We simulate a dense athermal suspension of soft particles sheared between hard walls of a prescribed roughness profile, fully accounting for the fluid mechanics of the solvent between the particles and for the solid mechanics of changes in the particle shapes. We, thus, capture the widely observed rheological phenomenon of wall slip. For imposed stresses below the material’s bulk yield stress, we show the slip to be dominated by a thin solvent layer of high shear at the wall. At higher stresses, it is augmented by an additional contribution from the fluidization of the first few layers of particles near the wall. By systematically varying the wall roughness, we quantify a suppression of slip with increasing roughness. We also elucidate the effects of slip on the dynamics of yielding following the imposition of constant shear stress, characterizing the timescales at which bulk yielding arises and at which slip first sets in.

1.
Seth
,
J. R.
,
L.
Mohan
,
C.
Locatelli-Champagne
,
M.
Cloitre
, and
R. T.
Bonnecaze
, “
A micromechanical model to predict the flow of soft particle glasses
,”
Nat. Mater.
10
,
838
843
(
2011
).
2.
Cohen-Addad
,
S.
, and
R.
Höhler
, “
Rheology of foams and highly concentrated emulsions
,”
Curr. Opin. Colloid Interface Sci.
19
,
536
548
(
2014
).
3.
Fujii
,
S.
, and
W.
Richtering
, “
Size and viscoelasticity of spatially confined multilamellar vesicles
,”
Eur. Phys. J. E
19
,
139
148
(
2006
).
4.
Cloitre
,
M.
, and
D.
Vlassopoulos
, Block copolymers in external fields: Rheology, flow-induced phenomena, and applications, in Applied Polymer Rheology: Polymeric Fluids with Industrial Applications (Wiley, New York, 2011), pp. 209–239.
5.
Vlassopoulos
,
D.
, and
G.
Fytas
, “From polymers to colloids: Engineering the dynamic properties of hairy particles,” in High Solid Dispersions (Springer, Brelin, 2009), pp. 1–54.
6.
Divoux
,
T.
,
C.
Barentin
, and
S.
Manneville
, “
From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids
,”
Soft Matter
7
,
8409
8418
(
2011
).
7.
Bonn
,
D.
,
M. M.
Denn
,
L.
Berthier
,
T.
Divoux
, and
S.
Manneville
, “
Yield stress materials in soft condensed matter
,”
Rev. Mod. Phys.
89
,
035005
(
2017
).
8.
Divoux
,
T.
,
D.
Tamarii
,
C.
Barentin
,
S.
Teitel
, and
S.
Manneville
, “
Yielding dynamics of a Herschel–Bulkley fluid: A critical-like fluidization behaviour
,”
Soft Matter
8
,
4151
4164
(
2012
).
9.
Cloitre
,
M.
, and
R. T.
Bonnecaze
, “
A review on wall slip in high solid dispersions
,”
Rheol. Acta
56
,
283
305
(
2017
).
10.
Barnes
,
H. A.
, “
A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: Its cause, character, and cure
,”
J. Nonnewton. Fluid Mech.
56
,
221
251
(
1995
).
11.
Vinogradov
,
G.
,
G.
Froishteter
,
K.
Trilisky
, and
E.
Smorodinsky
, “
The flow of plastic disperse systems in the presence of the wall effect
,”
Rheol. Acta
14
,
765
775
(
1975
).
12.
Vinogradov
,
G.
,
G.
Froishteter
, and
K.
Trilisky
, “
The generalized theory of flow of plastic disperse systems with account of the wall effect
,”
Rheol. Acta
17
,
156
165
(
1978
).
13.
Dimitriou
,
C. J.
, and
G. H.
McKinley
, “
A comprehensive constitutive law for waxy crude oil: A thixotropic yield stress fluid
,”
Soft Matter
10
,
6619
6644
(
2014
).
14.
Meeker
,
S. P.
,
R. T.
Bonnecaze
, and
M.
Cloitre
, “
Slip and flow in pastes of soft particles: Direct observation and rheology
,”
J. Rheol.
48
,
1295
1320
(
2004
).
15.
Joseph
,
D. D.
,
R.
Bai
,
K.
Chen
, and
Y. Y.
Renardy
, “
Core-annular flows
,”
Annu. Rev. Fluid Mech.
29
,
65
90
(
1997
).
16.
Stokes
,
J. R.
,
M. W.
Boehm
, and
S. K.
Baier
, “
Oral processing, texture and mouthfeel: From rheology to tribology and beyond
,”
Curr. Opin. Colloid Interface Sci.
18
,
349
359
(
2013
).
17.
Roman
,
S.
,
A.
Merlo
,
P.
Duru
,
F.
Risso
, and
S.
Lorthois
, “
Going beyond 20 μm-sized channels for studying red blood cell phase separation in microfluidic bifurcations
,”
Biomicrofluidics
10
,
034103
(
2016
).
18.
Yoshimura
,
A.
, and
R. K.
Prud’homme
, “
Wall slip corrections for couette and parallel disk viscometers
,”
J. Rheol.
32
,
53
67
(
1988
).
19.
Meeker
,
S. P.
,
R. T.
Bonnecaze
, and
M.
Cloitre
, “
Slip and flow in soft particle pastes
,”
Phys. Rev. Lett.
92
,
198302
(
2004
).
20.
Poumaere
,
A.
,
M.
Moyers-González
,
C.
Castelain
, and
T.
Burghelea
, “
Unsteady laminar flows of a carbopol® gel in the presence of wall slip
,”
J. Nonnewton. Fluid Mech.
205
,
28
40
(
2014
).
21.
Salmon
,
J.-B.
,
L.
Bécu
,
S.
Manneville
, and
A.
Colin
, “
Towards local rheology of emulsions under couette flow using dynamic light scattering
,”
Eur. Phys. J. E
10
,
209
221
(
2003
).
22.
Geraud
,
B.
,
L.
Bocquet
, and
C.
Barentin
, “
Confined flows of a polymer microgel
,”
Eur. Phys. J. E
36
,
30
(
2013
).
23.
Péméja
,
J.
,
B.
Géraud
,
C.
Barentin
, and
M.
Le Merrer
, “
Wall slip regimes in jammed suspensions of soft microgels
,”
Phys. Rev. Fluids
4
,
033301
(
2019
).
24.
Seth
,
J. R.
,
C.
Locatelli-Champagne
,
F.
Monti
,
R. T.
Bonnecaze
, and
M.
Cloitre
, “
How do soft particle glasses yield and flow near solid surfaces?
,”
Soft Matter
8
,
140
148
(
2012
).
25.
Pérez-González
,
J.
,
J.
López-Durán
,
B.
Marín-Santibáñez
, and
F.
Rodríguez-González
, “
Rheo-PIV of a yield-stress fluid in a capillary with slip at the wall
,”
Rheol. Acta
51
,
937
946
(
2012
).
26.
Mansard
,
V.
,
L.
Bocquet
, and
A.
Colin
, “
Boundary conditions for soft glassy flows: Slippage and surface fluidization
,”
Soft Matter
10
,
6984
6989
(
2014
).
27.
Zhang
,
X.
,
E.
Lorenceau
,
P.
Basset
,
T.
Bourouina
,
F.
Rouyer
,
J.
Goyon
, and
P.
Coussot
, “
Wall slip of soft-jammed systems: A generic simple shear process
,”
Phys. Rev. Lett.
119
,
208004
(
2017
).
28.
Zhang
,
X.
,
E.
Lorenceau
,
T.
Bourouina
,
P.
Basset
,
T.
Oerther
,
M.
Ferrari
,
F.
Rouyer
,
J.
Goyon
, and
P.
Coussot
, “
Wall slip mechanisms in direct and inverse emulsions
,”
J. Rheol.
62
,
1495
1513
(
2018
).
29.
Divoux
,
T.
,
V.
Lapeyre
,
V.
Ravaine
, and
S.
Manneville
, “
Wall slip across the jamming transition of soft thermoresponsive particles
,”
Phys. Rev. E
92
,
060301(R)
(
2015
).
30.
Divoux
,
T.
,
D.
Tamarii
,
C.
Barentin
, and
S.
Manneville
, “
Transient shear banding in a simple yield stress fluid
,”
Phys. Rev. Lett.
104
,
208301
(
2010
).
31.
Grenard
,
V.
,
T.
Divoux
,
N.
Taberlet
, and
S.
Manneville
, “
Timescales in creep and yielding of attractive gels
,”
Soft Matter
10
,
1555
1571
(
2014
).
32.
Gibaud
,
T.
,
C.
Barentin
,
N.
Taberlet
, and
S.
Manneville
, “
Shear-induced fragmentation of laponite suspensions
,”
Soft Matter
5
,
3026
3037
(
2009
).
33.
Gibaud
,
T.
,
D.
Frelat
, and
S.
Manneville
, “
Heterogeneous yielding dynamics in a colloidal gel
,”
Soft Matter
6
,
3482
3488
(
2010
).
34.
Gibaud
,
T.
,
C.
Barentin
, and
S.
Manneville
, “
Influence of boundary conditions on yielding in a soft glassy material
,”
Phys. Rev. Lett.
101
,
258302
(
2008
).
35.
Kurokawa
,
A.
,
V.
Vidal
,
K.
Kurita
,
T.
Divoux
, and
S.
Manneville
, “
Avalanche-like fluidization of a non-Brownian particle gel
,”
Soft Matter
11
,
9026
9037
(
2015
).
36.
Perge
,
C.
,
N.
Taberlet
,
T.
Gibaud
, and
S.
Manneville
, “
Time dependence in large amplitude oscillatory shear: A rheo-ultrasonic study of fatigue dynamics in a colloidal gel
,”
J. Rheol.
58
,
1331
1357
(
2014
).
37.
Goyon
,
J.
,
A.
Colin
,
G.
Ovarlez
,
A.
Ajdari
, and
L.
Bocquet
, “
Spatial cooperativity in soft glassy flows
,”
Nature
454
,
84
87
(
2008
).
38.
Davies
,
G.
, and
J.
Stokes
, “
Thin film and high shear rheology of multiphase complex fluids
,”
J. Nonnewton. Fluid Mech.
148
,
73
87
(
2008
).
39.
Nicolas
,
A.
, and
J.-L.
Barrat
, “
A mesoscopic model for the rheology of soft amorphous solids, with application to microchannel flows
,”
Faraday Discuss.
167
,
567
600
(
2013
).
40.
Seth
,
J. R.
,
M.
Cloitre
, and
R. T.
Bonnecaze
, “
Influence of short-range forces on wall-slip in microgel pastes
,”
J. Rheol.
52
,
1241
1268
(
2008
).
41.
Christel
,
M.
,
R.
Yahya
,
M.
Albert
, and
B. A.
Antoine
, “
Stick-slip control of the carbopol microgels on polymethyl methacrylate transparent smooth walls
,”
Soft Matter
8
,
7365
7367
(
2012
).
42.
Chan
,
H. K.
, and
A.
Mohraz
, “
A simple shear cell for the direct visualization of step-stress deformation in soft materials
,”
Rheol. Acta
52
,
383
394
(
2013
).
43.
Rahimian
,
A.
,
S. K.
Veerapaneni
, and
G.
Biros
, “
Dynamic simulation of locally inextensible vesicles suspended in an arbitrary two-dimensional domain, a boundary integral method
,”
J. Comput. Phys.
229
,
6466
6484
(
2010
).
44.
Derzsi
,
L.
,
D.
Filippi
,
G.
Mistura
,
M.
Pierno
,
M.
Lulli
,
M.
Sbragaglia
,
M.
Bernaschi
, and
P.
Garstecki
, “
Fluidization and wall slip of soft glassy materials by controlled surface roughness
,”
Phys. Rev. E
95
,
052602
(
2017
).
45.
Derzsi
,
L.
,
D.
Filippi
,
M.
Lulli
,
G.
Mistura
,
M.
Bernaschi
,
P.
Garstecki
,
M.
Sbragaglia
, and
M.
Pierno
, “
Wall fluidization in two acts: From stiff to soft roughness
,”
Soft Matter
14
,
1088
1093
(
2018
).
46.
Plimpton
,
S.
, “
Fast parallel algorithms for short-range molecular dynamics
,”
J. Comput. Phys.
117
,
1
19
(
1995
).
47.
Swope
,
W. C.
,
H. C.
Andersen
,
P. H.
Berens
, and
K. R.
Wilson
, “
A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters
,”
J. Chem. Phys.
76
,
637
649
(
1982
).
48.
Peskin
,
C. S.
, “
The immersed boundary method
,”
Acta Numerica
11
,
479
517
(
2002
).
49.
Bao
,
Y.
,
A.
Donev
,
B. E.
Griffith
,
D. M.
McQueen
, and
C. S.
Peskin
, “
An immersed boundary method with divergence-free velocity interpolation and force spreading
,”
J. Comput. Phys.
347
,
183
206
(
2017
).
50.
Yang
,
X.
,
X.
Zhang
,
Z.
Li
, and
G.-W.
He
, “
A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations
,”
J. Comput. Phys.
228
,
7821
7836
(
2009
).
51.
Newren
,
P.
, Enhancing the immersed boundary method: Stability, volume conservation and implicit solvers, Ph.D. thesis, University of Utah, 2007.
52.
Hemingway
,
E.
,
A.
Clarke
,
J.
Pearson
, and
S.
Fielding
, “
Thickening of viscoelastic flow in a model porous medium
,”
J. Nonnewton. Fluid Mech.
251
,
56
68
(
2018
).
53.
Derzsi
,
L.
,
D.
Filippi
,
G.
Mistura
,
M.
Pierno
,
M.
Lulli
,
M.
Sbragaglia
,
M.
Bernaschi
, and
P.
Garstecki
, “
Fluidization and wall slip of soft glassy materials by controlled surface roughness
,”
Phys. Rev. E
95
,
052602
(
2017
).
54.
Lemaître
,
A.
, and
C.
Caroli
, “
Rate-dependent avalanche size in athermally sheared amorphous solids
,”
Phys. Rev. Lett.
103
,
065501
(
2009
).
55.
Pelusi
,
F.
,
M.
Sbragaglia
,
A.
Scagliarini
,
M.
Lulli
,
M.
Bernaschi
, and
S.
Succi
, “
On the impact of controlled wall roughness shape on the flow of a soft material
,”
Europhys. Lett.
127
,
34005
(
2019
).
56.
See the supplementary material at https://doi.org/10.1122/8.0000171 for movies of the yielding dynamics in two sample packings with flat and rough walls.

Supplementary Material

You do not currently have access to this content.