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

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

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 …….


The Very Basics: Mixing Low Viscosity Newtonian Fluids

The very basics – Po = f(Re).

Chhabra & Richardson (2008), Non-Newtonian Flow and Applied Rheology: Engineering Applications. Elsevier 2008.


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





Dimensional Analysis: P = f(μ, ρ, D, DT ,N, g, geometric dimensions)

𝑃

𝜌𝑁3𝐷5 = 𝑓𝜌𝑁𝐷2

𝝁,𝑁2𝐷

𝑔, 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑟𝑎𝑡𝑖𝑜𝑠

Viscosity

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


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


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


Complex Fluids

What is a complex fluid anyway?


Non-Newtonian Fluid: Apparent viscosity depends on shear rate

Newtonian Fluid



Newtonian Fluid Shear Thinning



Newtonian Fluid Shear Thinning Shear Thickening



Newtonian Fluid Shear Thinning Shear Thickening Yield Stress

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


Mixing (inelastic) non-Newtonian Fluids

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

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.


Complex Fluids II: Elasticity



Video courtesy of the Institute of Non-Newtonian Fluid Mechanics


Material has a characteristic relaxation time, 𝜆


Material has a characteristic relaxation time, 𝜆


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.




𝐷𝑒 =𝜆

𝑇

De < 1 : Process time is longer than relaxation time and coils can completely relax giving rise to viscous flow behaviour




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.




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?


Characterising Complex Fluids I: SAOS: A Traditional Approach

Traditional Approaches: SAOS

For a Newtonian liquid: For a Hookean Solid:

𝜎 ∝ 𝛾

𝜎 ∝ 𝛾 𝛿 = 90°

𝛿 = 0°

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°

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.

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


Characterising Complex Fluids II: Novel Approaches

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


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









25/04/2017 Advanced Rheology for Printing Large Area

Electronics (ARPLAE) 40


Ratio of energy loss to energy storage phenomena – Higher values – more “lossy” (viscous character). Lower values – dominated by energy storage (elastic character).




Ratio of energy loss to energy storage phenomena – Higher values – more “lossy” (viscous character). Lower values – dominated by energy storage (elastic character).



Time to acquire spectrum using FT-CSPS < 30 s

Time to acquire equivalent spectrum using standard

CSPS > 6 min

Silver-based Functional Ink














Can we get MORE data, MORE quickly?

More Recent Advances: OFR

Optimal Fourier Rheometry

More Recent Advances: OFR

Optimal Fourier Rheometry

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.













Possible to acquire detailed spectra in around 15s – the time normally taken to acquire data at a single moderate frequency.


Summary & Future work ….

(Industrial engagement welcome…..)

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

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’

Documents

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