Siloxane-based polymers (polysiloxanes) are susceptible to temporary shear-thinning that manifests as a reduction of elastohydrodynamic film thickness with increasing entrainment speed or effective shear rate. The departure from Newtonian film thickness can be predicted with the power-law exponent ns, an indicator of the severity of shear-thinning in a polymeric fluid that is influenced by the macromolecular structure. In this paper, a combination of extant rheological and tribological models is applied to determine the power-law exponent of several polysiloxanes using film thickness measurements. Film thickness data at several temperatures and slide-to-roll ratios are used to validate the methodology for several siloxane-based polymers with alkyl and aryl branches.
Issue Section:
Elastohydrodynamic Lubrication
Topics:
Film thickness,
Shear (Mechanics),
Temperature,
Viscosity,
Lubricants,
Fluids,
Pressure,
Stress,
Siloxanes,
Rheology
References
1.
Zolper
, T. J.
, Li
, Z.
, Chen
, C.
, Jungk
, M.
, Marks
, T. J.
, Chung
, Y.-W.
, and Wang
, Q.
, 2012
, “Lubrication Properties of Poly-Alpha-Olefin and Polysiloxane Lubricants: Molecular Structure-Tribology Relationships
,” Tribol. Lett.
, 48
, pp. 355
–365
.2.
Zolper
, T. J.
, Li
, Z.
, Jungk
, M.
, Stammer
, A.
, Stoegbauer
, H.
, Marks
, T. J.
, Chung
, Y.-W.
, and Wang
, Q.
, 2013
, “Traction Characteristics of Siloxanes With Aryl and Cyclohexyl Branches
,” Tribol. Lett.
, 49
(2
), pp. 301
–311
.10.1007/s11249-012-0066-x3.
Zolper
, T. J.
, Seyam
, A. M.
, Chen
, C.
, Jungk
, M.
, Stammer
, A.
, Stoegbauer
, H.
, Marks
, T. J.
, Chung
, Y.-W.
, and Wang
, Q.
, 2013
, “Energy Efficient Siloxane Lubricants Utilizing Temporary Shear-Thinning
,” Tribol. Lett.
, 49
(3
), pp. 525
–538
.10.1007/s11249-012-0093-74.
Zolper
, T. J.
, Seyam
, A.
, Li
, Z.
, Chen
, C.
, Jungk
, M.
, Stammer
, A.
, Marks
, T. J.
, Chung
, Y.-W.
, and Wang
, Q.
, 2013
, “Friction and Wear Protection Performance of Synthetic Siloxane Lubricants
,” Tribol. Lett.
, 51
(3
), pp. 365
–376
.10.1007/s11249-013-0169-z5.
Zolper
, T. J.
, Jungk
, M.
, Marks
, T. J.
, Chung
, Y.-W.
, and Wang
, Q.
, 2014
, “Modeling Polysiloxane Volume and Viscosity Variations With Molecular Structure and Thermodynamic State
,” ASME J. Tribol.
, 136
(1
), p. 011801
.10.1115/1.40253016.
Lewis
, G.
, 1916
, “The Atom and the Molecule
,” J. Am. Chem. Soc.
, 38
(4
), pp. 762
–785
.10.1021/ja02261a0027.
Flory
, P.
, 1969
, Statistical Mechanics of Chain Molecules
, Interscience
, New York
.8.
Brandup
, J.
, Immergut
, E.
, and Grulke
, E.
, 1975
, Polymer Handbook
, Interscience
, New York
.9.
Ziegler
, M.
, and Fearon
, F.
, 1990
, Silicon-Based Polymer Science: A Comprehensive Resource
(Advances in Chemistry Series), Vol. 224
, American Chemical Society
, Washington, DC
.10.1021/ba-1990-022410.
11.
Mackenzie
, K.
, and Jemmett
, A.
, 1971
, “Polymer Shear Stability
,” Wear
, 17
(5–6
), pp. 389
–398
.10.1016/0043-1648(71)90045-712.
Dyson
, A.
, and Wilson
, A.
, 1965
, “Film Thicknesses in Elastohydrodynamic Lubrication by Silicone Fluids
,” Prof. Inst. Eng. IMechE Conf.
, 180
(11
), pp. 97
–112
.10.1243/PIME_CONF_1965_180_323_0213.
Chapkov
, A.
, Bair
, S.
, Cann
, P.
, and Lubrecht
, A.
, 2007
, “Film Thickness in Point Contacts Under Generalized Newtonian EHL Conditions: Numerical and Experimental Analysis
,” Tribol. Int.
, 40
(10–12
), pp. 1474
–1478
.10.1016/j.triboint.2007.01.00214.
Bair
, S.
, and Qureshi
, F.
, 2003
, “The Generalized Newtonian Fluid Model and Elastohydrodynamic Film Thickness
,” ASME J. Tribol.
, 125
(1
), pp. 70
–75
.10.1115/1.150408615.
Zolper
, T. J.
, 2012
, “Understanding Siloxane-Based Lubricants and Developing a Polymer Chemistry-Based Rheological-Tribological Model
,” Doctoral thesis, Northwestern University, Evanston, IL.16.
Archard
, J.
, and Cowking
, E.
, 1965
, “Elastohydrodynamic Lubrication at Point Contacts
,” Prof. Inst. Eng. IMechE Conf.
, 180
(2
), pp. 47
–56
.10.1243/PIME_CONF_1965_180_063_0217.
Cameron
, A.
, and Gohar
, R.
, 1966
, “Theoretical and Experimental Studies of the Oil Film in Lubricated Point Contact
,” Proc. R. Soc. London, Ser. A
, 291
(1427
), pp. 520
–536
.10.1098/rspa.1966.011218.
Cheng
, H. S.
, 1970
, “A Numerical Solution of the Elastohydrodynamic Film Thickness in an Elliptical Contact
,” ASME J. Tribol.
, 92
(1
), pp. 155
–161
.10.1115/1.345131019.
Gohar
, R.
, 1971
, “Oil Film Thickness and Rolling Friction in Elastohydrodynamic Point Contact
,” J. Lubr. Technol.
, 93
(3
), pp. 371
–379
.10.1115/1.345159820.
Westlake
, F.
, and Cameron
, A.
, “Optical Elastohydrodynamic Fluid Testing
,” ASLE Trans.
, 15
(2
) pp. 81
–95
.10.1080/0569819720898140521.
Ranger
, A.
, Ettles
, C.
, and Cameron
, A.
, 1975
, “The Solution of the Point Contact Elasto-Hydrodynamic Problem
,” Proc. R. Soc. London A
, 346
(1645
), pp. 227
–244
.10.1098/rspa.1975.017422.
Grubin
, A.
, and Vinogradova
, I.
, 1949
, “Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces
,” Invest. Contact Mach. Compon.
, 30
, pp. 115
–166
.23.
Dowson
, D.
, and Higginson
, G.
, 1961
, “New Roller-Bearing Lubrication Formula
,” Eng. London
, 192
, pp. 158
–159
.24.
Dowson
, D.
, and Toyoda
, S.
, 1979
, “A Central Film Thickness Formula for Elastohydrodynamic Line Contacts
,” 5 Leeds-Lyon Symposium on Tribology
, pp. 60
–65
.25.
Hamrock
, B.
, and Dowson
, D.
, 1976
, “Isothermal Elastohydrodynamic Lubrication of Point Contacts. I—Theoretical Formulation
,” ASME J. Tribol.
, 98
(2
), pp. 223
–228
.26.
Hamrock
, B.
, and Dowson
, D.
, 1976
, “Isothermal Elastohydrodynamic Lubrication of Point Contacts. II—Ellipticity Parameter Results
,” ASME J. Tribol.
, 98
(3
), pp. 375
–381
.27.
Hamrock
, B.
, and Dowson
, D.
, 1977
, “Isothermal Elastohydrodynamic Lubrication of Point Contacts. III—Fully Flooded Results
,” ASME J. Tribol.
, 99
(2
), pp. 264
–276
.28.
Hamrock
, B.
, and Dowson
, D.
, 1977
, “Isothermal EHD Lubrication of Point Contacts, Part III
,” ASME J. Lubr. Technol.
, 99
(2
), pp. 15
–23
.10.1115/1.345297329.
Hu
, Y.
, and Zhu
, D.
, 2000
, “A Full Numerical Solution to the Mixed Lubrication in Point Contacts
,” ASME J. Tribol.
, 122
(1
), pp. 1
–9
.10.1115/1.55532230.
Bair
, S.
, and Winer
, W.
, 1997
, “A Simple Formula for EHD Film Thickness of Non-Newtonian Liquids
,” Tribol. Ser.
, 32
, pp. 235
–241
.10.1016/S0167-8922(08)70452-831.
Bair
, S.
, 2004
, “A Rough Shear-Thinning Correction for EHD Film Thickness
,” Tribol. Trans.
, 47
(3
), pp. 361
–365
.10.1080/0569819049045551932.
Greenwood
, J.
, and Kauzlarich
, J.
, 1998
, “Elastohydrodynamic Film Thickness for Shear-Thinning Lubricants
,” Proc. Inst. Mech. Eng., Part J
, 212
(3
), pp. 179
–191
.10.1243/135065098154199433.
Novak
, J.
, and Winer
, W.
, 1968
, “Some Measurements of High Pressure Lubricant Rheology
,” ASME J. Lubr. Technol.
, 90
(3
), pp. 580
–591
.10.1115/1.360162534.
Cogswell
, F.
, 1973
, “Influence of Pressure on Viscosity of Polymer Melts
,” Plast. Polym.
, 41
(151
), pp. 39
–43
.35.
Kamal
, M.
, and Nyun
, H.
, 1973
, “The Effect of Pressure on the Shear Viscosity of Polymer Melts
,” Trans. Soc. Rheol.
, 17
(2
), pp. 271
–285
.10.1122/1.54931536.
Hutton
, J.
, Jones
, B.
, and Bates
, T.
, 1983
, “Effects of Isotropic Pressure on the High Temperature High Shear Viscosity of Motor Oils
,” SAE
Technical Paper No. 830030(1).10.4271/83003037.
Hutton
, J. F.
, 1972
, “Interdisciplinary Approach to Liquid Lubricant Technology
,” NASA Technical Document, Technical Paper No. SP-318, pp. 187
–261
.38.
Kauzlarich
, J.
, and Greenwood
, J.
, 1972
, “Elastohydrodynamic Lubrication With Herschel-Bulkley Model Greases
,” Tribol. Trans.
, 15
(4
), pp. 269
–277
.10.1080/0569819720898142739.
Bair
, S.
, 2006
, “A More Complete Description of the Shear Rheology of High-Temperature, High-Shear Journal Bearing Lubrication
,” Tribol. Trans.
, 49
(1
), pp. 39
–45
.10.1080/0569819050041439140.
Bair
, S.
, 2006
, “Reference Liquids for Quantitative Elastohydrodynamics: Selection and Rheological Characterization
,” Tribol. Lett.
, 22
(2
), pp. 197
–206
.10.1007/s11249-006-9083-y41.
Berry
, G.
, and Fox
, T.
, 1968
, “The Viscosity of Polymers and Their Concentrated Solutions
,” Fortschr. Hochpolym.-Forsch., Adv. Polymer Sci.
, 5
, pp. 261
–357
.10.1007/BFb005098442.
Bair
, S.
, 2004
, “Actual Eyring Models for Thixotropy and Shear-Thinning: Experimental Validation and Application to EHD
,” ASME J. Tribol.
, 126
(4
), pp. 728
–732
.10.1115/1.179269343.
Plazek
, D.
, Dannhauser
, W.
, and Ferry
, J.
, 1961
, “Viscoelastic Dispersion of Polydimethyl Siloxane in the Rubberlike Plateau Zone
,” J. Colloid Sci.
, 16
(2
), pp. 101
–126
.10.1016/0095-8522(61)90011-344.
Barlow
, A.
, Harrison
, G.
, and Lamb
, J.
, 1964
, “Viscoelastic Relaxation of Polydimethylsiloxane Liquids
,” Proc. R. Soc. London Ser. A
, 471
(2176
), pp. 228
–251
.10.1098/rspa.1964.022945.
Kataoka
, T.
, and Ueda
, S.
, 1966
, “Viscosity-Molecular Weight Relationship for Polydimethylsiloxane
,” J. Polym. Sci. Part B: Polym. Lett.
, 4
(5
), pp. 317
–322
.10.1002/pol.1966.11004050346.
Mills
, N.
, 1969
, “The Rheological Properties and Molecular Weight Distribution of Polydimethylsiloxane
,” Eur. Polym. J.
, 5
(5
), pp. 675
–695
.10.1016/0014-3057(69)90130-X47.
Graessley
, W.
, 1974
, The Entanglement Concept in Polymer Rheology
, Springer
, Heidelberg
.10.1007/BFb003103748.
Van Krevelen
, D. W.
, 1990
, Properties of Polymers. Their Correlation With Chemical Structure, Their Numerical Estimation and Prediction From Additive Group Contribution
, Elsevier
, New York
.49.
Valles
, E.
, and Macosko
, C.
, 1979
, “Structure and Viscosity of Poly (Dimethylsiloxanes) With Random Branches
,” Macromolecules
, 12
(3
), pp. 521
–526
.10.1021/ma60069a03650.
Rahalkar
, R.
, Lamb
, J.
, Harrison
, G.
, Barlow
, A.
, Hawthorne
, W.
, Semlyen
, J.
, North
, A.
, and Pethrick
, R.
, 1983
, “Viscoelastic Studies of Reptational Motion of Linear Polydimethylsiloxanes
,” R. Soc. Chem.
, 18
, pp. 103
–114
.10.1039/fs983180010351.
Orrah
, D.
, Semlyen
, J.
, and Ross-Murphy
, S.
, 1988
, “Studies of Cyclic and Linear Poly (Dimethylsiloxanes): 27. Bulk Viscosities Above the Critical Molar Mass for Entanglement
,” Polymer
, 29
(8
), pp. 1452
–1454
.10.1016/0032-3861(88)90310-252.
McGuiggan
, P.
, Gee
, M.
, Yoshizawa
, H.
, Hirz
, S.
, and Israelachvili
, J.
, 2007
, “Friction Studies of Polymer Lubricated Surfaces
,” Macromolecules
, 40
(6
), pp. 2126
–2133
.10.1021/ma061750h53.
Hadjistamov
, D.
, 2008
, “Determination of the Onset of Shear-Thinning of Polydimethylsiloxane
,” J. Appl. Polym. Sci.
, 108
(4
), pp. 2356
–2364
.10.1002/app.2768554.
Verdier
, C.
, Longin
, P.
, and Piau
, M.
, 1998
, “Dynamic Shear and Compressional Behavior of Polydimethylsiloxanes: Ultrasonic and Low Frequency Characterization
,” Rheol. Acta
, 37
(3
), pp. 234
–244
.10.1007/s00397005011155.
Longin
, P.
, Verdier
, C.
, and Piau
, M.
, 1998
, “Dynamic Shear Rheology of High Molecular Weight Polydimethylsiloxanes: Comparison of Rheometry and Ultrasound
,” J. Non-Newtonian Fluid Mech.
, 76
(1–3
), pp. 213
–232
.10.1016/S0377-0257(97)00119-556.
Yamada
, S.
, 2002
, “General Shear-Thinning Dynamics of Confined Fluids
,” Tribol. Lett.
, 13
(3
), pp. 167
–171
.10.1023/A:102015182427457.
Cross
, M. M.
, 1965
, “Rheology of Non-Newtonian Fluids: A New Flow Equation for Pseudoplastic Systems
,” J. Colloid Sci.
, 20
(5
), pp. 417
–437
.10.1016/0095-8522(65)90022-X58.
Tanner
, R.
, 1985
, Engineering Rheology
, Clarendon
, Oxford
.59.
Bird
, R. B.
, Armstrong
, R. C.
, and Hassager
, O.
, 1987
, Dynamics of Polymeric Liquids: Fluid Mechanics
, Vol. 1
, John Wiley and Sons, New York.60.
Yasuda
, K.
, Armstrong
, R.
, and Cohen
, R.
, 1981
, “Shear Flow Properties of Concentrated Solutions of Linear and Star Branched Polystyrenes
,” Rheol. Acta
, 20
(2
), pp. 163
–178
.10.1007/BF0151305961.
Bair
, S.
, 2001
, “The High-Pressure, High-Shear Stress Rheology of a Polybutene
,” J. Non-Newtonian Fluid Mech.
, 97
(1
), pp. 53
–65
.10.1016/S0377-0257(00)00197-X62.
Carreau
, P. J.
, 1972
, “Rheological Equations From Molecular Network Theories
,” J. Rheol.
, 16
, pp. 99
–127
.10.1122/1.54927663.
Habchi
, W.
, Vergne
, P.
, Bair
, S.
, Andersson
, O.
, Eyheramendy
, D.
, and Morales-Espejel
, G. E.
, 2010
, “Influence of Pressure and Temperature Dependence of Thermal Properties of a Lubricant on the Behaviour of Circular TEHD Contacts
,” Tribol. Int.
, 43
(10
), pp. 1842
–1850
.10.1016/j.triboint.2009.10.00264.
Habchi
, W.
, Vergne
, P.
, Fillot
, N.
, Bair
, S.
, and Morales-Espejel
, G. E.
, 2011
, “A Numerical Investigation of Local Effects on the Global Behavior of TEHD Highly Loaded Circular Contacts
,” Tribol. Int.
, 44
(12
), pp. 1987
–1996
.10.1016/j.triboint.2011.08.01065.
Greenwood
, J.
, 2000
, “Two-Dimensional Flow of a Non-Newtonian Lubricant
,” Proc. Inst. Mech. Eng., Part J
, 214
(1
), pp. 29
–41
.10.1243/135065000154299066.
Bair
, S.
, and Qureshi
, F.
, 2003
, “The High Pressure Rheology of Polymer-Oil Solutions
,” Tribol. Int.
, 36
(8
), pp. 637
–645
.10.1016/S0301-679X(03)00008-267.
Granick
, S.
, 1991
, “Motions and Relaxations of Confined Liquids
,” Science (Washington)
, 253
(5026
), pp. 1374
–1379
.10.1126/science.253.5026.137468.
Hu
, H.
, Carson
, G.
, and Granick
, S.
, 1991
, “Relaxation Time of Confined Liquids Under Shear
,” Phys. Rev. Lett.
, 66
(21
), pp. 2758
–2761
.10.1103/PhysRevLett.66.275869.
Luengo
, G.
, Schmitt
, F.
, Hill
, R.
, and Israelachvili
, J.
, 1997
, “Thin Film Rheology and Tribology of Confined Polymer Melts: Contrasts With Bulk Properties
,” Macromolecules
, 30
(8
), pp. 2482
–2494
.10.1021/ma951912270.
Luengo
, G.
, Israelachvili
, J.
, and Granick
, S.
, 1996
, “Generalized Effects in Confined Fluids: New Friction Map for Boundary Lubrication
,” Wear
, 200
(1–2
), pp. 328
–335
.10.1016/S0043-1648(96)07248-171.
Yamada
, S.
, Nakamura
, G.
, and Amiya
, T.
, 2001
, “Shear Properties for Thin Films of Star and Linear Polymer Melts
,” Langmuir
, 17
(5
), pp. 1693
–1699
.10.1021/la000916j72.
Flores
, F.
, Graebling
, D.
, Allal
, A.
, and Guerret-Piécourt
, C.
, 2007
, “Modelization of Flow Electrification in a Polymer Melt
,” J. Phys. D: Appl. Phys.
, 40
, pp. 2911
–2925
.10.1088/0022-3727/40/9/03773.
Bair
, S.
, 2002
, “The Shear Rheology of Thin Compressed Liquid Films
,” Proc. Inst. Mech. Eng.
, 216
(1
), pp. 1
–17
.10.1243/135065002154383474.
Kioupis
, L. I.
, and Maginn
, E. J.
, 1999
, “Molecular Simulation of Poly-α-Olefin Synthetic Lubricants: Impact of Molecular Architecture on Performance Properties
,” J. Phys. Chem. B
, 103
(49
), pp. 10781
–10790
.10.1021/jp992399n75.
Kioupis
, L. I.
, and Maginn
, E. J.
, 2000
, “Impact of Molecular Architecture on the High-Pressure Rheology of Hydrocarbon Fluids
,” J. Phys. Chem. B
, 104
(32
), pp. 7774
–7783
.10.1021/jp000966x76.
Katyal
, P.
, and Kumar
, P.
, 2012
, “Central Film Thickness Formula for Shear Thinning Lubricants in EHL Point Contacts Under Pure Rolling
,” Tribol. Int.
, 48
, pp. 113
–121
.10.1016/j.triboint.2011.11.00777.
Bair
, S.
, 2005
, “Shear Thinning Correction for Rolling/Sliding Elastohydrodynamic Film Thickness
,” Proc. Inst. Mech. Eng.
, 219
(1
), pp. 69
–74
.10.1243/135065005X970978.
Nichetti
, D.
, and Manas-Zloczower
, I.
, 1998
, “Viscosity Model for Polydisperse Polymer Melts
,” J. Rheol.
, 42
(4), pp. 951
–969
.10.1122/1.55090879.
Horowitz
, H.
, 1958
, “Predicting Effects of Temperature and Shear Rate on Viscosity of Viscosity Index–Improved Lubricants
,” Ind. Eng. Chem.
, 50
(7
), pp. 1089
–1094
.10.1021/ie50583a05080.
Qureshi
, F.
, and Bair
, S.
, 2014
, “Time-Temperature-Pressure Superposition in Polymer Thickened Liquid Lubricants
,” ASME J. Tribol.
, 136
(2
), p. 021505
.10.1115/1.402659181.
Bair
, S.
, Vergne
, P.
, and Querry
, M.
, 2005
, “A Unified Shear-Thinning Treatment of Both Film Thickness and Traction in EHD
,” Tribol. Lett.
, 18
(2
), pp. 145
–152
.10.1007/s11249-004-1770-y82.
Akbarzadeh
, S.
, and Khonsari
, M.
, 2008
, “Performance of Spur Gears Considering Surface Roughness and Shear Thinning Lubricant
,” ASME J. Tribol.
, 130
(2
), p. 021503
.10.1115/1.280543183.
Bird
, R.
, Curtiss
, C.
, Armstrong
, R.
, and Hassager
, O.
, 1987
, Dynamics of Polymer Liquids Vol. 2 Kinetic Theory
, John Wiley and Sons
, New York
.84.
Bair
, S.
, and Winer
, W.
, 2007
, “A Quantitative Test of the Einstein–Debye Relation for Low Molecular Weight Liquids Using the Shear Dependence of Viscosity
,” Tribol. Lett.
, 26
(3
), pp. 223
–228
.10.1007/s11249-007-9195-z85.
Debye
, P. J. W.
, 1929
, Polar Molecules
, Dover
, New York
.86.
Dyson
, A.
, 1970
, “Frictional Traction and Lubricant Rheology in Elastohydrodynamic Lubrication
,” Philos. Trans. R. Soc. London Ser. A
, 266
(1170
), pp. 1
–33
.10.1098/rsta.1970.000187.
Bair
, S.
, 2001
, “Ordinary Shear-Thinning Behavior in Liquids and Its Effect Upon EHL Traction
,” Tribol. Interface Eng. Ser.
, 39
, pp. 733
–742
.88.
Macosko
, C.
, 1994
, Rheology: Principles, Measurements, and Applications
, Wiley-VCH
, Poughkeepsie, NY
.89.
Bair
, S. S.
, 2007
, High-Pressure Rheology for Quantitative Elastohydrodynamics
, Elsevier Science
, Oxford, UK.90.
Ferry
, J.
, 1980
, Viscoelastic Properties of Polymers
, John Wiley and Sons
, New York.91.
Villegas
, J.
, Olayo
, R.
, and Cervantes
, J.
, 2003
, “Effect of Side Groups on the Conformation of a Series of Polysiloxanes in Solution
,” J. Inorg. Organomet. Polym.
, 13
(4
), pp. 205
–222
.10.1023/A:102619192674292.
Huglin
, M. B.
, 1972
, Light Scattering From Polymer Solutions
, Academic
, New York.93.
Strohriegl
, P.
, 1986
, “Polymers With Pendant Carbazole Groups, 1. Synthesis and Characterization of Some Novel Polysiloxanes
,” Die Makromol. Chem., Rapid Commun.
, 7
(12
), pp. 771
–775
.10.1002/marc.1986.03007120494.
Jakobsen
, J.
, Sanborn
, D.
, and Winer
, W.
, 1974
, “Pressure Viscosity Characteristics of a Series of Siloxane Fluids
,” ASME J. Lubr. Technol.
, 96
(3
), pp. 410
–417
.10.1115/1.345198095.
Kuss
, E.
, 1974
, “Viskositats-Druckverhalten von Flussigen Methyl-Phenylmethyl- und Cyclohexylmethyl-Siloxeanen
,” Erdol Kohle-Erdgas-Petrochem. Brennst.-Chem.
, 27
(8
), pp. 416
–422
.96.
ASME
, 1953
, Viscosity and Density of Over 40 Lubricating Fluids of Known Composition at Pressures to 150,000 psi and Temperatures to 425 F
, American Society of Mechanical Engineers
, New York.97.
Winer
, W. O.
, 1977
, A Study of the Elastohydrodynamic Lubrication and High Pressure Rheological Behavior of a Series of Silicone Fluids
, Georgia Institute of Technology
, Atlanta, GA, Technical Report No. E-25-619.98.
Bridgman
, P.
, 1949
, “Viscosities to 30,000 kg/cm2
,” Proc. Am. Acad. Arts Sci.
, 77
(4
), pp. 117
–128
.99.
Smeeth
, M.
, Spikes
, H.
, and Gunsel
, S.
, 1996
, “The Formation of Viscous Surface Films by Polymer Solutions: Boundary or Elastohydrodynamic Lubrication?
,” Tribol. Trans.
, 39
(3
), pp. 720
–725
.10.1080/10402009608983589100.
Bair
, S.
, 2002
, “The High Pressure Rheology of Some Simple Model Hydrocarbons
,” Proc. Inst. Mech. Eng., Part J
, 216
(3
), pp. 139
–149
.10.1243/1350650021543960Copyright © 2015 by ASME
You do not currently have access to this content.
