A comprehensive review of current analytical models, experimental techniques, and influencing factors is carried out to highlight the current challenges in this area. The study of fluid–solid boundary conditions has been ongoing for more than a century, starting from gas–solid interfaces and progressing to that of the more complex liquid–solid case. Breakthroughs have been made on the theoretical and experimental fronts but the mechanism behind the phenomena remains a puzzle. This paper provides a review of the theoretical models, and numerical and experimental investigations that have been carried out till date. Probable mechanisms and factors that affect the interfacial discontinuity are also documented.
Issue Section:
Review Article
Keywords:
Fluid mechanics
References
1.
Helmholtz
, H.
, and Piotrowski
, G.
, 1860
, Über Reibung Tropfbarer Flüssigkeiten
, K. K. Hof- & Staatsdruckerei, Wien
, Austria
(in German).2.
Gad-el-Hak
, M.
, 2003
, “Comments on ‘Critical View on New Results in Micro-Fluid Mechanics
,”’ Int. J. Heat Mass Transfer
, 46
(20
), pp. 3941
–3945
.3.
Lamb
, H.
, 2015
, Hydrodynamics
, Scholar's Choice
.4.
Navier
, C. L. M. H.
, 1823
, “Mémoires de l'Académie
,” Royale des Sciences de l'Institut de France
, Vol. 1
, Firmin Didot, Paris, pp. 414
–416
.5.
Fukui
, S.
, and Kaneko
, R.
, 1988
, “Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report—Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow
,” ASME J. Tribol.
, 110
(2
), pp. 253
–261
.6.
Huang
, W. D.
, Bogy
, D. B.
, and Garcia
, A. L.
, 1997
, “Three-Dimensional Direct Simulation Monte Carlo Method for Slider Air Bearings
,” Phys. Fluids
, 9
(6
), pp. 1764
–1769
.7.
Neto
, C.
, Evans
, D. R.
, Bonaccurso
, E.
, Butt
, H.-J.
, and Craig
, V. S. J.
, 2005
, “Boundary Slip in Newtonian Liquids: A Review of Experimental Studies
,” Rep. Prog. Phys.
, 68
(12
), pp. 2859
–2897
.8.
Lauga
, E.
, Brenner
, M. P.
, and Stone
, H. A.
, 2007
, “Microfluidics: The No-Slip Boundary Condition
,” Springer Handbook of Experimental Fluid Mechanics
, C.
Tropea
, A.
Yarin
, and J. F.
Foss
, eds., Springer
, Berlin, pp. 1219
–1240
.9.
Léger
, L.
, Hervet
, H.
, Massey
, G.
, and Durliat
, E.
, 1997
, “Wall Slip in Polymer Melts
,” J. Phys.: Condens. Matter
, 9
(37
), pp. 7719
–7740
.10.
Kapitza
, P. L.
, 1941
, “The Study of Heat Transfer in Helium II
,” J. Phys.-USSR
, 4
(1–6
), pp. 181
–210
.11.
Maali
, A.
, and Bhushan
, B.
, 2008
, “Slip-Length Measurement of Confined Air Flow Using Dynamic Atomic Force Microscopy
,” Phys. Rev. E
, 78
(2
), p. 027302
.12.
Honig
, C. D. F.
, Sader
, J. E.
, Mulvaney
, P.
, and Ducker
, W. A.
, 2010
, “Lubrication Forces in Air and Accommodation Coefficient Measured by a Thermal Damping Method Using an Atomic Force Microscope
,” Phys. Rev. E
, 81
(5
), p. 056305
.13.
Rodrigues
, T. S.
, Butt
, H.-J.
, and Bonaccurso
, E.
, 2010
, “Influence of the Spring Constant of Cantilevers on Hydrodynamic Force Measurements by the Colloidal Probe Technique
,” Colloids Surf., A
, 354
(1–3
), pp. 72
–80
.14.
Zhu
, Y.
, and Granick
, S.
, 2002
, “Limits of the Hydrodynamic No-Slip Boundary Condition
,” Phys. Rev. Lett.
, 88
(10
), p. 106102
.15.
Cottin-Bizonne
, C.
, Cross
, B.
, Steinberger
, A.
, and Charlaix
, E.
, 2005
, “Boundary Slip on Smooth Hydrophobic Surfaces: Intrinsic Effects and Possible Artifacts
,” Phys. Rev. Lett.
, 94
(5
), p. 056102
.16.
Shu
, J.-J.
, Teo
, J. B. M.
, and Chan
, W. K.
, 2016
, “A New Model for Fluid Velocity Slip on a Solid Surface
,” Soft Matter
, 12
(40
), pp. 8388
–8397
.17.
Shu
, J.-J.
, Teo
, J. B. M.
, and Chan
, W. K.
, 2016
, “A New Model for Temperature Jump at a Fluid-Solid Interface
,” PLoS One
, 11
(10
), p. e0165175
.18.
Sharatchandra
, M. C.
, Sen
, M.
, and Gad-el-Hak
, M.
, 1998
, “Thermal Aspects of a Novel Viscous Pump
,” ASME J. Heat Transfer
, 120
(1
), pp. 99
–107
.19.
Bataineh
, K. M.
, and Al-Nimr
, M. A.
, 2009
, “2D Navier–Stokes Simulations of Microscale Viscous Pump With Slip Flow
,” ASME J. Fluids Eng.
, 131
(5
), p. 051105
.20.
Murad
, S.
, and Puri
, I. K.
, 2013
, “A Thermal Logic Device Based on Fluid-Solid Interfaces
,” Appl. Phys. Lett.
, 102
(19
), p. 193109
.21.
Patankar
, N. A.
, 2004
, “Mimicking the Lotus Effect: Influence of Double Roughness Structures and Slender Pillars
,” Langmuir
, 20
(19
), pp. 8209
–8213
.22.
Rothstein
, J. P.
, 2010
, “Slip on Superhydrophobic Surfaces
,” Annu. Rev. Fluid Mech.
, 42
(1
), pp. 89
–109
.23.
Ternes
, M.
, Lutz
, C. P.
, Hirjibehedin
, C. F.
, Giessibl
, F. J.
, and Heinrich
, A. J.
, 2008
, “The Force Needed to Move an Atom on a Surface
,” Science
, 319
(5866
), pp. 1066
–1069
.24.
Gomes
, K. K.
, Mar
, W.
, Ko
, W.
, Guinea
, F.
, and Manoharan
, H. C.
, 2012
, “Designer Dirac Fermions and Topological Phases in Molecular Graphene
,” Nature
, 483
(7389
), pp. 306
–310
.25.
Israelachvili
, J. N.
, 2012
, Intermolecular and Surface Forces
, 3rd ed., World Publishing Corporation
Beijing
, Beijing, China.26.
Cheng
, L.
, Fenter
, P.
, Nagy
, K. L.
, Schlegel
, M. L.
, and Sturchio
, N. C.
, 2001
, “Molecular-Scale Density Oscillations in Water Adjacent to a Mica Surface
,” Phys. Rev. Lett.
, 87
(15
), p. 156103
.27.
Barrat
, J.-L.
, and Bocquet
, L.
, 1999
, “Influence of Wetting Properties on Hydrodynamic Boundary Conditions at a Fluid/Solid Interface
,” Faraday Discuss.
, 112
, pp. 119
–127
.28.
Groß
, A.
, 2009
, Theoretical Surface Science: A Microscopic Perspective
, 2nd ed., Springer
, Berlin.29.
Brenner
, H.
, and Ganesan
, V.
, 2000
, “Molecular Wall Effects: Are Conditions at a Boundary ‘Boundary Conditions’?
,” Phys. Rev. E
, 61
(6B
), pp. 6879
–6897
.30.
Cucchetti
, A.
, and Ying
, S. C.
, 1996
, “Memory Effects in the Frictional Damping of Diffusive and Vibrational Motion of Adatoms
,” Phys. Rev. B
, 54
(5
), pp. 3300
–3310
.31.
de Gennes
, P. G.
, 2002
, “On Fluid/Wall Slippage
,” Langmuir
, 18
(9
), pp. 3413
–3414
.32.
Gutfreund
, P.
, Wolff
, M.
, Maccarini
, M.
, Gerth
, S.
, Ankner
, J. F.
, Browning
, J.
, Halbert
, C. E.
, Wacklin
, H.
, and Zabel
, H.
, 2011
, “Depletion at Solid/Liquid Interfaces: Flowing Hexadecane on Functionalized Surfaces
,” J. Chem. Phys.
, 134
(6
), p. 064711
.33.
Ala-Nissila
, T.
, Ferrando
, R.
, and Ying
, S. C.
, 2002
, “Collective and Single Particle Diffusion on Surfaces
,” Adv. Phys.
, 51
(3
), pp. 949
–1078
.34.
Richardson
, S.
, 1973
, “On the No-Slip Boundary Condition
,” J. Fluid Mech.
, 59
(4
), pp. 707
–719
.35.
Dussan
, E. B.
, and Davis
, S. H.
, 1974
, “On the Motion of a Fluid–Fluid Interface Along a Solid Surface
,” J. Fluid Mech.
, 65
(1
), pp. 71
–95
.36.
Brigo
, L.
, Natali
, M.
, Pierno
, M.
, Mammano
, F.
, Sada
, C.
, Fois
, G.
, Pozzato
, A.
, dal Zilio
, S.
, Tormen
, M.
, and Mistura
, G.
, 2008
, “Water Slip and Friction at a Solid Surface
,” J. Phys.: Condens. Matter
, 20
(35
), p. 354016
.37.
Cottin-Bizonne
, C.
, Barrat
, J.-L.
, Bocquet
, L.
, and Charlaix
, E.
, 2003
, “Low-Friction Flows of Liquid at Nanopatterned Interfaces
,” Nat. Mater.
, 2
(4
), pp. 237
–240
.38.
Bonaccurso
, E.
, Butt
, H.-J.
, and Craig
, V. S. J.
, 2003
, “Surface Roughness and Hydrodynamic Boundary Slip of a Newtonian Fluid in a Completely Wetting System
,” Phys. Rev. Lett.
, 90
(14
), p. 144501
.39.
Truesdell
, R.
, Mammoli
, A.
, Vorobieff
, P.
, van Swol
, F.
, and Brinker
, C. J.
, 2006
, “Drag Reduction on a Patterned Superhydrophobic Surface
,” Phys. Rev. Lett.
, 97
(4
), p. 044504
.40.
Sbragaglia
, M.
, Benzi
, R.
, Biferale
, L.
, Succi
, S.
, and Toschi
, F.
, 2006
, “Surface Roughness-Hydrophobicity Coupling in Microchannel and Nanochannel Flows
,” Phys. Rev. Lett.
, 97
(20
), p. 204503
.41.
Ziarani
, A. S.
, and Mohamad
, A. A.
, 2008
, “Effect of Wall Roughness on the Slip of Fluid in a Microchannel
,” Nanoscale Microscale Thermophys. Eng.
, 12
(2
), pp. 154
–169
.42.
Cottin-Bizonne
, C.
, Barentin
, C.
, Charlaix
, É.
, Bocquet
, L.
, and Barrat
, J.-L.
, 2004
, “Dynamics of Simple Liquids at Heterogeneous Surfaces: Molecular-Dynamics Simulations and Hydrodynamic Description
,” Eur. Phys. J. E
, 15
(4
), pp. 427
–438
.43.
Vinogradova
, O. I.
, and Yakubov
, G. E.
, 2006
, “Surface Roughness and Hydrodynamic Boundary Conditions
,” Phys. Rev. E
, 73
(4
), p. 45302
.44.
Bartell
, F. E.
, and Shepard
, J. W.
, 1953
, “Surface Roughness as Related to Hysteresis of Contact Angles. II. The Systems Paraffin-3 Molar Calcium Chloride Solution-Air and Paraffin-Glycerol-Air
,” J. Phys. Chem.
, 57
(4
), pp. 455
–458
.45.
Patankar
, N. A.
, 2003
, “On the Modeling of Hydrophobic Contact Angles on Rough Surfaces
,” Langmuir
, 19
(4
), pp. 1249
–1253
.46.
Extrand
, C. W.
, 2003
, “Contact Angles and Hysteresis on Surfaces With Chemically Heterogeneous Islands
,” Langmuir
, 19
(9
), pp. 3793
–3796
.47.
Lauga
, E.
, and Squires
, T. M.
, 2005
, “Brownian Motion Near a Partial-Slip Boundary: A Local Probe of the No-Slip Condition
,” Phys. Fluids
, 17
(10
), p. 103102
.48.
Gao
, L.
, and McCarthy
, T. J.
, 2007
, “How Wenzel and Cassie Were Wrong
,” Langmuir
, 23
(7
), pp. 3762
–3765
.49.
McHale
, G.
, 2007
, “Cassie and Wenzel: Were They Really So Wrong?
,” Langmuir
, 23
(15
), pp. 8200
–8205
.50.
Govardhan
, R. N.
, Srinivas
, G. S.
, Asthana
, A.
, and Bobji
, M. S.
, 2009
, “Time Dependence of Effective Slip on Textured Hydrophobic Surfaces
,” Phys. Fluids
, 21
(5
), p. 052001
.51.
Öner
, D.
, and McCarthy
, T. J.
, 2000
, “Ultrahydrophobic Surfaces: Effects of Topography Length Scales on Wettability
,” Langmuir
, 16
(20
), pp. 7777
–7782
.52.
Lau
, K. K. S.
, Bico
, J.
, Teo
, K. B. K.
, Chhowalla
, M.
, Amaratunga
, G. A. J.
, Milne
, W. I.
, McKinley
, G. H.
, and Gleason
, K. K.
, 2003
, “Superhydrophobic Carbon Nanotube Forests
,” Nano Lett.
, 3
(12
), pp. 1701
–1705
.53.
Ou
, J.
, Perot
, B.
, and Rothstein
, J. P.
, 2004
, “Laminar Drag Reduction in Microchannels Using Ultrahydrophobic Surfaces
,” Phys. Fluids
, 16
(12
), pp. 4635
–4643
.54.
Choi
, C.-H.
, and Kim
, C.-J.
, 2006
, “Large Slip of Aqueous Liquid Flow Over a Nanoengineered Superhydrophobic Surface
,” Phys. Rev. Lett.
, 96
(6
), p. 066001
.55.
Vinogradova
, O. I.
, 1995
, “Drainage of a Thin Liquid Film Confined Between Hydrophobic Surfaces
,” Langmuir
, 11
(6
), pp. 2213
–2220
.56.
Ybert
, C.
, Barentin
, C.
, Cottin-Bizonne
, C.
, Joseph
, P.
, and Bocquet
, L.
, 2007
, “Achieving Large Slip With Superhydrophobic Surfaces: Scaling Laws for Generic Geometries
,” Phys. Fluids
, 19
(12
), p. 123601
.57.
Teo
, C. J.
, and Khoo
, B. C.
, 2010
, “Flow Past Superhydrophobic Surfaces Containing Longitudinal Grooves: Effects of Interface Curvature
,” Microfluid. Nanofluid.
, 9
(2–3
), pp. 499
–511
.58.
Ng
, C.-O.
, Chu
, H. C. W.
, and Wang
, C. Y.
, 2010
, “On the Effects of Liquid-Gas Interfacial Shear on Slip Flow Through a Parallel-Plate Channel With Superhydrophobic Grooved Walls
,” Phys. Fluids
, 22
(10
), p. 102002
.59.
Davis
, A. M. J.
, and Lauga
, E.
, 2010
, “Hydrodynamic Friction of Fakir-Like Superhydrophobic Surfaces
,” J. Fluid Mech.
, 661
, pp. 402
–411
.60.
Basson
, A.
, and Gérard-Varet
, D.
, 2008
, “Wall Laws for Fluid Flows at a Boundary With Random Roughness
,” Commun. Pure Appl. Math.
, 61
(7
), pp. 941
–987
.61.
Samaha
, M. A.
, Tafreshi
, H. V.
, and Gad-el-Hak
, M.
, 2011
, “Modeling Drag Reduction and Meniscus Stability of Superhydrophobic Surfaces Comprised of Random Roughness
,” Phys. Fluids
, 23
(1
), p. 012001
.62.
Priezjev
, N. V.
, and Troian
, S. M.
, 2006
, “Influence of Periodic Wall Roughness on the Slip Behaviour at Liquid/Solid Interfaces: Molecular-Scale Simulations Versus Continuum Predictions
,” J. Fluid Mech.
, 554
, pp. 25
–46
.63.
Choi
, C.-H.
, Westin
, K. J. A.
, and Breuer
, K. S.
, 2003
, “Apparent Slip Flows in Hydrophilic and Hydrophobic Microchannels
,” Phys. Fluids
, 15
(10
), pp. 2897
–2902
.64.
Ho
, T. A.
, Papavassiliou
, D. V.
, Lee
, L. L.
, and Striolo
, A.
, 2011
, “Liquid Water Can Slip on a Hydrophilic Surface
,” Proc. Natl. Acad. Sci. U.S.A.
, 108
(39
), pp. 16170
–16175
.65.
Blake
, T. D.
, 1990
, “Slip Between a Liquid and a Solid: D. M. Tolstoi’s (1952) Theory Reconsidered
,” Colloids Surf.
, 47
(1
), pp. 135
–145
.66.
Ellis
, J. S.
, McHale
, G.
, Hayward
, G. L.
, and Thompson
, M.
, 2003
, “Contact Angle-Based Predictive Model for Slip at the Solid–Liquid Interface of a Transverse-Shear Mode Acoustic Wave Device
,” J. Appl. Phys.
, 94
(9
), pp. 6201
–6207
.67.
Voronov
, R. S.
, Papavassiliou
, D. V.
, and Lee
, L. L.
, 2008
, “Review of Fluid Slip Over Superhydrophobic Surfaces and Its Dependence on the Contact Angle
,” Ind. Eng. Chem. Res.
, 47
(8
), pp. 2455
–2477
.68.
Voronov
, R. S.
, Papavassiliou
, D. V.
, and Lee
, L. L.
, 2007
, “Slip Length and Contact Angle Over Hydrophobic Surfaces
,” Chem. Phys. Lett.
, 441
(4–6
), pp. 273
–276
.69.
Thompson
, P. A.
, and Robbins
, M. O.
, 1990
, “Shear Flow Near Solids—Epitaxial Order and Flow Boundary Conditions
,” Phys. Rev. A
, 41
(12
), pp. 6830
–6837
.70.
Hall
, R. O. A.
, and Martin
, D. G.
, 1987
, “The Evaluation of Temperature Jump Distances and Thermal Accommodation Coefficients From Measurements of the Thermal Conductivity of UO2 Packed Sphere Beds
,” Nucl. Eng. Des.
, 101
(3
), pp. 249
–258
.71.
Hersht
, I.
, and Rabin
, Y.
, 1994
, “Shear Melting of Solid-Like Boundary Layers in Thin Liquid Films
,” J. Non-Cryst. Solids
, 172–174
(2
), pp. 857
–861
.72.
Zhu
, Y.
, and Granick
, S.
, 2004
, “Superlubricity: A Paradox About Confined Fluids Resolved
,” Phys. Rev. Lett.
, 93
(9
), p. 096101
.73.
Tretheway
, D. C.
, and Meinhart
, C. D.
, 2004
, “A Generating Mechanism for Apparent Fluid Slip in Hydrophobic Microchannels
,” Phys. Fluids
, 16
(5
), pp. 1509
–1515
.74.
Wolff
, M.
, Akgun
, B.
, Walz
, M.
, Magerl
, A.
, and Zabel
, H.
, 2008
, “Slip and Depletion in a Newtonian Liquid
,” EPL
, 82
(3
), p. 36001
.75.
Ruckenstein
, E.
, and Rajora
, P.
, 1983
, “On the No-Slip Boundary Condition of Hydrodynamics
,” J. Colloid Interface Sci.
, 96
(2
), pp. 488
–491
.76.
Alexeyev
, A. A.
, and Vinogradova
, O. I.
, 1996
, “Flow of a Liquid in a Nonuniformly Hydrophobized Capillary
,” Colloids Surf., A
, 108
(2–3
), pp. 173
–179
.77.
Oron
, A.
, Davis
, S. H.
, and Bankoff
, S. G.
, 1997
, “Long-Scale Evolution of Thin Liquid Films
,” Rev. Mod. Phys.
, 69
(3
), pp. 931
–980
.78.
Andrienko
, D.
, Dünweg
, B.
, and Vinogradova
, O. I.
, 2003
, “Boundary Slip as a Result of a Prewetting Transition
,” J. Chem. Phys.
, 119
(24
), pp. 13106
–13112
.79.
Ishida
, N.
, Inoue
, T.
, Miyahara
, M.
, and Higashitani
, K.
, 2000
, “Nano Bubbles on a Hydrophobic Surface in Water Observed by Tapping-Mode Atomic Force Microscopy
,” Langmuir
, 16
(16
), pp. 6377
–6380
.80.
Lou
, S.-T.
, Ouyang
, Z.-Q.
, Zhang
, Y.
, Li
, X.-J.
, Hu
, J.
, Li
, M.-Q.
, and Yang
, F.-J.
, 2000
, “Nanobubbles on Solid Surface Imaged by Atomic Force Microscopy
,” J. Vac. Sci. Technol. B
, 18
(5
), pp. 2573
–2575
.81.
Yang
, J.
, Duan
, J.
, Fornasiero
, D.
, and Ralston
, J.
, 2003
, “Very Small Bubble Formation at the Solid-Water Interface
,” J. Phys. Chem. B
, 107
(25
), pp. 6139
–6147
.82.
Zhang
, X. H.
, Zhang
, X. D.
, Lou
, S. T.
, Zhang
, Z. X.
, Sun
, J. L.
, and Hu
, J.
, 2004
, “Degassing and Temperature Effects on the Formation of Nanobubbles at the Mica/Water Interface
,” Langmuir
, 20
(9
), pp. 3813
–3815
.83.
Boehnke
, U.-C.
, Remmler
, T.
, Motschmann
, H.
, Wurlitzer
, S.
, Hauwede
, J.
, and Fischer
, T. M.
, 1999
, “Partial Air Wetting on Solvophobic Surfaces in Polar Liquids
,” J. Colloid Interface Sci.
, 211
(2
), pp. 243
–251
.84.
Granick
, S.
, Zhu
, Y.
, and Lee
, H.
, 2003
, “Slippery Questions About Complex Fluids Flowing Past Solids
,” Nat. Mater.
, 2
(4
), pp. 221
–227
.85.
Steinberger
, A.
, Cottin-Bizonne
, C.
, Kleimann
, P.
, and Charlaix
, E.
, 2007
, “High Friction on a Bubble Mattress
,” Nat. Mater.
, 6
(9
), pp. 665
–668
.86.
Hyväluoma
, J.
, and Harting
, J.
, 2008
, “Slip Flow Over Structured Surfaces With Entrapped Microbubbles
,” Phys. Rev. Lett.
, 100
(24
), p. 246001
.87.
Davis
, A. M. J.
, and Lauga
, E.
, 2009
, “Geometric Transition in Friction for Flow Over a Bubble Mattress
,” Phys. Fluids
, 21
(1
), p. 011701
.88.
Haase
, A. S.
, Wood
, J. A.
, Lammertink
, R. G. H.
, and Snoeijer
, J. H.
, 2016
, “Why Bumpy is Better: The Role of the Dissipation Distribution in Slip Flow Over a Bubble Mattress
,” Phys. Rev. Fluids
, 1
(5
), p. 054101
.89.
Tretheway
, D. C.
, and Meinhart
, C. D.
, 2002
, “Apparent Fluid Slip at Hydrophobic Microchannel Walls
,” Phys. Fluids
, 14
(3
), pp. L9
–L12
.90.
Thompson
, P. A.
, and Troian
, S. M.
, 1997
, “A General Boundary Condition for Liquid Flow at Solid Surfaces
,” Nature
, 389
(6649
), pp. 360
–362
.91.
Harting
, J.
, Kunert
, C.
, and Herrmann
, H. J.
, 2006
, “Lattice Boltzmann Simulations of Apparent Slip in Hydrophobic Microchannels
,” Europhys. Lett.
, 75
(2
), pp. 328
–334
.92.
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
.93.
Zhu
, Y.
, and Granick
, S.
, 2001
, “Rate-Dependent Slip of Newtonian Liquid at Smooth Surfaces
,” Phys. Rev. Lett.
, 87
(9
), p. 96105
.94.
Spikes
, H.
, and Granick
, S.
, 2003
, “Equation for Slip of Simple Liquids at Smooth Solid Surfaces
,” Langmuir
, 19
(12
), pp. 5065
–5071
.95.
Lauga
, E.
, and Brenner
, M. P.
, 2004
, “Dynamic Mechanisms for Apparent Slip on Hydrophobic Surfaces
,” Phys. Rev. E
, 70
(2
), p. 026311
.96.
Martini
, A.
, Hsu
, H.-Y.
, Patankar
, N. A.
, and Lichter
, S.
, 2008
, “Slip at High Shear Rates
,” Phys. Rev. Lett.
, 100
(20
), p. 206001
.97.
Gao
, P.
, and Feng
, J. J.
, 2009
, “Enhanced Slip on a Patterned Substrate Due to Depinning of Contact Line
,” Phys. Fluids
, 21
(10
), p. 102102
.98.
Ulmanella
, U.
, and Ho
, C.-M.
, 2008
, “Molecular Effects on Boundary Condition in Micro/Nanoliquid Flows
,” Phys. Fluids
, 20
(10
), p. 101512
.99.
Maxwell
, J. C.
, 1879
, “On Stresses in Rarefied Gases Arising From Inequalities of Temperature
,” Philos. Trans. R. Soc.
, 170
(1
), pp. 231
–256
.100.
Burgdorfer
, A.
, 1959
, “The Influence of the Molecular Mean Free Path on the Performance of Hydrodynamic Gas Lubricated Bearings
,” J. Basic Eng.
, 81
(1
), pp. 94
–100
.101.
Bhattacharya
, D. K.
, and Eu
, B. C.
, 1987
, “Nonlinear Transport Processes and Fluid-Dynamics: Effects of Thermoviscous Coupling and Nonlinear Transport Coefficients on Plane Couette Flow of Lennard-Jones Fluids
,” Phys. Rev. A
, 35
(2
), pp. 821
–836
.102.
Myong
, R. S.
, 2004
, “Gaseous Slip Models Based on the Langmuir Adsorption Isotherm
,” Phys. Fluids
, 16
(1
), pp. 104
–117
.103.
Tolstoi
, D. M.
, 1952
, “Molecular Theory of the Slip of Liquids on Solid Surfaces
,” Dokl. Akad. Nauk SSSR
, 85
(5
), pp. 1089
–1092
(in Russian).104.
Lichter
, S.
, Martini
, A.
, Snurr
, R. Q.
, and Wang
, Q.
, 2007
, “Liquid Slip in Nanoscale Channels as a Rate Process
,” Phys. Rev. Lett.
, 98
(22
), p. 226001
.105.
Bowles
, A. P.
, Honig
, C. D. F.
, and Ducker
, W. A.
, 2011
, “No-Slip Boundary Condition for Weak Solid–Liquid Interactions
,” J. Phys. Chem. C
, 115
(17
), pp. 8613
–8621
.106.
Yang
, F.
, 2009
, “Slip Boundary Condition for Viscous Flow Over Solid Surfaces
,” Chem. Eng. Commun.
, 197
(4
), pp. 544
–550
.107.
Wang
, F.-C.
, and Zhao
, Y.-P.
, 2011
, “Slip Boundary Conditions Based on Molecular Kinetic Theory: The Critical Shear Stress and the Energy Dissipation at the Liquid–Solid Interface
,” Soft Matter
, 7
(18
), pp. 8628
–8634
.108.
Teo
, J. B. M.
, Shu
, J.-J.
, and Chan
, W. K.
, 2017
, “Slip of Fluid Molecules on Solid Surfaces by Surface Diffusion
,” AIChE J.
, 63
, pp. 1
–15
.109.
Lichter
, S.
, Roxin
, A.
, and Mandre
, S.
, 2004
, “Mechanisms for Liquid Slip at Solid Surfaces
,” Phys. Rev. Lett.
, 93
(8
), p. 086001
.110.
Martini
, A.
, Roxin
, A.
, Snurr
, R. Q.
, Wang
, Q.
, and Lichter
, S.
, 2008
, “Molecular Mechanisms of Liquid Slip
,” J. Fluid Mech.
, 600
, pp. 257
–269
.111.
Bouzigues
, C. I.
, Bocquet
, L.
, Charlaix
, E.
, Cottin-Bizonne
, C.
, Cross
, B.
, Joly
, L.
, Steinberger
, A.
, Ybert
, C.
, and Tabeling
, P.
, 2008
, “Using Surface Force Apparatus, Diffusion and Velocimetry to Measure Slip Lengths
,” Philos. Trans. R. Soc. A
, 366
(1869
), pp. 1455
–1468
.112.
Maali
, A.
, and Bhushan
, B.
, 2012
, “Measurement of Slip Length on Superhydrophobic Surfaces
,” Philos. Trans. R. Soc. A
, 370
(1967
), pp. 2304
–2320
.113.
Honig
, C. D. F.
, and Ducker
, W. A.
, 2007
, “No-Slip Hydrodynamic Boundary Condition for Hydrophilic Particles
,” Phys. Rev. Lett.
, 98
(2
), p. 028305
.114.
Henry
, C. L.
, and Craig
, V. S. J.
, 2009
, “Measurement of No-Slip and Slip Boundary Conditions in Confined Newtonian Fluids Using Atomic Force Microscopy
,” Phys. Chem. Chem. Phys.
, 11
(41
), pp. 9514
–9521
.115.
Lauga
, E.
, 2004
, “Apparent Slip Due to the Motion of Suspended Particles in Flows of Electrolyte Solutions
,” Langmuir
, 20
(20
), pp. 8924
–8930
.116.
Li
, Z.
, D’eramo
, L.
, Monti
, F.
, Vayssade
, A.-L.
, Chollet
, B.
, Bresson
, B.
, Tran
, Y.
, Cloitre
, M.
, and Tabeling
, P.
, 2014
, “Slip Length Measurements Using mu PIV and TIRF-Based Velocimetry
,” Isr. J. Chem.
, 54
(11–12
), pp. 1589
–1601
.117.
Joly
, L.
, Ybert
, C.
, and Bocquet
, L.
, 2006
, “Probing the Nanohydrodynamics at Liquid-Solid Interfaces Using Thermal Motion
,” Phys. Rev. Lett.
, 96
(4
), p. 046101
.118.
Daikhin
, L.
, Gileadi
, E.
, Tsionsky
, V.
, Urbakh
, M.
, and Zilberman
, G.
, 2000
, “Slippage at Adsorbate-Electrolyte Interface: Response of Electrochemical Quartz Crystal Microbalance to Adsorption
,” Electrochim. Acta
, 45
(22–23
), pp. 3615
–3621
.119.
Du
, B.
, Goubaidoulline
, I.
, and Johannsmann
, D.
, 2004
, “Effects of Laterally Heterogeneous Slip on the Resonance Properties of Quartz Crystals Immersed in Liquids
,” Langmuir
, 20
(24
), pp. 10617
–10624
.120.
McHale
, G.
, and Newton
, M. I.
, 2004
, “Surface Roughness and Interfacial Slip Boundary Condition for Quartz Crystal Microbalances
,” J. Appl. Phys.
, 95
(1
), pp. 373
–380
.121.
Willmott
, G. R.
, and Tallon
, J. L.
, 2007
, “Measurement of Newtonian Fluid Slip Using a Torsional Ultrasonic Oscillator
,” Phys. Rev. E
, 76
(6
), p. 066306
.122.
Churaev
, N. V.
, Ralston
, J.
, Sergeeva
, I. P.
, and Sobolev
, V. D.
, 2002
, “Electrokinetic Properties of Methylated Quartz Capillaries
,” Adv. Colloid Interface Sci.
, 96
(1–3
), pp. 265
–278
.123.
Watanabe
, K.
, Takayama
, T.
, Ogata
, S.
, and Isozaki
, S.
, 2003
, “Flow Between Two Coaxial Rotating Cylinders With a Highly Water-Repellent Wall
,” AIChE J.
, 49
(8
), pp. 1956
–1963
.124.
Perisanu
, S.
, and Vermeulen
, G.
, 2006
, “Curvature, Slip, and Viscosity in He-3-He-4 Mixtures
,” Phys. Rev. B
, 73
(13
), p. 134517
.125.
Bocquet
, L.
, Tabeling
, P.
, and Manneville
, S.
, 2006
, “Comment on ‘Large Slip of Aqueous Liquid Flow Over a Nanoengineered Superhydrophobic Surface
,”’ Phys. Rev. Lett.
, 97
(10
), p. 109601
.126.
Harting
, J.
, Kunert
, C.
, and Hyvaluoma
, J.
, 2010
, “Lattice Boltzmann Simulations in Microfluidics: Probing the No-Slip Boundary Condition in Hydrophobic, Rough, and Surface Nanobubble Laden Microchannels
,” Microfluid. Nanofluid.
, 8
(1
), pp. 1
–10
.127.
Pahlavan
, A. A.
, and Freund
, J. B.
, 2011
, “Effect of Solid Properties on Slip at a Fluid–Solid Interface
,” Phys. Rev. E
, 83
(2
), p. 021602
.128.
Yong
, X.
, and Zhang
, L. T.
, 2013
, “Slip in Nanoscale Shear Flow: Mechanisms of Interfacial Friction
,” Microfluid. Nanofluid.
, 14
(1–2
), pp. 299
–308
.129.
Arkilic
, E. B.
, Schmidt
, M. A.
, and Breuer
, K. S.
, 1997
, “Gaseous Slip Flow in Long Microchannels
,” J. Microelectromech. Syst.
, 6
(2
), pp. 167
–178
.130.
Harley
, J. C.
, Huang
, Y.
, Bau
, H. H.
, and Zemel
, J. N.
, 1995
, “Gas Flow in Micro-Channels
,” J. Fluid Mech.
, 284
, pp. 257
–274
.131.
Bentz
, J. A.
, Tompson
, R. V.
, and Loyalka
, S. K.
, 2001
, “Measurements of Viscosity, Velocity Slip Coefficients, and Tangential Momentum Accommodation Coefficients Using a Modified Spinning Rotor Gauge
,” J. Vac. Sci. Technol. A
, 19
(1
), pp. 317
–324
.132.
Bentz
, J. A.
, Tompson
, R. V.
, and Loyalka
, S. K.
, 1999
, “Viscosity and Velocity Slip Coefficients for Gas Mixtures: Measurements With a Spinning Rotor Gauge
,” J. Vac. Sci. Technol. A
, 17
(1
), pp. 235
–241
.133.
Graur
, I. A.
, Perrier
, P.
, Ghozlani
, W.
, and Méolans
, J. G.
, 2009
, “Measurements of Tangential Momentum Accommodation Coefficient for Various Gases in Plane Microchannel
,” Phys. Fluids
, 21
(10
), p. 102004
.134.
Bird
, G. A.
, 1994
, Molecular Gas Dynamics and the Direct Simulation of Gas Flows
, 2nd ed., Clarendon Press
, Oxford, UK.135.
Shen
, C.
, 2010
, Rarefied Gas Dynamics: Fundamentals, Simulations and Micro Flows
, Springer
, Berlin.136.
Kennard
, E. H.
, 1954
, Kinetic Theory of Gases
, McGraw-Hill
, New York.137.
Pollack
, G. L.
, 1969
, “Kapitza Resistance
,” Rev. Mod. Phys.
, 41
(1
), pp. 48
–81
.138.
Swartz
, E. T.
, and Pohl
, R. O.
, 1989
, “Thermal Boundary Resistance
,” Rev. Mod. Phys.
, 61
(3
), pp. 605
–668
.139.
Cahill
, D. G.
, Ford
, W. K.
, Goodson
, K. E.
, Mahan
, G. D.
, Majumdar
, A.
, Maris
, H. J.
, Merlin
, R.
, and Phillpot
, S. R.
, 2003
, “Nanoscale Thermal Transport
,” J. Appl. Phys.
, 93
(2
), pp. 793
–818
.140.
Goicochea
, J. V.
, Hu
, M.
, Michel
, B.
, and Poulikakos
, D.
, 2011
, “Surface Functionalization Mechanisms of Enhancing Heat Transfer at Solid–Liquid Interfaces
,” ASME J. Heat Transfer
, 133
(8)
, p. 082401
.141.
Acharya
, H.
, Mozdzierz
, N. J.
, Keblinski
, P.
, and Garde
, S.
, 2012
, “How Chemistry, Nanoscale Roughness, and the Direction of Heat Flow Affect Thermal Conductance of Solid-Water Interfaces
,” Ind. Eng. Chem. Res.
, 51
(4
), pp. 1767
–1773
.142.
Wang
, Y.
, and Keblinski
, P.
, 2011
, “Role of Wetting and Nanoscale Roughness on Thermal Conductance at Liquid-Solid Interface
,” Appl. Phys. Lett.
, 99
(7
), p. 073112
.143.
Ge
, Z.
, Cahill
, D. G.
, and Braun
, P. V.
, 2006
, “Thermal Conductance of Hydrophilic and Hydrophobic Interfaces
,” Phys. Rev. Lett.
, 96
(18
), p. 186101
.144.
Shenogina
, N.
, Godawat
, R.
, Keblinski
, P.
, and Garde
, S.
, 2009
, “How Wetting and Adhesion Affect Thermal Conductance of a Range of Hydrophobic to Hydrophilic Aqueous Interfaces
,” Phys. Rev. Lett.
, 102
(15
), p. 156101
.145.
Murad
, S.
, and Puri
, I. K.
, 2008
, “Thermal Transport Across Nanoscale Solid-Fluid Interfaces
,” Appl. Phys. Lett.
, 92
(13
), p. 133105
.146.
Xue
, L.
, Keblinski
, P.
, Phillpot
, S. R.
, Choi
, S. U.-S.
, and Eastman
, J. A.
, 2003
, “Two Regimes of Thermal Resistance at a Liquid–Solid Interface
,” J. Chem. Phys.
, 118
(1
), pp. 337
–339
.147.
Hu
, M.
, Goicochea
, J. V.
, Michel
, B.
, and Poulikakos
, D.
, 2009
, “Thermal Rectification at Water/Functionalized Silica Interfaces
,” Appl. Phys. Lett.
, 95
(15
), p. 151903
.148.
Murad
, S.
, and Puri
, I. K.
, 2012
, “Communication: Thermal Rectification in Liquids by Manipulating the Solid–Liquid Interface
,” J. Chem. Phys.
, 137
(8
), p. 081101
.149.
Smoluchowski
, M. S.
, 1898
, “Ueber Wärmeleitung in Verdünnten Gasen
,” Ann. Phys.
, 300
(1
), pp. 101
–130
.150.
Schäfer
, K.
, Rating
, W.
, and Eucken
, A.
, 1942
, “Influence of the Inhibited Exchanges of Translation and Vibration Energy to Heat Conduction of Gases
,” Ann. Phys.
, 434
(2/3
), pp. 176
–202
.151.
Dadzie
, S. K.
, and Méolans
, J. G.
, 2005
, “Temperature Jump and Slip Velocity Calculations From an Anisotropic Scattering Kernel
,” Physica A
, 358
(2–4
), pp. 328
–346
.152.
Baule
, B.
, 1914
, “Theoretische Behandlung der Erscheinungen in Verdünnten Gasen
,” Ann. Phys.
, 44
(1
), pp. 145
–176
.153.
Deissler
, R. G.
, 1964
, “An Analysis of Second-Order Slip Flow and Temperature-Jump Boundary Conditions for Rarefied Gases
,” Int. J. Heat Mass Transfer
, 7
(6
), pp. 681
–694
.154.
Lees
, L.
, and Liu
, C.-Y.
, 1960
, “Kinetic Theory Description of Plane, Compressible Couette Flow
,” California Institute of Technology
, Pasadena, CA.155.
Mazo
, R. M.
, 1955
, “Theoretical Studies on Low Temperature Phenomena
,” Yale University
, New Haven, CT.156.
Prasher
, R. S.
, and Phelan
, P. E.
, 2001
, “A Scattering-Mediated Acoustic Mismatch Model for the Prediction of Thermal Boundary Resistance
,” ASME J. Heat Transfer
, 123
(1
), pp. 105
–112
.157.
Bolmatov
, D.
, Brazhkin
, V. V.
, and Trachenko
, K.
, 2012
, “The Phonon Theory of Liquid Thermodynamics
,” Sci. Rep.
, 2
(421
), pp. 1
–6
.158.
Devienne
, F. M.
, 1965
, “Low Density Heat Transfer
,” Adv. Heat Transfer
, 2
, pp. 271
–356
.159.
Trott
, W. M.
, Rader
, D. J.
, Castañeda
, J. N.
, Torczynski
, J. R.
, and Gallis
, M. A.
, 2008
, “Measurement of Gas-Surface Accommodation
,” 26th International Symposium on Rarefied Gas Dynamics
, Kyoto, Japan, July 20–25, pp. 621
–628
.160.
Ge
, Z.
, Cahill
, D. G.
, and Braun
, P. V.
, 2004
, “AuPd Metal Nanoparticles as Probes of Nanoscale Thermal Transport in Aqueous Solution
,” J. Phys. Chem. B
, 108
(49
), pp. 18870
–18875
.161.
Kim
, B. H.
, Beskok
, A.
, and Cagin
, T.
, 2008
, “Molecular Dynamics Simulations of Thermal Resistance at the Liquid–Solid Interface
,” J. Chem. Phys.
, 129
(17
), p. 174701
.Copyright © 2017 by ASME
You do not currently have access to this content.
