Rheology and microstructure in concentrated non-Brownian suspensions

Frédéric Blanc, Talib Dbouk, Stany Gallier, Giovanni GhigliottiLaurent Lobry, François Peters, Elisabeth Lemaire

Ubiquitous suspensionssandcement

muds

Blood

Propergols

Stone

Model suspensions Spherical mono-dispersed particles nearly hard spheres buoyant particles

Model experiments: Local measurements of viscosity of normal stresses Of microstructure

Various behaviors various particle interactions various shapes and sizes effect of the flow

Main question: are there solid contacts betweenparticles? What is their effect?

Hydrodynamic collision, rigid particles reversible trajectory

But: the microstructure is anisotropic

trajectories are anisotropic

N spheres hydrodynamic Interactions Pine et al. Nature (2005)

contact Interactions Metzger & Butler Phys.Rev. E (2010)

Why perform local measurements ?

After migrationBefore migration

Outline

Vicosity measurement using PIV and PTVTransient behavior under shear reversalViscous and contact contribution to the

viscosityMicrostructure characterizationDependence on the particle concentrationQuantitative information on contacts

Normal stresses

PIV facility

PMMA particles + Cargille oil nparticules=nfluide

particules=fluide

Themostated box

R1=1.4cmR2=2.4cm

Suspensions and flow regime

0=1 Pa.s. 20%<<55%

Negligible Brownian motion

Negligible inertia

35 906 aPe 10 10

kT

2 29 6 4 2

p0 0

a RRe 10 10 Re 10 10

=55%=44%

PIV experiments2a=30µm0.25% fluorescent particles

PTV experiments 2a=170µmFluorescent suspending fluid

High shear deformations

Newtonian fluid2 2in out

2 2 2out in

R R 1(r) 2R R r

2(r)2 Lr

Migration toward the stator

vr

(r) rr

=44%

0.6 0.7 0.8 0.9 1

20

40

60

/R

/ 0

2000 revolutions

2 revolutions (first plateau)

0.7710 revolutions

cste

cste

Newtonian fluid2 2in out

2 2 2out in

R R 1(r) 2R R r

2(r)2 Lr

Migration toward the stator

=44%

High shear deformations

Viscosity vs particle concentration

Kriegger Dougherty :

02( )

1*

0 1 2 30

10

20

30

40

/

0

Transient response

t

0 1 2 30

10

20

30

40

/

0

Transient response

t

compression

Gadala-Maria and Acrivos (1980) Couette small gap

Kolli et al. (2002), Narumi et al. (2002)Torsionnal flow

Dilatat

ion

Variation with particle concentration

0.5 1 1.5 2 2.5

101

102

/

0

=0.30

=0.40

=0.444

=0.47

=0.50

0.3 0.4 0.50

0.2

0.4

0.6

0/min

(0/plateau)0.5

(0/plateau)0.5= - 2.117 + 1.124

0/min = - 1.243 + 0.667

*=0.538

*=0.531

Viscosité de plateau

Kriegger Dougherty

plateau 2

1( )

1*

Minimum viscosity

min1( )

1*

Mills & Snabre EPJ E (2009)4

3

hydro ( )1

*

Sierou & Brady JFM (2001)

Stokesian dynamics

Random suspension

0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

/ *

(0/

)PIV *=0.53SD *=0.64 [Sierou and Brady (2001)

Structural viscosity

0.1 0.2 0.3 0.4 0.5 0.60

0.2

0.4

0.6

0.8

1

pa

rt/pl

atea

u

0 1 2 30

10

20

30

40

/

0

part plateau min struct

struct

=0.44

Microsture characterization

fluorescent liquid

Particules 170µm

Laser sheet d30µm

R1=1.9cm

R1=2.4cm

=55%

PDF for =0

(r, )g(r, )

r/2a

<2a>=170 µm

compression

Dilatat

ion

=35%Parsi & Gadala-Maria J. Rheol. (1987)

Expérimental Numéric (DS)=32% Pe =1700

Gao et al. PRL (2010)

=40%

PDF for 0

PDF versus

Structure en aller-retour (1)

0 1 2 3 4 5 6 7 83

3.5

4

4.5

5

local

[

pa.s

]

0 2 4 6 80.3

0.35

0.4

moyen

[r

pm]

Retour

=35%

Aller

Da Cunha & Hinch (1996)

expérimental PDF f=5% interactions de paires

2(a+e)

PDF of diluted suspension

experimental PDF f=5% theoretical PDF

AFM200 nm

model 250 nm

PDF of diluted suspension

Normal stresses

• Experimental state of art

11

22

F=21S

33

Negative compressional normal stresses

1 11 22 1 0

2 22 33 2 0

NN

Gadala-Maria (1979) N1, N2

Zarraga J. Rheol. (2000) N1<0, N2<0

Singh & Nott J.F.M. (2003) N1<0, N2<0

Boyer, Couturier Guazzelli, Pouliquen (2011)

profilometry

s

N10 N2()<0

1) Normal stress differences

V J J

2

0

2a f ( )9

J p. Nott & Brady, J. Fluid Mech. (1994).Morris & Boulay, J. Rheol. (1999).

2) Particle normal stresses Experiment from Deboeuf et al. Phys. Rev. Lett. 102, 108301(2009)

Prasad D. & Kytomaa H.. Int J Multiphase Flow; 21(5):775 (1995)

Paroi semi-perméable

≠0=0

|P|=

colloïdes

Motivation : Shear induced migarationSuspension Balance Model :

Measurement of N1, N2 andTorsionnal flow

zv rh

rh

h

Capteurs directs 22 Capteurs à grille

Pf

h=2 mm

R=5.5 cm

Direct pressure sensors 22(r)

33 33 11 0r r

1. .e

22 0 R 1 2 1 2r(r) 2R

33(R)=pa=0

11

33

22

pii

p p11 22 1p p33 22 2

N

N

N1 et N2

p f f22 22 22 22Σ =Σ -Σ =Σ +P

fluid pressure sensors

Experiment (1)

SuspensionsPolystyrene particles (2a=40 ou 140 µm) 0.2<<0.5Mixture water, ucon oil, Zinc Bromide 1 Pa.s.

Stress controlled rheometerR=5.5 cm h2 mm

11 100 s

Protocol

t

40 s

20 s

Experiment (2)

Direct sensors Grid sensors

Experiment (3)direct sensors

22 R 1 2 1 2r(r) 2R

Experiment (4)

Grid sensors

Normal stress differences

1 11 22 1 0

2 22 33 2 0

NN

-N1/ -N2/

Normal stress differences comparison

Boyer Couturier GuazzelliPouliquen JFM (2011)

2

1+2 2

1+2 2 21 0

Some numerical results, Force Coupling Method

Hertz contact, rugosity 5 10-3 a 10 a

Measurement at center Average measurement

2 frictionless

1 friction (µ=0.5) 1 friction (µ=0.5)

1 frictionless

2 friction (µ=0.5)

2 friction (µ=0.5)

2 frictionless

1 frictionless

Comparison between numerical and experimental results

1 friction (µ=0.5)

1 frictionless

2 friction (µ=0.5)

2 frictionless

Role of friction on viscosity

Results ( )

p11

p 211 12

p11

p 211 12

p11 p11

p 211 12

Re-suspensionp33 Re-suspensionp33

0 0 p( ) 2 ( ) Q EpΣ

n 2

3

1 0 0( ) ( ) 0 0

0 0

Q 2=0.8 ; 3=0.5

p22

12

p11

12

0 0 p( ) 2 ( ) Q EpΣ

n 2

3

1 0 0( ) ( ) 0 0

0 0

Q 2=0.8 ; 3=0.5

p22

12

p11

12

pii

F

Boyer F., Guazzelli E. & Pouliquen O.Phys Rev Lett. 107 (2011)

p 110

/

stru

ct

=0.21

Déplétion angle

0 0 .1 0 .2 0 .3 0 .4 0 .50

0 .2

0 .4

0 .6

0 .8

1

Boyer et al.JFM 2011

1+2 2s 2a=140µm

0 0 .1 0 .2 0 .3 0 .4 0 .50

0 .2

0 .4

0 .6

0 .8

1

Boyer et al.JFM 2011

1+2 2s

1+2 2s 2a=140µm

Rheology-microstructure

Conclusions / Perspectives

Coupling between rheology and microstructure(0.5, hmax 10 min )

Importance of the contact forces Change the particle rugosity

Study of emulsuions

Difficulties of measuring the bulk properties of a suspension, effect of confinementNumerical simulations and back-and-forth with experiments

Nanoparticlesgraftted