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LABORATOIRE RHEOLOGIE ET PROCEDESLABORATOIRE RHEOLOGIE ET PROCEDESGrenoble INP Grenoble INP -- UJF UJF -- CNRS (UMR 5520)CNRS (UMR 5520)

INFLUENCE OF SURFACE PROPERTIESON THE CREEPING FLOW

OF A YIELD STRESS FLUID AROUND SPHERES

Laurent JOSSIC, Fiacre AHONGUIO et Albert MAGNIN

Viscoplastic fluids : From theory to application18 – 21 novembre 2013

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OUTLINEOUTLINE

Objectives

Experimental set-up

Bulk and interface behaviour of Carbopol gel

Results and discussionInfluence of slip on

- Drag coefficient- flow morphology

Concluding remarks

4

Flow of a yield stress fluid around a sphere

o Influence of the tribological conditions at the fluid/sphere interfaceo Drag coefficient and stability criteriono Flow morphology : size and shape of yielded and unyielded

regions

Frame of the study

o Very low controled velocity : no inertia o Plastic effects >> viscous effects >> inertia effectso Steady stateo Controled surface conditions : rough and smooth hydrophobic

OBJECTIVESOBJECTIVES

Literature

Andres (1961) Beris et al (1985) Attapatu et al. (1990,1995)Dolejs et al (1998) Beaulne et al (1997) Tabuteau et al. (2007)He et al (2001)… Yu et al (2007)… Putz et al. (2008)…

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EXPERIMENTAL SETEXPERIMENTAL SET--UPUP

U

Table movedat very low

controled velocity

LASER

Forcesensor

PasµmUsµm

100/200/1

0Inertiaeffects

Plasticeffects

Viscous effects<< <<

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MICROMICRO--GELS SUSPENSIONGELS SUSPENSION

micro-gels diameter : from 2 to 20 µm

Weight concentration : 1%, yield stress 100 Pa

(Piau, 2007)

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Roughsphere

Smooth hydrophobic

sphere

Roughness 200 µm 0.5 µm

Diameter 27.3 mm 23 mm

Mass 11.27 g 13.65 g

SPHERESSPHERES

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BULK BEHAVIOUR BULK BEHAVIOUR

10

100

1000

0,0001 0,001 0,01 0,1 1 10 100Shear rate (s-1)

Shea

r str

ess

(Pa)

Gel 1

Gel 2

Herschel-Bulkley model

00 siK n

00 siAdherence at the surface of the tools

Non thixotropic fluid Moller et al (2009)

Viscoelastic effects appear to be low : 10-2 < We < 8.10-2

if

if

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INTERFACE BEHAVIOURINTERFACE BEHAVIOUR

1

10

100

1000

0,0001 0,001 0,01 0,1 1 10 100

Apparent shear rate (s-1)

Shea

r str

ess

(Pa)

Gel 1 Rough surfaceGel 1 Smooth hydrophobic surface

Gel 2 Rough surfaceGel 2 mooth hydrophobic surfaceHerschel-Bulkley model

fit curve

Stresses at the wall decreases when fluid slips

Adherence at the surface of the tools

Slip at the surface of the tools

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SLIP MODELSLIP MODEL

m

s VV

1

00

0

''*

Meeker et al (2004)

Seth et al (2008)

0

0,05

0,1

0,15

0,2

0,25

0 10 20 30 40 50 60 70 80

Shear stress (Pa)

Slip

vel

ocity

(mm

/s)

Experimental data

Seth, Cloître and Bonnecaze model (2008)

smV /3,0*

Pa3'0

4,0m

'0

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DIMENSIONLESS NUMBERS DIMENSIONLESS NUMBERS

U

A

Fd

KdU nn

2

Re Reynolds Number :

ndUKOd 0Oldroyd Number :

gd

Y 0Yield stress/ gravity ratio :

AFCd d

0

*

Plastic drag coefficient :

Stabilitycriterion:

*3

2Cd

Ycrit

Slip model :

Flow index : n

0

0 '

*

UV

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DRAG COEFFICIENTDRAG COEFFICIENT

Od

Cd * Rough sphere

Smooth hydrophobic sphere

Ycrit =0.07

Ycrit =0.11

0

5

10

15

20

0 20 40 60 80 100Od

Cd*

Rough surfaceSmooth hydrophobic surfaceFit curve

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FLOW MORPHOLOGYFLOW MORPHOLOGY

Zam

Zav

U

Mobilerigidzone

Numerical modeling : flow field is symetric Beris et al (1985)

Shearedzone

Rs

Experimental results : flow field is asymetric Putz et al (2008)

Staticrigidzones

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STREAMLINESSTREAMLINES

Flowdirection

hup

hdown

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0

0,2

0,4

0,6

0,8

1

0 0,5 1 1,5 2

z/d

Uz/

U

Od=76

Od=12

UPSTREAM FLOWUPSTREAM FLOW

No significant influence of the Oldroyd number in the range considered

Rough surface

Flowdirection

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UPSTREAM FLOWUPSTREAM FLOW

0

0,2

0,4

0,6

0,8

1

0 0,5 1 1,5 2

Uz/

U

Rough sphere

Smooth hydrophobic sphere

z/d Od=12

Flowdirection

2d

Zup

)(53.0 smoothdhup )(55.0 rough

dhup

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DOWNSTREAM FLOWDOWNSTREAM FLOW

0

0,2

0,4

0,6

0,8

1

1,2

-2,5 -2 -1,5 -1 -0,5 0

z/d

Uz/

U

Rough sphereSmooth hydrophobic sphere

Od=12

Flowdirection

2d

Zdown

)(51.0 smoothdhup )(52.0 rough

dhup

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0

0,2

0,4

0,6

0,8

1

1,2

0 0,5 1 1,5

Uz/

U

Smooth hydrophobic sphere

Rough sphere

r/D

VELOCITY PROFILE IN THE EQUATOR PLANEVELOCITY PROFILE IN THE EQUATOR PLANE

Od=12

Flowdirection

2.1dRs

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SLIP VELOCITY ALONG THE WALLSLIP VELOCITY ALONG THE WALL

-90 -60 -30 0 30 60 90

U s/U

θ (°)

0.2

0.4

0.6

0.8

1

1.2

0

UpstreamDownstrea

Flowdirection

Us

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STRESSES ALONG THE WALLSTRESSES ALONG THE WALL

0

20

40

60

80

100

120

-90 -60 -30 0 30 60 90θ(°)

w (P

a)

0 = 79.4 Pa

's = 3 Pa

Flowdirection

w

Od=12

Od=77

Od=12

Od=77

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SHEAR AND NORMAL STRESSES CONTRIBUTIONSHEAR AND NORMAL STRESSES CONTRIBUTIONTO THE DRAG FORCETO THE DRAG FORCE

Newtonian fluid :

Stokes law

URUR

FF

dsPdsF

vp

Sr

Sd

42

2

p

v

FF

Viscoplastic fluid : S

rv dsF vdp FFF

Rough sphere :

Smooth hydrophobic sphere :

4.0p

v

FF

04.0p

v

FF

Pressure +Normalstresses

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Drag coefficients and stability criteria have been measured

Drag force is mainly governed by pressure and normal stresses

The shape and size of the sheared and static rigid zones have been measured

Flow field is asymetric

CONCLUSIONSCONCLUSIONS

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THANK YOUTHANK YOUFOR YOUR ATTENTIONFOR YOUR ATTENTION

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NEGATIVE WAKENEGATIVE WAKE

Rough surface Hydrophobicsmooth surface

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0,01

0,1

1

10

100

1000

0,0001 0,001 0,01 0,1 1 10

Shear rate (s-1)

t r (s

)

Experimental data

Fit curve Eq. (4)

0.0001 0.01 0.10.0010.01

0 1

0.0001

RELAXATION TIMERELAXATION TIME

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10

100

1000

Shear rate (s-1)

N 1 (P

a)

Experimental dataFit curve Eq. (8)

0.00010.00001 0.01 10.1 100100.001

NORMAL STRESSESNORMAL STRESSES

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PROFIL DE VITESSE AVALPROFIL DE VITESSE AVAL

0

0,2

0,4

0,6

0,8

1

1,2

1,4

-2,5 -2 -1,5 -1 -0,5 0

z/d

Uz/

U

Od=12

Od=77

Influence du nombre d’Oldroyd dans le cas d’une sphère rugueuse

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Surface rugueuse

Od = 12

CHAMP DE VITESSE AMONTCHAMP DE VITESSE AMONT

Surface lisse hydrophobe

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FLOW RECIRCULATIONFLOW RECIRCULATION

Od = 12

Rough surface Hydrophobicsmooth surface

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Od = 12

DOWNSTREAM STATIC RIGID ZONEDOWNSTREAM STATIC RIGID ZONE

Rough surface Hydrophobicsmooth surface