid
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What is a complex fluid anyway?
Non-Newtonian Fluid: Apparent viscosity depends on shear rate
Newtonian Fluid Shear Thinning
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What is a complex fluid anyway?
Non-Newtonian Fluid: Apparent viscosity depends on shear rate
Newtonian Fluid Shear Thinning Shear Thickening
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What is a complex fluid anyway?
Non-Newtonian Fluid: Apparent viscosity depends on shear rate
Newtonian Fluid Shear Thinning Shear Thickening Yield Stress
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Characterising an inelastic non-Newtonian Fluid
𝜂 𝛾 = 𝑘2𝛾 𝑛−1
The Power Law
n is the power law index
n < 1 : Shear Thinning
n = 1 : Newtonian
n > 1 : Shear Thickening
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Recent advances in Rheometry for process relevant material characterisation
Mixing (inelastic) non-Newtonian Fluids
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Metzner & Otto (1957)
Is there a relationship between Po and Re for inelastic non-Newtonian fluids?
Question 1: What viscosity should be used in determining the Reynolds Number?
Question 2: What is the characteristic shear rate of the mixer?
1) Using the fluid & mixer of interest, determine Po. 2) Determine Re from a Newtonian Po(Re) curve (for the same geometry) 3) Obtain an estimate of an equivalent viscosity from the value of Re. 4) Determine the characteristic shear rate from the flow curve 5) Determine ks from the equation 6) Use Po(Re) curves (Re < 10) to determine Po given that 𝜇𝑒𝑓𝑓 = 𝑓 𝑘𝑠𝑁
𝑘𝑠 = 𝛾 𝑐 𝑁
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Metzner & Otto (1957)
1) Using the fluid & mixer of interest, determine Po. 2) Determine Re from a Newtonian Po(Re) curve (for the same geometry) 3) Obtain an estimate of an equivalent viscosity from the value of Re. 4) Determine the characteristic shear rate from the flow curve 5) Determine ks from the equation 6) Use Po(Re) curves (Re < 10) to determine Po given that 𝜇𝑒𝑓𝑓 = 𝑓 𝑘𝑠𝑁
𝑘𝑠 = 𝛾 𝑐 𝑁
Generally gives adequate predictions of Power consumption PROVIDED that the value of ks is determined for a fluid and geometry that closely relate to the application.
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Recent advances in Rheometry for process relevant material characterisation
Complex Fluids II: Elasticity
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What is a complex fluid anyway?
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What is a complex fluid anyway?
Video courtesy of the Institute of Non-Newtonian Fluid Mechanics
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What is a complex fluid anyway?
Material has a characteristic relaxation time, 𝜆
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What is a complex fluid anyway?
Material has a characteristic relaxation time, 𝜆
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What is a complex fluid anyway?
The Deborah & Weissenberg Numbers can be used to determine the extent to which elasticity will affect a process
Characteristic time of material Characteristic time of the process
𝐷𝑒 =𝜆
𝑇
𝑊𝑖 =λ𝑈
𝐿
Weissenberg number is used where the material undergoes a time and space invariant strain rate.
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What is a complex fluid anyway?
The Deborah & Weissenberg Numbers can be used to determine the extent to which elasticity will affect a process
Characteristic time of material Characteristic time of the process
𝐷𝑒 =𝜆
𝑇
De < 1 : Process time is longer than relaxation time and coils can completely relax giving rise to viscous flow behaviour
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What is a complex fluid anyway?
The Deborah & Weissenberg Numbers can be used to determine the extent to which elasticity will affect a process
Characteristic time of material Characteristic time of the process
𝐷𝑒 =𝜆
𝑇
De > 1: The process time is not sufficient to allow relaxation of the coils and hence the flow process will be effected by the fluid elasticity.
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What is a complex fluid anyway?
The Deborah & Weissenberg Numbers can be used to determine the extent to which elasticity will affect a process
Characteristic time of material Characteristic time of the process
𝐷𝑒 =𝜆
𝑇
De > 1: The process time is not sufficient to allow relaxation of the coils and hence the flow process will be effected by the fluid elasticity.
How can we determine the relaxation time?
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Recent advances in Rheometry for process relevant material characterisation
Characterising Complex Fluids I: SAOS: A Traditional Approach
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Traditional Approaches: SAOS
For a Newtonian liquid: For a Hookean Solid:
𝜎 ∝ 𝛾
𝜎 ∝ 𝛾 𝛿 = 90°
𝛿 = 0°
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Traditional Approaches: SAOS
For a Newtonian liquid: For a Hookean Solid:
𝜎 ∝ 𝛾
𝜎 ∝ 𝛾
Ph
ase
An
gle
𝛿 = 90°
𝛿 = 0° 𝛿 = 90° 𝛿 = 0°
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Traditional Approaches: FTMS
How can I get information regarding as wide a range of frequency (time scales) as possible in as short as possible a time
Use Fourier Analysis……
Fourier Transform to extract Rheological Information at frequencies corresponding to the component waveforms.
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Traditional Approaches: Summary
“No satisfactory correlations are available enabling the estimation of power
consumption in viscoelastic fluids” Chhabra & Richardson (2008), Non-Newtonian Flow and
Applied Rheology: Engineering Applications. Elsevier 2008.
FLOW PROCESS Material with
complex rheology Controlled Stress Parallel Superposition Rheometry
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Recent advances in Rheometry for process relevant material characterisation
Characterising Complex Fluids II: Novel Approaches
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Recent Advances: Superposition Rheometry
SAOS (Quiescent)
CSPS (Flow Conditions)
G’ Storage Modulus
G’ Loss Modulus
d Balance of Loss and Storage moduli
G’|| Storage Modulus under CSPS
G’’|| Loss Modulus under CSPS
d|| Balance of Loss and Storage moduli under CSPS
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Recent Advances: Superposition Rheometry
Optimum balance between elastic and viscous properties appears
to exist but this is ONLY apparent under CSPS conditions
EPSRC Centre for Innovative Manufacturing in Large Area Electronics
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Recent Advances: Superposition Rheometry
Optimum balance between elastic and viscous properties appears
to exist but this is ONLY apparent under CSPS conditions
EPSRC Centre for Innovative Manufacturing in Large Area Electronics
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EPSRC Centre for Innovative Manufacturing in Large Area Electronics
Recent Advances: Superposition Rheometry
Optimum balance between elastic and viscous properties appears
to exist but this is ONLY apparent under CSPS conditions
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25/04/2017 Advanced Rheology for Printing Large Area
Electronics (ARPLAE) 40
Recent Advances: Superposition Rheometry
Ratio of energy loss to energy storage phenomena – Higher values – more “lossy” (viscous character). Lower values – dominated by energy storage (elastic character).
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25/04/2017 Advanced Rheology for Printing Large Area
Electronics (ARPLAE) 41
Recent Advances: Superposition Rheometry
Ratio of energy loss to energy storage phenomena – Higher values – more “lossy” (viscous character). Lower values – dominated by energy storage (elastic character).
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25/04/2017 Advanced Rheology for Printing Large Area
Electronics (ARPLAE) 42
Time to acquire spectrum using FT-CSPS < 30 s
Time to acquire equivalent spectrum using standard
CSPS > 6 min
Silver-based Functional Ink
Recent Advances: Superposition Rheometry
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25/04/2017 Advanced Rheology for Printing Large Area
Electronics (ARPLAE) 43
Silver-based Functional Ink
Recent Advances: Superposition Rheometry
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25/04/2017 Advanced Rheology for Printing Large Area
Electronics (ARPLAE) 44
Silver-based Functional Ink
Recent Advances: Superposition Rheometry
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25/04/2017 Advanced Rheology for Printing Large Area
Electronics (ARPLAE) 45
Silver-based Functional Ink
Recent Advances: Superposition Rheometry
Can we get MORE data, MORE quickly?
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More Recent Advances: OFR
Optimal Fourier Rheometry
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More Recent Advances: OFR
Optimal Fourier Rheometry
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Very Recent Advances: OWCh!
Optimally Windowed Chirp
Collaboration with Prof. G. McKinley (MIT) and Prof. C. Clasen (KU Leuven)
Original OFR waveform….. FFT require that the signal is periodic Wave time selected such that signal was initially and finally zero Derivative not periodic.
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Very Recent Advances: OWCh!
Optimally Windowed Chirp
Collaboration with Prof. G. McKinley (MIT) and Prof. C. Clasen (KU Leuven)
![Page 50: Recent advances in Rheometry for process relevant material ...1 Barnes (2000) Handbook of Elementary Rheology, INNFM 2 Brookfield DV1 3 TA Instruments, AR-G2 U-tube Viscometer1 1 Flow](https://reader036.fdocuments.us/reader036/viewer/2022071606/6143f6ad6cc38f259c25df10/html5/thumbnails/50.jpg)
Very Recent Advances: OWCh!
Optimally Windowed Chirp
Collaboration with Prof. G. McKinley (MIT) and Prof. C. Clasen (KU Leuven)
![Page 51: Recent advances in Rheometry for process relevant material ...1 Barnes (2000) Handbook of Elementary Rheology, INNFM 2 Brookfield DV1 3 TA Instruments, AR-G2 U-tube Viscometer1 1 Flow](https://reader036.fdocuments.us/reader036/viewer/2022071606/6143f6ad6cc38f259c25df10/html5/thumbnails/51.jpg)
Very Recent Advances: OWCh!
Optimally Windowed Chirp
Collaboration with Prof. G. McKinley (MIT) and Prof. C. Clasen (KU Leuven)
![Page 52: Recent advances in Rheometry for process relevant material ...1 Barnes (2000) Handbook of Elementary Rheology, INNFM 2 Brookfield DV1 3 TA Instruments, AR-G2 U-tube Viscometer1 1 Flow](https://reader036.fdocuments.us/reader036/viewer/2022071606/6143f6ad6cc38f259c25df10/html5/thumbnails/52.jpg)
Very Recent Advances: OWCh!
Optimally Windowed Chirp
Collaboration with Prof. G. McKinley (MIT) and Prof. C. Clasen (KU Leuven)
Possible to acquire detailed spectra in around 15s – the time normally taken to acquire data at a single moderate frequency.
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Recent advances in Rheometry for process relevant material characterisation
Summary & Future work ….
(Industrial engagement welcome…..)
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Future direction….. (collaborations / project partners welcome)
+ Superposition
Rheometry
Fast acquisition of full viscoelastic/relaxation time spectra UNDER PROCESS RELEVANT CONDITIONS
and the resulting influence on process performance, optimization and control
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Finally - (a few) take home points…
Viscous characteristics alone are often insufficient to characterise material behaviour. For mixing - established techniques are available for linking power requirements to flow for non-Newtonian fluids through ‘Newtonian Equivalents’. Elastic properties of liquids are very important and often dominate the materials response to deformation/flow. Mixing: No satisfactory correlations. Material relaxation times can be determined using traditional techniques (SAOS). Recent developments have allowed a significant improvement in the time required to measure the viscoelastic spectrum of a material. Further developments have allowed us to begin looking at the effect of flow on the relaxation spectrum of a material….. ……. these developments are a step towards REALLY ‘process relevant Rheometry’