Multi-phase flows, encountered in nature or in industry, exhibit non-trivial rheological properties, which we attempt to better understand thanks to model materials and appropriate rheometers. Unsaturated wet granular flows down a rough inclined plane turn out to be steady and uniform for a wide range of parameters, despite the cohesion and the grain aggregates. The cohesive Mohr–Coulomb yield criterion extended to inertial granular flows, with a cohesion stress dependent on the liquid content and an internal friction coefficient dependent on the inertial number, allows for predictions in good agreement with our experimental measurements, when one introduces a grain aggregate size, which defines the appropriate length and relaxation time scales in the inertial number. We found that the grain aggregate size depends not monotonically on the liquid content and does not scale with the cohesion length induced by the cohesion stress, due to the non-trivial distribution of the liquid within the granular material.

1.
Scheel
,
M.
,
R.
Seemann
,
M.
Brinkmann
,
M.
Di Michiel
,
A.
Sheppard
, and
S.
Herminghaus
, “
Liquid distribution and cohesion in wet granular assemblies beyond the capillary bridge regime
,”
J. Phys.: Condens. Matter
20
,
494236
(
2008
).
2.
Badetti
,
M.
,
A.
Fall
,
D.
Hautemayou
,
F.
Chevoir
,
P.
Aimedieu
,
S.
Rodts
, and
J.-N.
Roux
, “
Rheology and microstructure of unsaturated granular materials: Experiments and simulations
,”
J. Rheol.
62
,
1175
1186
(
2018
).
3.
Pierrat
,
P.
,
D. K.
Agrawal
, and
H. S.
Caram
, “
Effect of moisture on the yield locus of granular materials: Theory of shift
,”
Powder Technol.
99
,
220
227
(
1998
).
4.
Cleaver
,
J. A. S.
,
R. M.
Nedderman
, and
R. B.
Thorpe
, “
Accounting for granular material dilation during the operation of an annular shear cell
,”
Adv. Powder Technol.
11
,
385
400
(
2000
).
5.
Mitchell
,
J. K.
, and
K.
Soga
,
Fundamentals of Soil Behavior
(
John Wiley & Sons
,
New York
,
2005
), Vol. 3.
6.
Berger
,
N.
,
E.
Azéma
,
J.-F.
Douce
, and
F.
Radjai
, “
Scaling behaviour of cohesive granular flows
,”
Europhys. Lett.
112
,
64004
(
2015
).
7.
Boyer
,
F.
,
E.
Guazzelli
, and
O.
Pouliquen
, “
Unifying suspension and granular rheology
,”
Phys. Rev. Lett.
107
,
188301
(
2011
).
8.
Tapia
,
F.
,
O.
Pouliquen
, and
É.
Guazzelli
, “
Influence of surface roughness on the rheology of immersed and dry frictional spheres
,”
Phys. Rev. Fluids
4
,
104302
(
2019
).
9.
Rognon
,
P. G.
,
J.-N.
Roux
,
D.
Wolf
,
M.
Naaïm
, and
F.
Chevoir
, “
Rheophysics of cohesive granular materials
,”
Europhys. Lett.
74
,
644
650
(
2006
).
10.
Kovalcinova
,
L.
,
S.
Karmakar
,
M.
Schaber
,
A.-L.
Schuhmacher
,
M.
Scheel
,
M.
DiMichiel
,
M.
Brinkmann
,
R.
Seemann
, and
L.
Kondic
, “
Energy dissipation in sheared wet granular assemblies
,”
Phys. Rev. E
98
,
032905
(
2018
).
11.
Abramian
,
A.
,
L.
Staron
, and
P.-Y.
Lagrée
, “
The slumping of a cohesive granular column: Continuum and discrete modeling
,”
J. Rheol.
64
,
1227
1235
(
2020
).
12.
Abramian
,
A.
,
P.-Y.
Lagrée
, and
L.
Staron
, “
How cohesion controls the roughness of a granular deposit
,”
Soft Matter
17
,
10723
10729
(
2021
).
13.
Rognon
,
P. G.
,
J.-N.
Roux
,
M.
Naaim
, and
F.
Chevoir
, “
Dense flows of cohesive granular materials
,”
J. Fluid Mech.
596
,
21
47
(
2008
).
14.
Mandal
,
S.
,
M.
Nicolas
, and
O.
Pouliquen
, “
Insights into the rheology of cohesive granular media
,”
Proc. Nat. Acad. Sci. U.S.A.
117
,
8366
8373
(
2020
).
15.
Mitarai
,
N.
, and
F.
Nori
, “
Wet granular materials
,”
Adv. Phys.
55
,
1
45
(
2006
).
16.
Strauch
,
S.
, and
S.
Herminghaus
, “
Wet granular matter: A truly complex fluid
,”
Soft Matter
8
,
8271
8280
(
2012
).
17.
Andreotti
,
B.
,
Y.
Forterre
, and
O.
Pouliquen
,
Granular Media: Between Fluid and Solid
(
Cambridge University
,
Cambridge
,
2013
).
18.
Bocquet
,
L.
,
E.
Charlaix
,
S.
Ciliberto
, and
J.
Crassous
, “
Moisture-induced ageing in granular media and the kinetics of capillary condensation
,”
Nature
396
,
735
737
(
1998
).
19.
Pakpour
,
M.
,
M.
Habibi
,
P.
Møller
, and
D.
Bonn
, “
How to construct the perfect sandcastle
,”
Sci. Rep.
2
,
1
3
(
2012
).
20.
Tegzes
,
P.
,
T.
Vicsek
, and
P.
Schiffer
, “
Development of correlations in the dynamics of wet granular avalanches
,”
Phys. Rev. E
67
,
051303
(
2003
).
21.
Brewster
,
R.
,
G. S.
Grest
, and
A. J.
Levine
, “
Effects of cohesion on the surface angle and velocity profiles of granular material in a rotating drum
,”
Phys. Rev. E
79
,
011305
(
2009
).
22.
Jarray
,
A.
,
V.
Magnanimo
, and
S.
Luding
, “
Wet granular flow control through liquid induced cohesion
,”
Powder Technol.
341
,
126
139
(
2019
).
23.
Preud’Homme
,
N.
,
G.
Lumay
,
N.
Vandewalle
, and
E.
Opsomer
, “
Numerical measurement of flow fluctuations to quantify cohesion in granular materials
,”
Phys. Rev. E
104
,
064901
(
2021
).
24.
GDRMiDi
, “
On dense granular flows
,”
Eur. Phys. J. E
14
,
341
365
(
2004
).
25.
Da Cruz
,
F.
,
S.
Emam
,
M.
Prochnow
,
J.-N.
Roux
, and
F.
Chevoir
, “
Rheophysics of dense granular materials: Discrete simulation of plane shear flows
,”
Phys. Rev. E
72
,
021309
(
2005
).
26.
Cassar
,
C.
,
M.
Nicolas
, and
O.
Pouliquen
, “
Submarine granular flows down inclined planes
,”
Phys. Fluids
17
,
103301
(
2005
).
27.
Ovarlez
,
G.
,
F.
Bertrand
, and
S.
Rodts
, “
Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging
,”
J. Rheol.
50
,
259
292
(
2006
).
28.
Trulsson
,
M.
,
B.
Andreotti
, and
P.
Claudin
, “
Transition from the viscous to inertial regime in dense suspensions
,”
Phys. Rev. Lett.
109
,
118305
(
2012
).
29.
Amarsid
,
L.
,
J.-Y.
Delenne
,
P.
Mutabaruka
,
Y.
Monerie
,
F.
Perales
, and
F.
Radjai
, “
Viscoinertial regime of immersed granular flows
,”
Phys. Rev. E
96
,
012901
(
2017
).
30.
Coulomb
,
C. A.
, “
Sur une application des règles de maximis et minimis à quelques problèmes de statique, relatifs à l’architecture
,”
Mém. Math. Phys.
7
,
343
382
(
1773
).
31.
Jop
,
P.
,
Y.
Forterre
, and
O.
Pouliquen
, “
A constitutive law for dense granular flows
,”
Nature
441
,
727
730
(
2006
).
32.
Forterre
,
Y.
, and
O.
Pouliquen
, “
Flows of dense granular media
,”
Annu. Rev. Fluid Mech.
40
,
1
24
(
2008
).
33.
Gilabert
,
F.
,
J.-N.
Roux
, and
A.
Castellanos
, “
Computer simulation of model cohesive powders: Influence of assembling procedure and contact laws on low consolidation states
,”
Phys. Rev. E
75
,
011303
(
2007
).
34.
Khamseh
,
S.
,
J.-N.
Roux
, and
F.
Chevoir
, “
Flow of wet granular materials: A numerical study
,”
Phys. Rev. E
92
,
022201
(
2015
).
35.
Badetti
,
M.
,
A.
Fall
,
F.
Chevoir
, and
J.-N.
Roux
, “
Shear strength of wet granular materials: Macroscopic cohesion and effective stress – discrete numerical simulations, confronted to experimental measurements
,”
Eur. Phys. J. E
41
,
68
(
2018
).
36.
Vo
,
T. T.
,
S.
Nezamabadi
,
P.
Mutabaruka
,
J.-Y.
Delenne
, and
F.
Radjai
, “
Additive rheology of complex granular flows
,”
Nat. Commun.
11
,
1
8
(
2020
).
37.
Savage
,
S. B.
, “Granular flows down rough inclines—Review and extension,” in
Mechanics of Granular Materials
, Studies Applied Mechanics Vol. 7, edited by J. T. Jenkins and M. Satake (Elsevier, New York, 1983), pp. 261–282.
38.
Savage
,
S. B.
, “The mechanics of rapid granular flows,” in
Advances in Applied Mechanics
, edited by J. W. Hutchinson and T. Y. Wu (Elsevier, New York, 1984), Vol. 24, pp. 289–366.
39.
Pouliquen
,
O.
, and
N.
Renaut
, “
Onset of granular flows on an inclined rough surface: Dilatancy effects
,”
J. Phys. II
6
,
923
935
(
1996
).
40.
Saingier
,
G.
,
S.
Deboeuf
, and
P.-Y.
Lagrée
, “
On the front shape of an inertial granular flow down a rough incline
,”
Phys. Fluids
28
,
053302
(
2016
).
41.
Brewster
,
R.
,
G. S.
Grest
,
J. W.
Landry
, and
A. J.
Levine
, “
Plug flow and the breakdown of bagnold scaling in cohesive granular flows
,”
Phys. Rev. E
72
,
061301
(
2005
).
42.
Fournier
,
Z.
,
D.
Geromichalos
,
S.
Herminghaus
,
M. M.
Kohonen
,
F.
Mugele
,
M.
Scheel
,
M.
Schulz
,
B.
Schulz
,
C.
Schier
,
R.
Seemann
, and
A.
Skudelny
, “
Mechanical properties of wet granular materials
,”
J. Phys.: Condens. Matter
17
,
S477
(
2005
).
43.
Scheel
,
M.
,
R.
Seemann
,
M.
Brinkmann
,
M.
Di Michiel
,
A.
Sheppard
,
B.
Breidenbach
, and
S.
Herminghaus
, “
Morphological clues to wet granular pile stability
,”
Nat. Mater.
7
,
189
193
(
2008
).
44.
Raux
,
P. S.
, and
A.-L.
Biance
, “
Cohesion and agglomeration of wet powders
,”
Phys. Rev. Fluids
3
,
014301
(
2018
).
45.
Jop
,
P.
,
Y.
Forterre
, and
O.
Pouliquen
, “
Crucial role of sidewalls in granular surface flows: Consequences for the rheology
,”
J. Fluid Mech.
541
,
167
192
(
2005
).
46.
Freyssingeas
,
E.
,
M.-J.
Dalbe
, and
J.-C.
Géminard
, “
Flowers in flour: Avalanches in cohesive granular matter
,”
Phys. Rev. E
83
,
051307
(
2011
).
47.
Pouliquen
,
O.
, “
Scaling laws in granular flows down rough inclined planes
,”
Phys. Fluids
11
,
542
548
(
1999a
).
48.
Deboeuf
,
S.
,
E.
Lajeunesse
,
O.
Dauchot
, and
B.
Andreotti
, “
Flow rule, self-channelization, and levees in unconfined granular flows
,”
Phys. Rev. Lett.
96
,
158303
(
2006
).
49.
Pitois
,
O.
,
P.
Moucheront
, and
X.
Chateau
, “
Liquid bridge between two moving spheres: An experimental study of viscosity effects
,”
J. Colloid Interface Sci.
231
,
26
31
(
2000
).
50.
Chateau
,
X.
,
P.
Moucheront
, and
O.
Pitois
, “
Micromechanics of unsaturated granular media
,”
J. Eng. Mech.
128
,
856
863
(
2002
).
51.
Richefeu
,
V.
,
M. S.
El Youssoufi
,
R.
Peyroux
, and
F.
Radjai
, “
A model of capillary cohesion for numerical simulations of 3D polydisperse granular media
,”
Int. J. Numer. Anal. Methods Geomech.
32
,
1365
1383
(
2008
).
52.
Rumpf
,
H.
, “
Zur theorie der zugfestigkeit von agglomeraten bei kraftuebertragung an kontaktpunkten
,”
Chem. Ing. Tech.
42
,
538
540
(
1970
).
53.
Courrech du Pont
,
S.
,
P.
Gondret
,
B.
Perrin
, and
M.
Rabaud
, “
Wall effects on granular heap stability
,”
Europhys. Lett.
61
,
492
498
(
2003
).
54.
Mani
,
R.
,
D.
Kadau
,
D.
Or
, and
H. J.
Herrmann
, “
Fluid depletion in shear bands
,”
Phys. Rev. Lett.
109
,
248001
(
2012
).
55.
Mani
,
R.
,
D.
Kadau
, and
H. J.
Herrmann
, “
Liquid migration in sheared unsaturated granular media
,”
Granular Matter
15
,
447
454
(
2013
).
56.
Delenne
,
J.-Y.
,
V.
Richefeu
, and
F.
Radjai
, “
Liquid clustering and capillary pressure in granular media
,”
J. Fluid Mech.
762
,
R5
(
2015
).
57.
Roux
,
J.-N.
, “
A numerical toolkit to understand the mechanics of partially saturated granular materials
,”
J. Fluid Mech.
770
,
1
4
(
2015
).
58.
Gans
,
A.
,
O.
Pouliquen
, and
M.
Nicolas
, “
Cohesion-controlled granular material
,”
Phys. Rev. E
101
,
032904
(
2020
).
You do not currently have access to this content.