The slipping effect during creeping flow of viscoplastic fluids around a circular cylinder has been investigated via numerical simulations. For the bulk behavior of the fluid, a Herschel–Bulkley law is considered. For the parietal behavior, an original and recent slip law based on an elastohydrodynamic lubrication model defined with a physical approach has been implemented. In particular, this law represents the behavior of Carbopol gels, which are commonly used during experimental studies on yield stress fluid mechanics and in industry. This law has two parameters that control the kinematic conditions at the fluid–structure interface. Variations in the plastic drag coefficient are given as a function of these parameters. It has been shown in particular the decreasing of the drag coefficient when there is slipping at the fluid–structure interface. The kinematic field has been analyzed and the evolution of rigid zones is illustrated. Results are provided for different slipping conditions ranging from the no-slip to the perfect-slip (PS) case. The sheared zone becomes smaller so the flow is more and more confined due to the slip, which induces modifications on the rigid zones. Some of the results are compared with existing asymptotic plastic drag coefficients and experimental data.

References

References
1.
Balmforth
,
N. J.
,
Frigaard
,
I. A.
, and
Ovarlez
,
G.
,
2014
, “
Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics
,”
Annu. Rev. Fluid Mech.
,
46
(
1
), pp.
121
146
.10.1146/annurev-fluid-010313-141424
2.
Daprà
,
I.
, and
Scarpi
,
G.
,
2011
, “
Pulsatile Poiseuille Flow of a Viscoplastic Fluid in the Gap Between Coaxial Cylinders
,”
ASME J. Fluids Eng.
,
133
(
8
), p.
081203
.10.1115/1.4003926
3.
Kalombo
,
J. J. N.
,
Haldenwang
,
R.
,
Chhabra
,
R. P.
, and
Fester
,
V. G.
,
2014
, “
Centrifugal Pump Derating for Non-Newtonian Slurries
,”
ASME J. Fluids Eng.
,
136
(
3
), p.
031302
.10.1115/1.4025989
4.
Barnes
,
H. A.
,
1999
, “
The Yield Stress—A Review or ‘παντα ρει’—Everything Flows?
,”
J. Non-Newtonian Fluid Mech.
,
81
(
1–2
), pp.
133
178
.10.1016/S0377-0257(98)00094-9
5.
Barnes
,
H. A.
,
1995
, “
A Review of the Slip (Wall Depletion) of Polymer Solutions, Emulsions and Particle Suspensions in Viscometers: Its Cause, Character, and Cure
,”
J. Non-Newtonian Fluid Mech.
,
56
(
3
), pp.
221
251
.10.1016/0377-0257(94)01282-M
6.
Sochi
,
T.
,
2011
, “
Slip at Fluid–Solid Interface
,”
Polym. Rev.
,
51
(
4
), pp.
309
340
.10.1080/15583724.2011.615961
7.
Sunarso
,
A.
,
Yamamoto
,
T.
, and
Mori
,
N.
,
2006
, “
Numerical Analysis of Wall Slip Effects on Flow of Newtonian and Non-Newtonian Fluids in Macro and Micro Contraction Channels
,”
ASME J. Fluids Eng.
,
129
(
1
), pp.
23
30
. 10.1115/1.2375127
8.
Ahonguio
,
F.
,
Jossic
,
L.
, and
Magnin
,
A.
,
2014
, “
Influence of Surface Properties on the Flow of a Yield Stress Fluid Around Spheres
,”
J. Non-Newtonian Fluid Mech.
,
206
, pp.
57
70
.10.1016/j.jnnfm.2014.03.002
9.
Darbouli
,
M.
,
Métivier
,
C.
,
Piau
,
J.-M.
,
Magnin
,
A.
, and
Abdelali
,
A.
,
2013
, “
Rayleigh-Bénard Convection for Viscoplastic Fluids
,”
Phys. Fluids (1994-present)
,
25
(
2
), p.
023101
.10.1063/1.4790521
10.
Magnin
,
A.
, and
Piau
,
J. M.
,
1990
, “
Cone-and-Plate Rheometry of Yield Stress Fluids. Study of an Aqueous Gel
,”
J. Non-Newtonian Fluid Mech.
,
36
, pp.
85
108
.10.1016/0377-0257(90)85005-J
11.
Wang
,
C. Y.
,
2012
, “
Brief Review of Exact Solutions for Slip-Flow in Ducts and Channels
,”
ASME J. Fluids Eng.
,
134
(
9
), p.
094501
.10.1115/1.4007232
12.
Piau
,
J.-M.
, and
Piau
,
M.
,
2005
, “
Letter to the Editor: Comment on ‘Origin of Concentric Cylinder Viscometry’ [J. Rheol. 49, 807–818 (2005)]. The Relevance of the Early Days of Viscosity, Slip at the Wall, and Stability in Concentric Cylinder Viscometry
,”
J. Rheol.
,
49
(
6
), pp.
1539
1550
.10.1122/1.2072087
13.
Meeker
,
S. P.
,
Bonnecaze
,
R. T.
, and
Cloitre
,
M.
,
2004
, “
Slip and Flow in Pastes of Soft Particles: Direct Observation and Rheology
,”
J. Rheol.
,
48
(
6
), pp.
1295
1320
.10.1122/1.1795171
14.
Seth
,
J. R.
,
Cloitre
,
M.
, and
Bonnecaze
,
R. T.
,
2008
, “
Influence of Short-Range Forces on Wall-Slip in Microgel Pastes
,”
J. Rheol.
,
52
(
5
), pp.
1241
1268
.10.1122/1.2963135
15.
Piau
,
J.-M.
,
2007
, “
Carbopol Gels: Elastoviscoplastic and Slippery Glasses Made of Individual Swollen Sponges
,”
J. Non-Newtonian Fluid Mech.
,
144
(
1
), pp.
1
29
.10.1016/j.jnnfm.2007.02.011
16.
Mossaz
,
S.
,
Jay
,
P.
, and
Magnin
,
A.
,
2012
, “
Experimental Study of Stationary Inertial Flows of a Yield-Stress Fluid Around a Cylinder
,”
J. Non-Newtonian Fluid Mech.
,
189–190
, pp.
40
52
. 10.1016/j.jnnfm.2012.10.001
17.
Seth
,
J. R.
,
Locatelli-Champagne
,
C.
,
Monti
,
F.
,
Bonnecaze
,
R. T.
, and
Cloitre
,
M.
,
2012
, “
How do Soft Particle Glasses Yield and Flow Near Solid Surfaces?
,”
Soft Matter
,
8
(
1
), pp.
140
148
.10.1039/c1sm06074k
18.
Métivier
,
C.
, and
Magnin
,
A.
,
2011
, “
The Effect of Wall Slip on the Stability of the Rayleigh–Bénard Poiseuille Flow of Viscoplastic Fluids
,”
J. Non-Newtonian Fluid Mech.
,
166
(
14–15
), pp.
839
846
.10.1016/j.jnnfm.2011.04.017
19.
Métivier
,
C.
,
Rharbi
,
Y.
,
Magnin
,
A.
, and
Bou Abboud
,
A.
,
2012
, “
Stick-Slip Control of the Carbopol Microgels on Polymethyl Methacrylate Transparent Smooth Walls
,”
Soft Matter
,
8
(
28
), pp.
7365
7367
. 10.1039/c2sm26244d
20.
Navier
,
C. L. M. H.
,
1823
,
Mémoire sur les Lois du Mouvement des Fluides
,
Memoires de l'Academie Royale des Sciences de l'Institut de France
, Paris, pp.
389
440
.
21.
Damianou
,
Y.
,
Philippou
,
M.
,
Kaoullas
,
G.
, and
Georgiou
,
G. C.
,
2014
, “
Cessation of Viscoplastic Poiseuille Flow With Wall Slip
,”
J. Non-Newtonian Fluid Mech.
,
203
, pp.
24
37
.10.1016/j.jnnfm.2013.10.004
22.
Lawal
,
A.
, and
Kalyon
,
D. M.
,
1997
, “
Viscous Heating in Nonisothermal Die Flows of Viscoplastic Fluids With Wall Slip
,”
Chem. Eng. Sci.
,
52
(
8
), pp.
1323
1337
.10.1016/S0009-2509(96)00486-1
23.
Lawal
,
A.
, and
Kalyon
,
D. M.
,
1997
, “
Nonisothermal Extrusion Flow of Viscoplastic Fluids With Wall Slip
,”
Int. J. Heat Mass Transfer
,
40
(
16
), pp.
3883
3897
.10.1016/S0017-9310(97)00016-1
24.
Tang
,
H. S.
, and
Kalyon
,
D. M.
,
2004
, “
Estimation of the Parameters of Herschel–Bulkley Fluid Under Wall Slip Using a Combination of Capillary and Squeeze Flow Viscometers
,”
Rheol. Acta
,
43
(
1
), pp.
80
88
.10.1007/s00397-003-0322-y
25.
Pearson
,
J. R. A.
, and
Petrie
,
C. J. S.
,
1965
,
Proceedings of the Fourth International Congress on Rheology
,
Wiley
,
New York
.
26.
Fortin
,
A.
,
Côté
,
D.
, and
Tanguy
,
P. A.
,
1991
, “
On the Imposition of Friction Boundary Conditions for the Numerical Simulation of Bingham Fluid Flows
,”
Comput. Methods Appl. Mech. Eng.
,
88
(
1
), pp.
97
109
.10.1016/0045-7825(91)90234-W
27.
Roquet
,
N.
,
2000
, “
Résolution Numérique d’écoulement à Effets de Seuil Par Éléments Finis Mixtes et Adaptation de Maillage
,” Ph.D. thesis, Université de Grenoble, Grenoble.
28.
Roquet
,
N.
, and
Saramito
,
P.
,
2008
, “
An Adaptive Finite Element Method for Viscoplastic Flows in a Square Pipe With Stick–Slip at the Wall
,”
J. Non-Newtonian Fluid Mech.
,
155
(
3
), pp.
101
115
.10.1016/j.jnnfm.2007.12.003
29.
Tokpavi
,
D. L.
,
Magnin
,
A.
, and
Jay
,
P.
,
2008
, “
Very Slow Flow of Bingham Viscoplastic Fluid Around a Circular Cylinder
,”
J. Non-Newtonian Fluid Mech.
,
154
(
1
), pp.
65
76
.10.1016/j.jnnfm.2008.02.006
30.
Mitsoulis
,
E.
,
2004
, “
On Creeping Drag Flow of a Viscoplastic Fluid Past a Circular Cylinder: Wall Effects
,”
Chem. Eng. Sci.
,
59
(
4
), pp.
789
800
.10.1016/j.ces.2003.09.041
31.
Deglo De Besses
,
B.
,
Magnin
,
A.
, and
Jay
,
P.
,
2003
, “
Viscoplastic Flow Around a Cylinder in an Infinite Medium
,”
J. Non-Newtonian Fluid Mech.
,
115
(
1
), pp.
27
49
.10.1016/S0377-0257(03)00169-1
32.
Papanastasiou
,
T. C.
,
1987
, “
Flows of Materials With Yield
,”
J. Rheol.
,
31
(
5
), pp.
385
404
.10.1122/1.549926
33.
Mossaz
,
S.
,
Jay
,
P.
, and
Magnin
,
A.
,
2010
, “
Criteria for the Appearance of Recirculating and Non-Stationary Regimes Behind a Cylinder in a Viscoplastic Fluid
,”
J. Non-Newtonian Fluid Mech.
,
165
(
21–22
), pp.
1525
1535
.10.1016/j.jnnfm.2010.08.001
34.
Burgos
,
G. R.
,
Alexandrou
,
A. N.
, and
Entov
,
V.
,
1999
, “
On the Determination of Yield Surfaces in Herschel–Bulkley Fluids
,”
J. Rheol.
,
43
(
3
), pp.
463
483
.10.1122/1.550992
35.
Jossic
,
L.
, and
Magnin
,
A.
,
2009
, “
Drag of an Isolated Cylinder and Interactions Between Two Cylinders in Yield Stress Fluids
,”
J. Non-Newtonian Fluid Mech.
,
164
(
1–3
), pp.
9
16
.10.1016/j.jnnfm.2009.07.002
36.
Randolph
,
M. F.
, and
Houlsby
,
G. T.
,
1984
, “
The Limiting Pressure on a Circular Pile Loaded Laterally in Cohesive Soil
,”
Géotechnique
,
34
(
4
), pp.
613
623
. 10.1680/geot.1984.34.4.613
37.
Aubeny
,
C.
,
Shi
,
H.
, and
Murff
,
J.
,
2005
, “
Collapse Loads for a Cylinder Embedded in Trench in Cohesive Soil
,”
Int. J. Geomech.
,
5
(
4
), pp.
320
325
.10.1061/(ASCE)1532-3641(2005)5:4(320)
38.
Murff
,
J. D.
,
1989
, “
Pipe Penetration in Cohesive Soil
,”
Géotechnique
,
39
(
2
), pp.
213
229
. 10.1680/geot.1989.39.2.213
39.
Zollo
,
R. F.
,
1997
, “
Fiber-Reinforced Concrete: An Overview After 30 Years of Development
,”
Cem. Concr. Compos.
,
19
(
2
), pp.
107
122
.10.1016/S0958-9465(96)00046-7
40.
Shah
,
S. P.
, and
Rangan
,
B. V.
,
1971
, “
Fiber Reinforced Concrete Properties
,”
ACI J. Proc.
,
68
(
2
), pp.
126
137
.10.1016/S0958-9465(96)00046-7
41.
Chhabra
,
R. P.
,
1993
,
Bubbles, Drops, and Particles in Non-Newtonian Fluids
,
CRC Press
,
Boca Raton
.
You do not currently have access to this content.