A lubrication theory that includes the coupled effects of surface roughness and anisotropic slips is proposed. The anisotropic-slip phenomena originate from the microscale roughness at the atomic scale (microtexture) and surface properties of the lubricating surfaces. The lubricant flow between rough surfaces (texture) is defined as the flow in nominal film thickness multiplied by the flow factors. A modified average Reynolds equation (modified ARE) as well as the related factors (pressure and shear flow factors, and shear stress factors) is then derived. The present model can be applied to squeeze film problems for anisotropic-slip conditions and to sliding lubrication problems with restrictions to symmetric anisotropic-slip conditions (the two lubricating surfaces have the same principal slip lengths, i.e., b1x=b2x and b1y=b2y). The performance of journal bearings is discussed by solving the modified ARE numerically. Different slenderness ratios 5, 1, and 0.2 are considered to discuss the coupled effects of anisotropic slip and surface roughness. The results show that the existence of boundary slip can dilute the effects of surface roughness. The boundary slip tends to “smoothen” the bearings, i.e., the derived flow factors with slip effects deviate lesser from the values at smooth cases (pressure flow factors φxxp,φyyp=1; shear flow factors φxxs=0; and shear stress factors φf,φfp=1 and φfs=0) than no-slip one. The load ratio increases as the dimensionless slip length (B) decreases exception case is also discussed or the slenderness ratio (b/d) increases. By controlling the surface texture and properties, a bearing with desired performance can be designed.

References

References
1.
Bonaccurso
,
E.
,
Kappl
,
M.
, and
Butt
,
H. J.
,
2002
, “
Hydrodynamic Force Measurements: Boundary Slip of Water on Hydrophilic Surfaces and Electrokinetic Effects
,”
Phys. Rev. Lett.
,
88
(
7
), p.
076103
.
2.
Craig
,
V. S. J.
,
Neto
,
C.
, and
Williams
,
D. R. M.
,
2001
, “
Shear-Dependent Boundary Slip in an Aqueous Newtonian Liquid
,”
Phys. Rev. Lett.
,
87
(
5
), p.
054504
.
3.
Zhu
,
Y.
, and
Granick
,
S.
,
2001
, “
Rate-Dependent Slip of Newtonian Liquid at Smooth Surfaces
,”
Phys. Rev. Lett.
,
87
(
9
), p.
096105
.
4.
Zhu
,
Y.
, and
Granick
,
S.
,
2002
, “
Limits of Hydrodynamic No-Slip Boundary Condition
,”
Phys. Rev. Lett.
,
88
(
10
), p.
106102
.
5.
Zhu
,
Y.
, and
Granick
,
S.
,
2002
, “
Apparent Slip of Newtonian Fluids Past Adsorbed Polymer Layers
,”
Macromolecules
,
35
(
12
), pp.
4658
4663
.
6.
Zhu
,
Y.
, and
Granick
,
S.
,
2002
, “
The No Slip Boundary Condition Switches to Partial Slip When the Fluid Contains Surfactant
,”
Langmuir
,
18
(
26
), pp.
10058
10063
.
7.
Pit
,
R.
,
Hervet
,
H.
, and
Leger
,
L.
,
2000
, “
Direct Experimental Evidence of Slip in Hexadecane: Solid Interfaces
,”
Phys. Rev. Lett.
,
85
(
5
), pp.
85980
85983
.
8.
Granick
,
S.
,
Zhu
,
Y.
, and
Lee
,
H.
,
2003
, “
Slippery Questions About Complex Fluids Flowing Past Solids
,”
Nat. Mater.
,
2
(4), pp.
221
227
.
9.
Vinogradova
,
O. I.
,
1999
, “
Slippage of Water Over Hydrophobic Surfaces
,”
Int. J. Miner. Process.
,
56
(
1
), pp.
31
60
.
10.
Navier
,
C. L. M. H.
,
1823
, “
Mémoire sur les lois du mouvement des fluides
,” Mémoires de l'Académie Royale des Sciences de l'Institut de France, 6, pp.
389
416
.
11.
Spikes
,
H. A.
,
2003
, “
The Half-Wetted Bearing, Part 1: Extended Reynolds Equation
,”
Proc. Inst. Mech. Eng., Part J
,
217
(
1
), pp.
1
14
.
12.
Spikes
,
H. A.
,
2003
, “
The Half-Wetted Bearing, Part 2: Potential Application in Low Load Contacts
,”
Proc. Inst. Mech. Eng., Part J
,
217
(
1
), pp.
15
26
.
13.
Spikes
,
H.
, and
Granick
,
S.
,
2003
, “
Equation for Slip of Simple Liquids at Smooth Solid Surfaces
,”
Langmuir
,
19
(
12
), pp.
5065
5071
.
14.
Li
,
W. L.
,
Chu
,
H. M.
, and
Chen
,
M. D.
,
2006
, “
The Partially Wetted Bearing—Extended Reynolds Equation
,”
Tribol. Int.
,
39
(
11
), pp.
1428
1435
.
15.
Fortier
,
A. E.
, and
Salant
,
R. F.
,
2005
, “
Numerical Analysis of a Journal Bearing With a Heterogeneous Slip/No-Slip Surface
,”
ASME J. Tribol.
,
127
(
4
), pp.
820
825
.
16.
Rao
,
T. V. V. L. N.
,
2010
, “
Analysis of Single-Grooved Slider and Journal Bearing With Partial Slip Surface
,”
ASME J. Tribol.
,
132
(
1
), p.
014501
.
17.
Wang
,
L. L.
,
Lu
,
C. H.
,
Wang
,
M.
, and
Fu
,
W. X.
,
2012
, “
The Numerical Analysis of the Radial Sleeve Bearing With Combined Surface Slip
,”
Tribol. Int.
,
47
, pp.
100
104
.
18.
Aurelian
,
F.
,
Patrick
,
M.
, and
Mohamed
,
H.
,
2011
, “
Wall Slip Effects in (Elasto) Hydrodynamic Journal Bearings
,”
Tribol. Int.
,
44
(
7
), pp.
868
877
.
19.
Chen
,
C. Y.
,
Chung
,
C. J.
,
Wu
,
B. H.
,
Li
,
W. L.
,
Chien
,
C. W.
, and
Wu
,
P. H.
,
2012
, “
Microstructure and Lubricating Property of Ultrafast Laser Pulse Textured Silicon Carbide Seals
,”
Appl. Phys. A: Mater. Sci. Process.
,
107
(
2
), pp.
345
350
.
20.
Chen
,
C. Y.
,
Wu
,
B. H.
,
Chung
,
C. J.
,
Li
,
W. L.
,
Chien
,
C. W.
,
Wu
,
P. H.
, and
Cheng
,
C. W.
,
2013
, “
Low-Friction Characteristics of Nanostructured Surfaces on Silicon Carbide for Water-Lubricated Seals
,”
Tribol. Lett.
,
51
(
1
), pp.
127
133
.
21.
Ou
,
J.
, and
Rothstein
,
J. P.
,
2005
, “
Direct Velocity Measurements of the Flow Past Drag Reducing Ultrahydrophobic Surfaces
,”
Phys. Fluids
,
17
(10), p.
103606
.
22.
Joseph
,
P.
,
Cottin-Bizonne
,
C.
,
Benoît
,
J. M.
,
Ybert
,
C.
,
Journet
,
C.
,
Tabeling
,
P.
, and
Bocquet
,
L.
,
2006
, “
Slippage of Water Past Superhydrophobic Carbon Nanotube Forests in Microchannels
,”
Phys. Rev. Lett.
,
97
(
15
), p.
156104
.
23.
Choi
,
C. H.
,
Ulmanella
,
U.
,
Kim
,
J.
,
Ho
,
C. M.
, and
Kim
,
C. J.
,
2006
, “
Effective Slip and Friction Reduction in Nanograted Superhydrophobic Microchannels
,”
Phys. Fluids
,
18
(8), p.
087105
.
24.
Chen
,
F.
,
Zhang
,
D.
,
Yang
,
Q.
,
Wang
,
X.
,
Dai
,
B.
,
Li
,
X.
,
Hao
,
X.
,
Ding
,
Y.
,
Si
,
J.
, and
Hou
,
X.
,
2011
, “
Anisotropic Wetting on Microstrips Surface Fabricated by Femtosecond Laser
,”
Langmuir
,
27
(
1
), pp.
359
65
.
25.
Quéré
,
D.
,
2005
, “
Non-Sticking Drops
,”
Rep. Prog. Phys.
,
68
(
11
), pp.
2495
2532
.
26.
Choo
,
J. H.
,
Glovnea
,
R. P.
,
Forrest
,
A. K.
, and
Spikes
,
H. A.
,
2007
, “
A Low Friction Bearing Based on Liquid Slip at the Wall
,”
ASME J. Tribol.
,
129
(
3
), pp.
611
620
.
27.
Stroock
,
A. D.
,
Dertinger
,
S. K.
,
Whitesides
,
G. M.
, and
Ajdari
,
A.
,
2002
, “
Patterning Flows Using Grooved Surfaces
,”
Anal. Chem.
,
74
(
20
), pp.
5306
5312
.
28.
Stone
,
H. A.
,
Stroock
,
A. D.
, and
Ajdari
,
A.
,
2004
, “
Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip
,”
Annu. Rev. Fluid Mech.
,
36
, pp.
381
411
.
29.
Bazant
,
M. Z.
, and
Vinogradova
,
O. I.
,
2008
, “
Tensorial Hydrodynamic Slip
,”
J. Fluid Mech.
,
613
, pp.
125
134
.
30.
Belyaev
,
A. V.
, and
Vinogradova
,
O. I.
,
2010
, “
Effective Slip in Pressure-Driven Flow Past Superhydrophobic Stripes
,”
J. Fluid Mech.
,
652
, pp.
489
499
.
31.
Chen
,
C. Y.
,
Chen
,
Q. D.
, and
Li
,
W. L.
,
2013
, “
Characteristics of Journal Bearings With Anisotropic Slip
,”
Tribol. Int.
,
61
, pp.
144
155
.
32.
Patir
,
N.
, and
Cheng
,
H. S.
,
1978
, “
An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication
,”
ASME J. Tribol.
,
100
(
1
), pp.
12
17
.
33.
Patir
,
N.
, and
Cheng
,
H. S.
,
1979
, “
Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces
,”
ASME J. Tribol.
,
101
(
2
), pp.
220
229
.
34.
Tripp
,
J. H.
,
1983
, “
Surface Roughness Effects in Hydrodynamic Lubrication: The Flow Factor Method
,”
ASME J. Tribol.
,
105
(
3
), pp.
458
463
.
35.
Elrod
,
H. G.
,
1979
, “
A General Theory for Laminar Lubrication With Reynolds Roughness
,”
ASME J. Tribol.
,
101
(
1
), pp.
8
14
.
36.
Li
,
W. L.
,
Weng
,
C. I.
, and
Lue
,
J. I.
,
1996
, “
Surface Roughness Effects in Journal Bearings With Non-Newtonian Lubricants
,”
STLE Tribol. Trans.
,
39
(
4
), pp.
819
826
.
37.
Li
,
W. L.
,
Weng
,
C. I.
, and
Hwang
,
C. C.
,
1997
, “
An Average Reynolds Equation for Non-Newtonian Fluid, With Application to the Lubrication of the Magnetic Head-Disk Interface
,”
STLE Tribol. Trans.
,
40
(
1
), pp.
111
119
.
38.
Li
,
W. L.
,
1998
, “
Surface Roughness Effects in Hydrodynamic Lubrication Involving the Mixture of Two Fluids
,”
ASME J. Tribol.
,
120
(
4
), pp.
772
780
.
39.
Li
,
W. L.
,
2000
, “
Some Discussions on the Flow Factor Tensor-Considerations of Roughness Orientation and Flow Rheology
,”
ASME J. Tribol.
,
122
(
4
), pp.
869
872
.
40.
Li
,
W. L.
,
2003
, “
An Average Flow Model for Couple Stress Fluids
,”
Tribol. Lett.
,
15
(
3
), pp.
279
292
.
41.
Hamrock
,
B. J.
,
Schmid
,
S. R.
, and
Jacobson
,
B. O.
,
2004
,
Fundamentals of Fluid Film Lubrication
,
2nd ed.
,
Marcel Dekker
,
New York
, Chap. 10, Sec. 3.
42.
Li
,
W. L.
,
2004
, “
Modeling of Head Disk Interface an Average Flow Model
,”
Tribol. Lett.
,
17
(
3
), pp.
669
676
.
43.
Dowson
,
D.
, and
Taylor
,
C. M.
,
1979
, “
Cavitation in Bearings
,”
Annu. Rev. Fluid Mech.
,
11
(1), pp.
35
66
.
44.
Wu
,
S. R.
,
1986
, “
A Penalty Formulation and Numerical Approximation of the Reynolds–Hertz Problem of Elastohydrodynamic Lubrication
,”
Int. J. Eng. Sci.
,
24
(
6
), pp.
1001
1013
.
45.
Voronov
,
R. S.
, and
Papavassiliou
,
D. V.
,
2008
, “
Review of Fluid Slip Over Superhydrophobic Surfaces and Its Dependence on the Contact Angle
,”
Ind. Eng. Chem. Res.
,
47
(
8
), pp.
2455
2477
.
46.
Li
,
W. L.
,
Weng
,
C. I.
, and
Hwang
,
C. C.
,
1995
, “
Effects of Roughness Orientations on Thin Film Lubrication of Magnetic Recording System
,”
J. Phys. D: Appl. Phys.
,
28
(
6
), pp.
1011
1021
.
You do not currently have access to this content.