laurent jossic, fiacre ahonguio et albert...
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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
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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