RHEOLOGY AND FLOW-INDUCED STRUCTURES IN … › wp-content › uploads › 2009 › 11 › pm12_FSU-Jena_Navard.pdfII Rheology Rheology, term invented by Bingham in 1929: Rheology

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RHEOLOGY AND FLOW-INDUCED STRUCTURES IN POLYSACCHARIDE-BASED MATERIALS

Patrick NavardMines ParisTech

Materials Forming CenterCentre de Mise en Forme des Matériaux – CEMEF

Sophia-AntipolisFrance

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I Introduction

Polymers, including polysaccharides, are chemical species that can form many different organisation in space and time.

When subjected to a flow, these organisations can:• Remain unchanged• Change irreversibly• Change reversibly

Usually, experiments conducted under flow are performed in “blind”manner, i.e. without any indication of the organisational changes that are going on.

And flow is ALWAYS moving molecules from one place to another.

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I Introduction

One way to better understand which organisation is formed under flow is to perform some physical probing while flowing.

This is what is called rheo-physics.

In this talk we will • recall what is rheology• describe several complex fluids• give the basis of rheo-physics• give examples of flow-induced structure studies

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I. Introduction

II. Rheology

III. Complex fluids

IV. Rheo-physics

V. Examples of flow-induced structures

I Introduction

6(6)

CH2- CH2-

CH

2 -CH

2 -

CH2 -

CH2-CH2-

CH2-

CH 2-CH2-

CH

2 -CH2-CH2-

CH2-CH2- CH2-

CH 2-

CH 2-

CH2- CH

CH2-

CH

2-

CH2-

CH2- CH2-

CH2-CH2- CH2-CH2- CH2-

CH2-

CH 2-

CH 2-

CH2-

I Introduction

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Details do not matter

I Introduction

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Polymers: the different statesHermann STAUDINGER (Germany): Nobel prize in chemistry 1953

- polymer

Paul FLORY (USA): Nobel prize in chemistry 1974- physics and chemistry

Pierre Gilles de GENNES (France): Nobel prize in physics 1991- polymer dynamics

HEEGER, McDIARMID (USA), SHIRAKAWA (Japan), Nobel prize in physics 2000- conducting polymers

The different statestype of chain

movementstructure in space

I Introduction

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1- Type of chainLinear

f = 2

Branched

Cross-linked2 < f < 3

Functionality f : number of covalent bonds linking each unit to its neighbours. f drive the structure of the chain and for a large part the physical morphology

I Introduction

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2- Movement

At large scale (notion of glass transition)

At small scale (secondary transitions)

I Introduction

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Viscous (irreversible deformation)-liquid-solid

Gel or elastic network (reversible deformation)

3- Structure in space

- orientation

- order

3-a Not ordered Not oriented

I Introduction

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3-b Oriented Not orderedLiquid crystal (mesomorphic phases)

3-c Ordered Not orientedplastic crystals (CCl4)

3-d Oriented OrderedCrystal

I Introduction

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Simply by looking at a normal polymer, the amount of structures, morphologies, types of organisation is very large.Most of them can influence or change structures during flow.

Why is it important: • processing is always implying a flow.• flow is present in mixing, dissolving and most

preparation• flow is a tool to understand matter properties

and organisation

I Introduction

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II. Rheology

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II Rheology

Rheology, term invented by Bingham in 1929:Rheology is the study of flow and deformation of matter

We are thus considering the interrelation between stress (force over a surface), deformation and rate of deformation.

Uniaxial extension

Shear

Deformation

Rheology is a branch of mechanics. The relations between stress, deformation, rate of deformation are tensorial equations depending on time.

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II Rheology

Polymer are most mainly falling into three categories:

Viscous: stress is not a function of deformation, but of deformation rate (water, oil). Irreversible.

Plastic: stress is not a function of deformation rate, but of deformation (crystal). Irreversible.

Elastic: Reversible deformation (matter comes back to its initial position after stopping deformation)

A lot of materials are complex:• solid metals are visco-elasto-plastic• molten polymers are visco-elastic

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II Rheology

Uniaxial extension• Simpler to understand physically• Simpler to model• Can be easily added into the free energy equation describing

the materialBUT

• Very difficult to perform experiments

Shear• Difficult to understand and model since it couples extension

and rotationBUT

• Easy to perform experiments (capillary rheometers, rotational rheometers

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II Rheology

Rheometry

Conditions• Uniform fluid (same composition and properties in space, in

all the rheometer cell)

• No turbulence

• Laminar flow

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II Rheology

Rate of deformation in shear (shear rate)

Deformation : 0.2

shear rate time

104 s-1 2.10-5 second10 s-1 0.02 second10-1 s-1 2 seconds10-3 s-1 200 seconds

l

hhl

=γ

Shear deformation

timeγγ =&

Shear rate

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Linear regime (low shear rate)

Steady stateConstant viscosity

Newton law

Shear rate

Viscosity η

II Rheology

γση &=

γ&

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Non-linear regime

Steady state flow

Shear thinningeffect

II Rheology

log shear rate

log viscosity

11 −sθ

( )[ ] 2/)1(2

0

1−

∞

∞ +=−− n

γληηηη

&Ex of law: Carreau

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III. Complex fluids

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III Complex fluids

Let’s look at a series of complex polymer fluids

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steady extensional flow

a- Polymers alone

Single chain deformation

III Complex fluids

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Many long chainsEntanglements: topological constrains between chains

III Complex fluids

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Many long chainsEntanglements: topological constrains between chains

Chain orientation and chain stretching (decrease of entropy) will change the rheological response of the fluid

III Complex fluids

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III Complex fluids

b- Incompatible polymer blends

Globular

Layers

Co - continuous

Classical morphologies

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Grace curve (1982) :

III Complex fluids

Incompatible polymer blends: rupture of droplets

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III Complex fluids

Incompatible polymer blends: coalescence

PIB / PDMS

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III Complex fluids

c- Liquid crystalline polymers

Liquid crystal phases lies between the solid and isotropic phases.

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III Complex fluids

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Nematic Phase

• Molecules are rod-like. They can move as a fluid but they keep their main axis along a local common direction.

III Complex fluids

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III Complex fluids

d- Suspensions in polymer fluids

Dispersion of agglomerated particles (carbon black)

Suspension of rods (glass fibres)

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III Complex fluids

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IV. Rheo-physics

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Complex fluid = fluid where the structure changes under the action of flow

DeformationOrientation

CrystallisationFlow heterogeneities

Observation

IV Rheo-physics

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Rheo-physics = rheology + observation

Flow + Physical probing technique

In-situ study of the structure/morphology/orientation underflow

Determine relationships between:

PROCESSING

RHEOLOGY

FLOW MORPHOLOGY

PROPERTIES

IV Rheo-physics

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Objectives:

- To measure the structure induced by a flow in a complexmaterial

- polymers (solution, melts)- blends- phase separation- suspensions, colloids- liquid crystals

- To built adapted tools simulating processingconditions

FLOW

MATERIAL

PROBING TECHNIQUE

IV Rheo-physics

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• Transparent rheometers

Different flow geometries• shear (cone-plan, plate-plate, couette)

• elongation (opposite jets, four roller mill)

• Complex flows (dies, obstacles, …)

Flow geometries

IV Rheo-physics

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• Optical techniques (white light, laser, IR,...)– Optical microscopy (1 - 100 µm)– Light scattering (0,02 - 100 µm)– Birefringence– Dichroism– Polarization– Raman spectroscopy– IR spectroscopy– Diffraction

• X-rays (WAXS : 1 - 20 Å, SAXS : 20 - 1000 Å)– Scattering– Diffraction

• Neutrons (10 - 1000 Å)– Scattering

• NMR (nuclear magnetic resonance)– Imaging

IV Rheo-physics

Examples of useful physical techniques

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Examples of complex flows

Liquid cristalsPolymer flow

Birefringence

stress visualisation

Optics

visualisation of welding lines

IV Rheo-physics

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gap

Optical microscopy observations

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VClassical shear geometry

Counter-rotating shear geometry

The object is convected by flow.

Continuous observations ⇒ motion of the microscope at the same speed

The object is fixed in the laboratoryframework. Continuous observation of the object under shear is possible.

Counter-rotating shear cell

IV Rheo-physics

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• Advantages:– Observations in-situ– Fixed position of the object of interest– Work with low viscosity matrices around room temperature– Or with highly viscoelastic matrices at high temperature

R

ω sup

H

ω inf

HR)ω(ω

γ supinf ×+=&

Counter-rotating shear cell

IV Rheo-physics

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50µm

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

I / Im

ax

theta (deg)

300

250

200

150

100

50

00 5 10 15 20 25

angle polaire θ (degrés)

beamθ

Imax ≡ I (θ beam)

Polar angle θ (degrees)

I diff

(arb

itrar

yun

its)

Image analysis

White lightLaserSample Shear cell

Software

sizeInformation on shape

mechanismstimescale

10°

θ

Small-angle light scattering

IV Rheo-physics

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V. Examples of flow-induced structures

a- Dispersion of agglomeratesb- Liquid crystalline polymersc- Incompatible polymer blendsd- Flow-induced behaviour of gel particlese- Flow-induced organisation in yoghurt

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- study the effect of hydrodynamic parameters on dispersion of single pellets;

- determine dispersion criteria and laws;

- change the filler/matrix interactions and determine its role on dispersion;

- understand the role of infiltration on dispersion;

Applications:• tyres• filled polymers

Elastomer

Clusters ~ 100µm-a few mm

a- Dispersion of agglomerates

V Examples of flow-induced structures: dispersion of agglomerates

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Erosion

Rupture

Debonding

Collision

0

0,5

1

0 50000 100000 150000τ=ηγ

k erosioncτ α

0

1R

RuptureC ∝τ

( ) tγ ττ αRR τ),(R ErosionC

3t

300 &−=−∀

DWe a

debondingΓ

∝σ

V Examples of flow-induced structures: dispersion of agglomerates

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Nematic polymers are uniaxially oriented. Orientation is not fixed and many orientational defects are present. We have a polydomainstructure, with many orientation separated by orientation defects (disclinations)

b- Liquid crystalline polymers

V Examples of flow-induced structures: liquid crystalline polymers

splay twist

bent

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Starting point: a polydomainnematic

Under shear, all chains align, giving a uniaxially oriented material

Upon relaxation, a strange structure appears during a certain time


Crossed polarizers

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Different orientations like a composite


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Mixed shear and extensionStrain (and strain history) depends on position Slit flow, injection into moulds--transient flowFilling flow (with obstacle):

Weldline

Flow of liquid crystal polymers in complex geometries


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Mold filling: problem of weld lines


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Obstacle divides flow frontDivided fronts meet--what kinds of stresses and strains ? Expect elongation (velocity must be zero at obstacle)

Weld atobstacle

At side wall

Weld line

Obstacle

Air bubble

Weld line structure


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Orientation instabilities


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1 Mold filling2 Steady flow, crossed polars3 Steady flow, parralel polars

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Rupture

Deformation

At rest

Final morphology = result from competitionbetween hydrodynamicforces and interfacial

forces

AB

0m

0AB

m R

RCa

γγη

=γ

γη=

&&

c- Incompatible polymer blends

V Examples of flow-induced structures: incompatible polymer blends

Ca < Cacrit: small stable deformationCa = Cacrit: rupture in two dropsCa > Cacrit: affine long deformation

followed by rupture

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t = 0s

t = 0,6s

t = 2,6s

Shear of a 1% PDMS droplets suspended in PIB – Shear rate 10s-1


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t = 14,6s

t = 16,4s

t = 42,7s

Steady state


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Butterfly pattern

Pattern withrotational symmetry

Ellipsoidal pattern

Elongated pattern

Size distribution

Shape factor

Wavelength

Filament diameter

Rupture by Rayleigh instabilities

DL

Exact follow-up of morphology

evolution


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40000

Diameter (µm) 1% PDMS in PIB

Strainunits0

2

4

6

8

10

12

14

0

3 s-1

1 s-1

0,3 s-1

80000 200000

The lower is the shear rate: This is due the time to eject the fluid layer

the larger is the final size and the slower is the coalescence.

Convection Ejection ofinterparticular

fluid

Rupture of fluid film

Decrease of interfacial stress

coalescence


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Gel = biphasic system constituted by a tridimensional network swollen by solvant

stimulusNetworkSolvant

transport

MoleculeActive product release

Storage

Gel sensitive to pH stomach

Skin application : shear, compression….Drug release by mechanical

sollicitation?⇒ Observation: shear

particle deformationliquid release

Polyelectrolyte swollen in an aqueous solution of HPC

V Examples of flow-induced structures: flow of gel particles

d- Flow-induced behaviour of gel particles

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Stress ↑

At rest Deformation/Orientation Apparition of cones Lateral ejection of solvant

Transversal ejection of solvant

• Deformation controlled by the gel elasticity and interfacial stresses

GRCa 20forces elastic forces tensionlinterfaciaforces viscous* +Γ=+= γη &

Particle deformation Solvent release Solvent dispersion

PDMS

Gel particleswollen in solvent Solvent


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Behaviour of a droplet = multiphase system Droplet = starch granules swollen in water suspended in waterMatrix = PDMS

Droplet of suspension of starch granules

100µm

100µm

Droplet of a diluted suspension

100µm

100µm

Volume fract: ~ 10% Volume fract: ~ 100%

relationship between droplet deformation and organolepticproperties

Droplet of a concentrated suspension


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V Examples of flow-induced structures: yoghurt

Objective:

• see if the flow is homogeneous• See if it disrupts caseine aggregates• See how fat globules are behaving

Important information since flow is present during filling of pots.

e- Flow-induced organisation in yoghurt

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Huge local shear rate variations

020406080

100120140160

1 2 3 4 5

Zone of flow

Mea

sure

d sh

ear

rate

-im

pose

dsh

ear

rate

rat

io Zones of flow

1: around an obstacle.

2,3,4: passage through chanels

5: laminar flow, withoutobstacle (shear rate as the one imposed)


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Creaming

At high shear rates, fat droplets appear in the fluid

Fig 1. Illustration du phénomène d’écrémage dans un yoghourt Bio pendant le cisaillement (lespoches de graisse sont notées G, les agrégats de micelles de caséines A, le grossissement est de 10)


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CEMEF

http://www.cemef.mines-paristech.fr/

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RHEOLOGY AND FLOW-INDUCED STRUCTURES IN … › wp-content › uploads › 2009 › 11 › pm12_FSU-Jena_Navard.pdfII Rheology Rheology, term invented by Bingham in 1929: Rheology