Liquid lubricants break down at extreme temperatures and promote stiction in micro-/nanoscale environments. Consequently, using flows of solid granular particles as a “dry” lubrication mechanism in sliding contacts was proposed because of their ability to carry loads and accommodate surface velocities. Granular flows are highly complex flows that in many ways act similar to fluids, yet are difficult to predict because they are not well understood. Granular flows are composed of discrete particles that display liquid and solid lubricant behavior with time. This work describes the usefulness of employing lattice-based cellular automata (CA), a deterministic rule-based mathematics approach, as a tool for modeling granular flows in tribological contacts. In the past work, granular flows have been modeled using the granular kinetic lubrication (GKL) continuum modeling approach. While the CA modeling approach is constructed entirely from rules, results are in good agreement with results from the GKL model benchmark results. Velocity results of the CA model capture the well-known slip behavior of granular flows near boundaries. Solid fraction results capture the well-known granular flow characteristic of a highly concentrated center region. CA results for slip versus roughness also agree with GKL theory.

1.
Yu
,
C.
, and
Tichy
,
J. A.
, 1996, “
Granular Collision Lubrication: Effect of Surface Roughness, Particle Size, Solid Fraction
,”
STLE Tribol. Trans.
1040-2004,
39
, pp.
537
546
.
2.
Higgs
,
C. F.
, III
, and
Tichy
,
J.
, 2004, “
Granular Flow Lubrication: Continuum Modeling of Shear Behavior
,”
J. Tribol.
0742-4787,
126
, pp.
499
510
.
3.
Heshmat
,
H.
, 1995, “
The Quasi-Hydrodynamic Mechanism of Powder Lubrication. 3. On Theory and Rheology of Triboparticulates
,”
Tribol. Trans.
1040-2004,
38
, pp.
269
276
.
4.
Higgs
,
C. F.
,
Heshmat
,
C. A.
, and
Heshmat
,
H. S.
, 1999, “
Comparative Evaluation of MoS2 and WS2 as Powder Lubricants in High Speed, Multi-Pad Journal Bearings
,”
Trans. ASME, J. Tribol.
0742-4787,
121
, pp.
625
630
.
5.
Yu
,
C.-M.
,
Craig
,
K.
, and
Tichy
,
J.
, 1994, “
Granular Collision Lubrication
,”
J. Rheol.
0148-6055,
38
, pp.
921
936
.
6.
Iordanoff
,
I.
, and
Khonsari
,
M. M.
, 2004, “
Granular Lubrication: Toward an Understanding of the Transition Between Kinetic and Quasi-Fluid Regime
,”
J. Tribol.
0742-4787,
126
, pp.
137
145
.
7.
Lun
,
C. K.
et al.
, 1984, “
Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field
,”
J. Fluid Mech.
0022-1120,
140
, pp.
223
256
.
8.
Haff
,
P. K.
, 1983, “
Grain Flow as a Fluid-Mechanical Phenomenon
,”
J. Fluid Mech.
0022-1120,
134
, pp.
401
430
.
9.
Hui
,
K.
,
et al.
, 1984, “
Boundary Conditions For High Shear Grain Flows
,”
J. Fluid Mech.
0022-1120,
145
, pp.
223
233
.
10.
Sawyer
,
W. G.
, and
Tichy
,
J.
, 2001, “
Lubrication With Grain Flow: Continuum Theory, Particle Simulations, Comparison With Experiment
,”
J. Tribol.
0742-4787
123
, pp.
777
784
.
11.
Rosato
,
A. D.
, and
Kim
,
H.
, 1994, “
Particle Dynamics Calculations of Wall Stresses and Slip Velocities—For Couette-Flow of Smooth Inelastic Spheres
,”
Continuum Mech. Thermodyn.
0935-1175,
6
, pp.
1
20
.
12.
Herrmann
,
H. J.
, 1993, “
Molecular-Dynamics Simulations of Granular-Materials
,”
Int. J. Mod. Phys. C
0129-1831,
4
, pp.
309
316
.
13.
Hu
,
G. Q.
,
et al.
, 2004, “
The Molecular Dynamics Simulation of the Effect of Channel Width on Two-Dimensional Granular Flow
,”
Acta Phys. Sin.
1000-3290,
53
, pp.
4277
4281
.
14.
Ristow
,
G. H.
, 1992, “
Simulating Granular Flow With Molecular-Dynamics
,”
J. Phys. I
1155-4304,
2
, pp.
649
662
.
15.
Craig
,
K.
,
Buckholz
,
R. H.
, and
Domoto
,
G.
, 1986, “
An Experimental Study of the Rapid Flow of Dry Cohesionless Metal Powders
,”
J. Appl. Mech.
0021-8936,
53
, p.
935
.
16.
Elrod
,
H. G.
, 1988, “
Granular Flow as a Tribological Mechanism—A First Look
,”
Interface Dynamics
,
Proc. of the Leeds-Lyon Conference
, p.
75
.
17.
Zhou
,
L.
, and
Khonsari
,
M. M.
, 2000, “
Flow Characteristics of a Powder Lubricant Sheared Between Parallel Plates
,”
J. Tribol.
0742-4787,
122
, pp.
147
154
.
18.
Jenkins
,
J.
, and
Richman
,
M.
, 1986, “
Boundary Conditions for Plane Flows of Smooth, Nearly Elastic, Circular Disks
,”
J. Fluid Mech.
0022-1120,
171
, pp.
53
69
.
19.
Agarwal
,
H.
, 1998, “
Construction of Molecular Dynamic Like Cellular Automata Models for Simulation of Compressible Fluid Dynamic System
,” in Aerospace engineering,
Indian Institute of Technology, Kanpur
.
20.
Von Neumann
,
J.
, 1966,
Theory of Self-Reproducing Automata.
, edited by
A. W.
Bruks
,
University of Illinios Press
,
Urbana and London
.
21.
Wolfram
,
S.
, 2002,
A New Kind of Science
,
Wolfram Media, Inc.
,
Champaign, IL.
22.
Margolus
,
N.
, 1984, “
Physics-Like Models of Computation
,”
Physica D
0167-2789,
10D
, pp.
81
95
.
23.
Toffoli
,
T.
, 1984, “
Cellular Automata as an Alternative to (Rather Than an Approximation of) Differential-Equations in Modeling Physics
,”
Physica D
0167-2789,
10
, pp.
117
127
.
24.
Dhumieres
,
D.
, and
Lallemand
,
P.
, 1986, “
Lattice Gas Automata for Fluid-Mechanics
,”
Physica A
0378-4371,
140
, pp.
326
335
.
25.
Frisch
,
U.
,
Hasslacher
,
B.
, and
Pomeau
,
Y.
, 1986, “
Lattice-Gas Automata for the Navier-Stokes Equation
,”
Phys. Rev. Lett.
0031-9007,
56
, p.
1505
.
26.
Gutowitz
,
H. A.
, 1990, “
Maps of Recent Cellular Automata and Lattice Gas Automata Literature
,”
Physica D
0167-2789,
45
, pp.
477
479
.
27.
Weimar
,
J. R.
, and
Boon
,
J. P.
, 1994, “
Class of Cellular-Automata for Reaction-Diffusion Systems
,”
Phys. Rev. E
1063-651X,
49
, pp.
1749
1752
.
28.
Chopard
,
B.
,
Luthi
,
P.
, and
Droz
,
M.
, 1994, “
Reaction-Diffusion Cellular-Automata Model for the Formation of Liesegang Patterns
,”
Phys. Rev. Lett.
0031-9007,
72
, pp.
1384
1387
.
29.
Weimar
,
J. R.
, 2002, “
Three-Dimensional Cellular Automata for Reaction-Diffusion Systems
,”
Fund. Inform.
0169-2968,
52
, pp.
277
284
.
30.
Chahoud
,
M.
,
et al.
, 2000, “
Cellular-Automata-Based Simulation of Anisotropic Crystal Growth
,”
J. Cryst. Growth
0022-0248,
220
, pp.
471
479
.
31.
Mourachov
,
S.
, 1997, “
Cellular Automata Simulation of the Phenomenon of Multiple Crystallization
,”
Comput. Mater. Sci.
0927-0256,
7
, pp.
384
388
.
32.
Gerola
,
H.
, and
Seiden
,
P. E.
, 1978, “
Stochastic Star Formation and Spiral Structure of Galaxies
,”
Astrophys. J.
0004-637X,
223
, pp.
129
139
.
33.
Perdang
,
J.
, and
Lejeune
,
A.
, 1996, “
Cellular Automaton Experiments on Local Galactic Structure. 1. Model Assumptions
,”
Astron. Astrophys., Suppl. Ser.
0365-0138,
119
, pp.
231
248
.
34.
Puskar
,
K.
et al.
, 2004, “
Understanding Spatial Constraints on Biological Self-Assembly Systems Through Lattice Based Monte Carlo Modeling
,”
Biophys. J.
0006-3495,
86
, pp.
630A
630A
.
35.
Ermentrout
,
G. B.
, and
Edelsteinkeshet
,
L.
, 1993, “
Cellular Automata Approaches to Biological Modeling
,”
J. Theor. Biol.
0022-5193,
160
, pp.
97
133
.
36.
Green
,
D. G.
, 1990, “
Cellular Automata Models in Biology
,”
Math. Comput. Modell.
0895-7177,
13
, pp.
69
74
.
37.
Jhon
,
M.
,
et al.
, 2003, “
Simulation of Nanostructured Lubricant Films
,”
IEEE Trans. Magn.
0018-9464,
39
, pp.
754
758
.
38.
Ng
,
S. H.
,
et al.
, 2004, “
An Analysis of Mixed Lubrication in Chemical Mechanical Polishing
,”
ASME J. Tribol.
0742-4787,
126
, pp.
1
6
.
39.
Higgs
,
C. F.
, III
,
et al.
, 2003, “
Mechanical Modeling of the 2D Interfacial Slurry Pressure in CMP
,”
Mater. Res. Soc. Symp. Proc.
0272-9172,
767
, pp.
305
312
.
40.
Higgs
,
C. F.
, III
,
et al.
, 2005, “
A Mixed-Lubrication Approach to Predicting CMP Fluid Pressure: Modeling and Experiments
,”
J. Electrochem. Soc.
0013-4651,
152
, pp.
1
6
.
41.
Shan
,
L.
,
Zhou
,
C.
, and
Danyluk
,
S.
, 2001, “
Mechanical Interactions and Their Effects on Chemical Mechanical Polishing
,”
IEEE Trans. Semicond. Manuf.
0894-6507,
14
, pp.
207
213
.
42.
Wylie
,
J.
,
Koch
,
D.
, and
Ladd
,
A.
, 2003, “
Rheology of Suspensions With High Particle Inertia and Moderate Fluid Inertia
,”
J. Fluid Mech.
0022-1120,
480
, pp.
95
118
.
43.
Nguyen
,
N.-Q.
, and
Ladd
,
A.
, 2002, “
Lubrication Corrections for Lattice-Boltzmann Simulations of Particle Suspensions
,”
Phys. Rev. E
1063-651X,
66
, p.
046708
.
44.
Flekkoy
,
E. G.
, and
Herrmann
,
H. J.
, 1993, “
Lattice Boltzmann Models for Complex Fluids
,”
Physica A
0378-4371,
199
, pp.
1
11
.
45.
Hopkins
,
M. A.
, and
Shen
,
H. H.
, 1992, “
A Monte-Carlo Solution for Rapidly Shearing Granular Flows Based on the Kinetic-Theory of Dense Gases
,”
J. Fluid Mech.
0022-1120,
244
, pp.
477
491
.
46.
Brey
,
J. J.
, and
Ruiz-Montero
,
M. J.
, 1999, “
Direct Monte Carlo Simulation of Dilute Granular Flow
,”
Comput. Phys. Commun.
0010-4655,
122
, pp.
278
283
.
47.
Fitt
,
A. D.
, and
Wilmott
,
P.
, 1992, “
Cellular-Automaton Model for Segregation of a Two-Species Granular Flow
,”
Phys. Rev. A
1050-2947,
45
, p.
2383
.
48.
Karolyi
,
A.
et al.
, 1998, “
Filling a Silo With a Mixture of Grains: Friction-Induced Segregation
,”
Europhys. Lett.
0295-5075,
44
, pp.
386
392
.
49.
Cizeau
,
P.
,
Makse
,
H. A.
, and
Stanley
,
H. E.
, 1999, “
Mechanisms of Granular Spontaneous Stratification and Segregation in Two-Dimensional Silos
,”
Phys. Rev. E
1063-651X,
59
, p.
4408
.
50.
Alonso
,
J. J.
, and
Herrmann
,
H. J.
, 1996, “
Shape of the Tail of a Two-Dimensional Sandpile
,”
Phys. Rev. Lett.
0031-9007,
76
, p.
4911
.
51.
Goles
,
E.
, 1992, “
Sand Pile Automata
,”
Ann. Inst. Henri Poincare, Sect. A
0020-2339,
56
, pp.
75
90
.
52.
Karolyi
,
A.
, and
Kertesz
,
J.
, 1998, “
Lattice-Gas Model of Avalanches in a Granular Pile
,”
Phys. Rev. E
1063-651X,
57
, p.
852
.
53.
Peng
,
G.
, and
Herrmann
,
H. J.
, 1994, “
Density Waves of Granular Flow in a Pipe Using Lattice-Gas Automata
,”
Phys. Rev. E
1063-651X,
49
, p.
R1796
.
54.
Peng
,
G.
, and
Ohta
,
T.
, 1997, “
Velocity and Density Profiles of Granular Flow in Channels Using a Lattice Gas Automaton
,”
Phys. Rev. E
1063-651X,
55
, p.
6811
.
55.
Baxter
,
G. W.
,
et al.
, 1991, “
Time-Dependence, Scaling and Pattern-Formation for Flowing Sand
,”
Eur. J. Biochem.
0014-2956,
10
, pp.
181
186
.
56.
Kozicki
,
J.
, and
Tejchman
,
J.
, 2001, “
Simulations of Granular Flow in Silos With a Cellular Automata Model
,”
Powder Handl. Process.
0934-7348,
13
, pp.
267
273
.
57.
Gutt
,
G. M.
, and
Haff
,
P. K.
, 1990, “
An Automata Model of Granular Materials
,” in
Fifth Distributed Memory Comping Conference (1)
,
IEEE Computer Society Press
,
Charleston, SC.
58.
Deserable
,
D.
, 2001, “
A Versatile Two-Dimensional Cellular Automata Network for Granular Flow
,”
J. Appl. Math.
1110-757X,
62
, pp.
1414
1436
.
59.
Libbrecht
,
K.
, and
Rasmussen
,
P.
, 2003,
The Snowflake: Winter’s Secret Beauty
,
Voyageur Press
,
Stillwater, MN
.
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