Granular flows continue to be a complex problem in nature and industrial sectors where solid particles exhibit solid, liquid, and gaseous behavior, in a manner which is often unpredictable locally or globally. In tribology, they have also been proposed as lubricants because of their liquid-like behavior in sliding contacts and due to their ability to carry loads and accommodate surface velocities. The present work attempts to model a granular Couette flow using a lattice-based cellular automata computational modeling approach. Cellular automata (CA) is a modeling platform for obtaining fast first-order approximations of the properties of many physical systems. The CA framework has the flexibility to employ rule-based mathematics, first-principle physics, or both to rapidly model physical processes, such as granular flows. The model developed in this work incorporates dissipative effects due to friction between particles and between particles and boundaries, in addition to the derivative effects of friction, namely particle spin. This new model also includes a rigorous and physically relevant treatment of boundary–particle interactions. The current work compares this new friction and spin inclusive CA model and the author’s previous frictionless CA model against experimental results for an annular shear cell. The effects of granular collision properties were also examined through parametric studies on particle–particle coefficient of restitution (COR) and coefficient of friction (COF), which is a unique and added capability of the friction inclusive model.

References

References
1.
Higgs
,
C. F.
, III
, and
Tichy
,
J.
, 2004, “
Granular Flow Lubrication: Continuum Modeling of Shear Behavior
,”
J. Tribol.
,
126
(
3
), pp.
499
510
.
2.
Yu
,
C.-M.
,
Craig
,
K.
, and
Tichy
,
J.
, 1994, “
Granular Collision Lubrication
,”
J. Rheol.
,
38
(
4
), pp.
921
936.
3.
Jaeger
,
H. M.
,
Nagel
,
S. R.
, and
Behringer
,
R. P.
, 1996, “
Granular Solids, Liquids, and Gases
,”
Rev. Mod. Phys.
,
68
(
4
), pp.
1259
1273
.
4.
Sawyer
,
W. G.
, and
Tichy
,
J. A.
, 2001, “
Lubrication With Granular Flow: Continuum Theory, Particle Simulations, Comparison With Experiment
,”
J. Tribol.
,
123
(
4
), pp.
777
784.
5.
Johnson
,
P. C.
, and
Jackson
,
R.
, 1987, “
Frictional-Collisional Constitutive Relations for Granular Materials, With Application to Plane Shearing
,”
J. Fluid Mech.
,
176
, pp.
67
93
.
6.
Jeng
,
Y.-R.
, and
Tsai
,
H.-J.
, 2005, “
Grain Flow for Rough Surfaces Considering Grain/Grain Collision Elasticity
,”
J. Tribol.
,
127
(
4
), pp.
837
844
.
7.
Fillot
,
N.
,
Iordanoff
,
I.
, and
Berthier
,
Y.
, 2004, “
A Granular Dynamic Model for the Degradation of Material
,”
J. Tribol.
,
126
(
3
), pp.
606
614
.
8.
Fillot
,
N.
,
Iordanoff
,
I.
, and
Berthier
,
Y.
, 2005, “
Simulation of Wear Through Mass Balance in a Dry Contact
,”
J. Tribol.
,
127
(
1
), pp.
230
237
.
9.
Ketterhagen
,
W.
,
Curtis
,
J.
,
Wassgren
,
C.
,
Kong
,
A.
,
Narayan
,
P.
, and
Hancock
,
B.
, 2007, “
Granular Segregation in Discharging Cylindrical Hoppers: A Discrete Element and Experimental Study
,”
Chem. Eng. Sci.
,
62
(
22
), pp.
6423
6439
.
10.
Anand
,
A.
,
Curtis
,
J.
,
Wassgren
,
C.
,
Hancock
,
B.
, and
Ketterhagen
,
W.
, 2008, “
Predicting Discharge Dynamics from a Rectangular Hopper Using the Discrete Element Method (DEM)
,”
Chem. Eng. Sci.
,
63
(
24
), pp.
5821
5830
.
11.
Matuttis
,
H. G.
,
Luding
,
S.
, and
Herrmann
,
H. J.
, 2000, “
Discrete Element Simulations of Dense Packings and Heaps Made of Spherical and Non-Spherical Particles
,”
Powder Technol.
,
109
(
1
), pp.
278
292
.
12.
Iordanoff
,
I.
,
Elkholy
,
K.
, and
Khonsari
,
M. M.
, 2008, “
Effect of Particle Size Dispersion on Granular Lubrication Regimes
,”
Proc. Inst. Mech. Eng., Part J:J. Eng. Tribol.
,
222
(
6
), pp.
725
739
.
13.
McCarthy
,
J. J.
,
Jasti
,
V.
,
Marinack
,
M.
, and
Higgs
,
C. F.
, 2010, “
Quantitative Validation of the Discrete Element Method Using an Annular Shear Cell
,”
Powder Technol.
,
203
(
1
), pp.
70
77
.
14.
Ketterhagen
,
W.
,
Curtis
,
J.
, and
Wassgren
,
C.
, 2005, “
Stress Results from Two-Dimensional Granular Shear Flow Simulations Using Various Collision Models
,”
Phys. Rev. E
,
71
(
6
),
061307
.
15.
Dahl
,
S. R.
,
Clelland
,
R.
, and
Hrenya
,
C. M.
, 2003, “
Three-Dimensional, Rapid Shear Flow of Particles with Continuous Size Distributions
,”
Powder Technol.
,
138
(
1
), pp.
7
12
.
16.
Iordanoff
,
I.
,
Fillot
,
N.
, and
Berthier
,
Y.
, 2005, “
Numerical Study of a Thin Layer of Cohesive Particles Under Plane Shearing
,”
Powder Technol.
,
159
(
1
), pp.
46
54
.
17.
Kabir
,
M. A.
,
Lovell
,
M. R.
, and
Higgs
,
C. F.
III
, 2008, “
Utilizing the Explicit Finite Element Method for Studying Granular Flows
,”
Tribol. Lett.
,
29
(
2
), pp.
85
94
.
18.
Kabir
,
M. A.
,
Jasti
,
V. K.
,
Higgs
,
C. F.
III
, and
Lovell
,
M. R.
, 2008, “
An Evaluation of the Explicit Finite-Element Method Approach for Modelling Dense Flows of Discrete Grains in a Couette Shear Cell
,”
Proc. Inst. Mech. Eng., Part J:J. Eng. Tribol.
,
222
(
6
), pp.
715
723.
19.
Von Neumann
,
J.
, 1966,
Theory of Self-Reproducing Automata
,
A. W.
Burks
, ed.,
University of Illinois Press
,
Urbana and London.
20.
Fitt
,
A. D.
, and
Wilmott
,
P.
, 1992, “
Cellular-Automaton Model for Segregation of a Two-Species Granular Flow
,”
Phys. Rev. A
,
45
(
4
), pp.
2383
2389
.
21.
Karolyi
,
A.
,
Kertesz
,
J.
,
Havlin
,
S.
,
Makse
,
H. A.
, and
Stanley
,
H. E.
, 1998, “
Filling a Silo With a Mixture of Grains: Friction-Induced Segregation
,”
Europhys. Lett.
,
44
(
3
), pp.
386
392
.
22.
Cizeau
,
P.
,
Makse
,
H. A.
, and
Stanley
,
H. E.
, 1999, “
Mechanisms of Granular Spontaneous Stratification and Segregation in Two-Dimensional Silos
,”
Phys. Rev. E
,
59
(
4
), pp.
4408
4421
.
23.
Alonso
,
J. J.
, and
Herrmann
,
H. J.
, 1996, “
Shape of the Tail of a Two-Dimensional Sandpile
,”
Phys. Rev. Lett.
,
76
(
26
), pp.
4911
4914
.
24.
Goles
,
E.
, 1992, “
Sand Pile Automata
,”
Ann. Inst. Henri Poincare, Sect. A
,
56
(
1
), pp.
75
90
.
25.
Karolyi
,
A.
, and
Kertesz
,
J.
, 1998, “
Lattice-Gas Model of Avalanches in a Granular Pile
,”
Phys. Rev. E
,
57
(
1
), pp.
852
856
.
26.
Kozicki
,
J.
, and
Tejchman
,
J.
, 2005, “
Application of a Cellular Automaton to Simulations of Granular Flow in Silos
,”
Granular Matter
,
7
(
1
), pp.
45
54
.
27.
Baxter
,
W. G.
, and
Behringer
,
R. P.
, 1990, “
Cellular Automata Models of Granular Flow
,”
Phys. Rev. A
,
42
(
2
), pp.
1017
1020
.
28.
Jasti
,
V. K.
, and
Higgs
,
C. F.
III
, 2006, “
A Lattice-Based Cellular Automata Modeling Approach for Granular Flow Lubrication
,”
J. Tribol.
,
128
(
2
), pp.
358
364
.
29.
Jasti
,
V. K.
, and
Higgs
,
C. F.
III
, 2010, “
A Fast First Order Model of a Rough Annular Shear Cell Using Cellular Automata
,”
Granular Matter
,
12
(
1
), pp.
97
106
.
30.
Jenkins
,
J. T.
, and
Richman
,
M. W.
, 1986, “
Boundary Conditions for Plane Flows of Smooth, Nearly Elastic, Circular Disks
,”
J. Fluid Mech.
,
171
, pp.
53
69
.
31.
Jasti
,
V.
, and
Higgs
III,
C. F.
, 2008, “
Experimental Study of Granular Flows in a Rough Annular Shear Cell
,”
Phys. Rev. E
,
78
(
4
),
041306.
32.
Ilachinski
,
A.
, 2001,
Cellular Automata A Discrete Universe
,
World Scientific Publishing Co. Pte. Ltd.,
Singapore
.
33.
Hawkins
,
G. W.
, 1983, “
Simulation of Granular Flow
,”
Proc. Mechanics of Granular Materials: New Models and Constitutive Relations, Proceedings of the US/Japan Seminar.
,
Elsevier Science Publ Co
,
Amsterdam, Neth
, pp.
305
312
.
34.
Hopkins
,
M. A.
, and
Shen
,
H. H.
, 1988, “
A Monte Carlo Simulation of a Simple Shear Flow of Granular Materials
,”
Micromechanics of Granular Materials
,
M.
Satake
, and
J. T.
Jenkins
, eds.,
Elsevier Science Publications
,
Amsterdam.
35.
Walton
,
O. R.
, 1994, “
Numerical Simulation of Inelastic, Frictional Particle-Particle Interactions
,”
Particulate Two-Phase Flow
,
M. C.
Roco
, ed.,
Butterworth-Heinemann
,
Stoneham
, pp.
884
911
.
36.
Marinack
,
M. C.
Jr
,
Mpagazehe
,
J. N.
, and
Higgs
,
C. F.
III
, 2010, “
An Eulerian, Lattice-based Cellular Automata Approach for Modeling Multiphase Flows
,”
Proc. 2010 AIChE Annual Meeting, 10AIChE
,
American Institute of Chemical Engineers, 3 Park Avenue
,
New York, NY 10016-5991, United States.
37.
Bowden
,
F. P.
, and
Tabor
,
D.
, 1964,
The Friction and Lubrication of Solids: Part II
,
Oxford University Press
,
Oxford
.
38.
Williams
,
J.
, 1994,
Engineering Tribology
,
Oxford University Press
,
Oxford
.
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