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Springer Handbook of Experimental Fluid Mechanics pp 1219–1240Cite as

Microfluidics: The No-Slip Boundary Condition

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Part of the book series: Springer Handbooks ((SHB))

Abstract

The no-slip boundary condition at a solid–liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. In this chapter, we present a review of recent experimental, numerical and theoretical investigations on the subject. The physical picture that emerges is that of a complex behavior at a liquid/solid interface, involving an interplay of many physicochemical parameters, including wetting, shear rate, pressure, surface charge, surface roughness, impurities and dissolved gas.

In Sect. 19.1 we present a brief history of the no-slip boundary condition for Newtonian fluids, introduce some terminology, and discuss cases where the phenomenon of slip (more appropriately, this may often be apparent slip) has been observed. In Sect. 19.2 we present the different experimental methods that have been used to probe slip in Newtonian liquids and summarize their results in the form of tables. A short presentation of the principle and results of molecular dynamics simulations is provided in Sect. 19.3, as well as remarks about the relation between simulations and experiments. We then present in Sect. 19.4 an interpretation of experimental and simulation results in light of both molecular and continuum models, organized according to the parameters upon which slip has been found to depend. We conclude in Sect. 19.5 by offering a brief perspective on the subject.

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Abbreviations

AFM:

atomic force microscopy

CTA:

constant temperature anemometer

PDMS:

polydimethylsiloxane

PIV:

particle image velocimetry

PS:

polarization spectroscopy

PVA:

polyvinyl alcohol

SFA:

surface force apparatus

References

  1. T.M. Squires, S.R. Quake: Microfluidics: Fluid physics on the nanoliter scale, Rev. Mod. Phys. 77, 977–1026 (2005)

    Article  Google Scholar 

  2. H.A. Stone, A.D. Stroock, A. Ajdari: Engineering flows in small devices: Microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech. 36, 381–411 (2004)

    Article  Google Scholar 

  3. O.I. Vinogradova: Possible implications of hydrophobic slippage on the dynamic measurements of hydrophobic forces, J. Phys. Cond. Mat. 8, 9491–9495 (1996)

    Article  Google Scholar 

  4. O.I. Vinogradova: Implications of hydrophobic slippage for the dynamic measurements of hydrophobic forces, Langmuir 14, 2827–2837 (1998)

    Article  Google Scholar 

  5. O.I. Vinogradova, R.G. Horn: Attractive forces between surfaces: What can and cannot be learned from a jump-in study with the surface forces apparatus?, Langmuir 17, 1604–1607 (2001)

    Article  Google Scholar 

  6. S. Granick, Y.X. Zhu, H. Lee: Slippery questions about complex fluids flowing past solids, Nature Mat. 2, 221–227 (2003)

    Article  Google Scholar 

  7. P. Tabeling: Slip phenomena at liquid–solid interfaces., C. R. Physique 5, 531–537 (2004)

    Article  Google Scholar 

  8. O.I. Vinogradova: Slippage of water over hydrophobic surfaces, Int. J. Mineral Process. 56, 31–60 (1999)

    Article  Google Scholar 

  9. S. Goldstein: Note on the condition at the surface of contact of a fluid with a solid body. In: Modern Development in Fluid Dynamics, Vol. 2, ed. by S. Goldstein (Clarendon, Oxford 1938) pp. 676–680

    Google Scholar 

  10. S. Goldstein: Fluid mechanics in first half of this century, Ann. Rev. Fluid Mech. 1, 1–28 (1969)

    Article  Google Scholar 

  11. C.L.M.H. Navier: Mémoire sur les lois du mouvement des fluides, Mémoires de lʼAcadémie Royale des Sciences de lʼInstitut de France VI, 389–440 (1823)

    Google Scholar 

  12. J.C. Maxwell: On stresses in rarefied gases arising from inequalities of temperature, Phil. Trans. R. Soc. Lond. 170, 231–256 (1879)

    Article  MATH  Google Scholar 

  13. D. Einzel, P. Panzer, M. Liu: Boundary condition for fluid flow – curved or rough surfaces, Phys. Rev. Lett. 64, 2269–2272 (1990)

    Article  Google Scholar 

  14. H. Lamb: Hydrodynamics (Dover, New York 1932)

    MATH  Google Scholar 

  15. G.K. Batchelor: An Introduction to Fluid Dynamics (Cambridge Univ. Press, Cambridge 1967)

    MATH  Google Scholar 

  16. W.B. Russel, D.A. Saville, W.R. Schowalter: Colloidal Dispersions (Cambridge Univ. Press, Cambridge 1989)

    Google Scholar 

  17. E.P. Muntz: Rarefied-gas dynamics, Ann. Rev. Fluid Mech. 21, 387–417 (1989)

    Article  MathSciNet  Google Scholar 

  18. L. Bocquet: Slipping of a fluid on a surface of controlled roughness, C. R. Acad. Sci. Ser. II 316, 7–12 (1993)

    MATH  Google Scholar 

  19. M. Gad-el-Hak: The fluid mechanics of microdevices – The Freeman Scholar Lecture, J. Fluids Eng. 121, 5–33 (1999)

    Article  Google Scholar 

  20. F. Brochard, P.G. de Gennes: Shear-dependent slippage at a polymer/solid interface, Langmuir 8, 3033–3037 (1992)

    Article  Google Scholar 

  21. P.G. de Gennes: Viscometric flows of tangled polymers, C. R. Acad. Sci. Paris B 288, 219–220 (1979)

    Google Scholar 

  22. M.M. Denn: Extrusion instabilities and wall slip, Ann. Rev. Fluid Mech. 33, 265–287 (2001)

    Article  Google Scholar 

  23. L. Léger, E. Raphael, H. Hervet: Surface-anchored polymer chains: Their role in adhesion and friction, Adv. Polymer Sci. 138, 185–225 (1999)

    Article  Google Scholar 

  24. Y. Inn, S.Q. Wang: Hydrodynamic slip: Polymer adsorption and desorption at melt/solid interfaces, Phys. Rev. Lett. 76, 467–470 (1996)

    Article  Google Scholar 

  25. A.M. Kraynik, W.R. Schowalter: Slip at the wall and extrudate roughness with aqueous solutions of polyvinyl alcohol and sodium borate, J. Rheol. 25, 95–114 (1981)

    Article  Google Scholar 

  26. K.B. Migler, H. Hervet, L. Léger: Slip transition of a polymer melt under shear stress, Phys. Rev. Lett. 70, 287–290 (1993)

    Article  Google Scholar 

  27. W.R. Schowalter: The behavior of complex fluids at solid boundaries, J. Non-Newtonian Fluid Mech. 29, 25–36 (1988)

    Article  Google Scholar 

  28. S.Q. Wang: Molecular transitions and dynamics at polymer/wall interfaces: Origins of flow instabilities and wall slip, Adv. Polymer Sci. 138, 227–275 (1999)

    Article  Google Scholar 

  29. P.G. de Gennes: Wetting – statics and dynamics, Rev. Mod. Phys. 57, 827–863 (1985)

    Article  Google Scholar 

  30. E.B.V. Dussan: Spreading of liquids on solid surfaces – Static and dynamic contact lines, Ann. Rev. Fluid Mech. 11, 371–400 (1979)

    Article  Google Scholar 

  31. C. Huh, L.E. Scriven: Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid Int. Sci. 35, 85–101 (1971)

    Article  Google Scholar 

  32. L.M. Hocking: Moving fluid interface on a rough surface, J. Fluid Mech. 76, 801–817 (1976)

    Article  MATH  Google Scholar 

  33. E.B.V. Dussan: Moving contact line – slip boundary condition, J. Fluid Mech. 77, 665–684 (1976)

    Article  MATH  Google Scholar 

  34. E.B.V. Dussan, S.H. Davis: Motion of a fluid-fluid interface along a solid surface, J. Fluid Mech. 65, 71–95 (1974)

    Article  MATH  Google Scholar 

  35. J. Eggers, H.A. Stone: Characteristic lengths at moving contact lines for a perfectly wetting fluid: The influence of speed on the dynamic contact angle, J. Fluid Mech. 505, 309–321 (2004)

    Article  MATH  Google Scholar 

  36. K.M. Jansons: Moving contact lines at nonzero capillary number, J. Fluid Mech. 167, 393–407 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  37. J. Koplik, J.R. Banavar, J.F. Willemsen: Molecular dynamics of Poiseuille flow and moving contact lines, Phys. Rev. Lett. 60, 1282–1285 (1988)

    Article  Google Scholar 

  38. A.M.J. Davis, M.T. Kezirian, H. Brenner: On the Stokes-Einstein model of surface diffusion along solid surfaces: Slip boundary conditions, J. Colloid Int. Sci. 165, 129–140 (1994)

    Article  Google Scholar 

  39. L.M. Hocking: Effect of slip on motion of a sphere close to a wall and of two adjacent spheres, J. Eng. Math. 7, 207–221 (1973)

    Article  MATH  Google Scholar 

  40. J.N. Israelachvili, G.E. Adams: Measurement of forces between two mica surfaces in aqueous-electrolyte solutions in range 0 to 100 nm, J. Chem. Soc. Faraday Trans. I 74, 975–1001 (1978)

    Article  Google Scholar 

  41. J.N. Israelachvili, D. Tabor: The measurement of van der Waals dispersion forces in the range 1.5 to 130 nm, Proc. R. Soc. Lond. A 331, 19–38 (1972)

    Article  Google Scholar 

  42. D. Tabor, R.H.S. Winterton: The direct measurement of normal and retarded van der Waals forces, Proc. R. Soc. Lond. A 312, 435–450 (1969)

    Article  Google Scholar 

  43. D.Y.C. Chan, R.G. Horn: The drainage of thin liquid films between solid surfaces, J. Chem. Phys. 83, 5311–5324 (1985)

    Article  Google Scholar 

  44. M.L. Gee, P.M. McGuiggan, J.N. Israelachvili, A.M. Homola: Liquid to solid-like transitions of molecularly thin films under shear, J. Chem. Phys. 93, 1885–1906 (1990)

    Google Scholar 

  45. J.M. Georges, S. Millot, J.L. Loubet, A. Tonck: Drainage of thin liquid films between relatively smooth surfaces, J. Chem. Phys. 98, 7345–7360 (1993)

    Article  Google Scholar 

  46. R.G. Horn, D.T. Smith, W. Haller: Surface forces and viscosity of water measured between silica sheets, Chem. Phys. Lett. 162, 404–408 (1989)

    Article  Google Scholar 

  47. J.N. Israelachvili: Measurement of the viscosity of liquids in very thin films, J. Colloid Int. Sci. 110, 263–271 (1986)

    Article  Google Scholar 

  48. J.N. Israelachvili, P.M. McGuiggan, A.M. Homola: Dynamic properties of molecularly thin liquid films, Science 240, 189–191 (1988)

    Article  Google Scholar 

  49. J. Klein, E. Kumacheva: Confinement-induced phase transitions in simple liquids, Science 269, 816–819 (1995)

    Article  Google Scholar 

  50. J. Klein, E. Kumacheva: Simple liquids confined to molecularly thin layers, I: Confinement-induced liquid-to-solid phase transitions, J. Chem. Phys. 108, 6996–7009 (1998)

    Article  Google Scholar 

  51. E. Kumacheva, J. Klein: Simple liquids confined to molecularly thin layers, II: Shear and frictional behaviour of solidified films, J. Chem. Phys. 108, 7010–7022 (1998)

    Article  Google Scholar 

  52. U. Raviv, S. Giasson, J. Frey, J. Klein: Viscosity of ultra-thin water films confined between hydrophobic or hydrophilic surfaces, J. Phys. Cond. Mat. 14, 1–9 (2002)

    Article  Google Scholar 

  53. U. Raviv, P. Laurat, J. Klein: Fluidity of water confined to subnanometre films, Nature 413, 51–54 (2001)

    Article  Google Scholar 

  54. S.E. Campbell, G. Luengo, V.I. Srdanov, F. Wudl, J.N. Israelachvili: Very low viscosity at the solid-liquid interface induced by adsorbed C60 monolayers, Nature 382, 520–522 (1996)

    Article  Google Scholar 

  55. S. Granick: Motions and relaxations of confined fluids, Science 253, 1374–1379 (1991)

    Article  Google Scholar 

  56. M.O. Robbins, M.H. Muser: Computer simulations of friction, lubrication and wear. In: Handbook of Modern Tribology, ed. by B. Bhushan (CRC, Boca Raton 2000) pp. 717–765

    Google Scholar 

  57. J.L. Anderson, J.A. Quinn: Ionic mobility in microcapillaries, J. Chem. Soc. Faraday Trans. I 68, 608–612 (1972)

    Article  Google Scholar 

  58. T.K. Knudstrup, I.A. Bitsanis, G.B. Westermann-Clark: Pressure-driven flow experiments in molecularly narrow, straight pores of molecular dimension in mica, Langmuir 11, 893–897 (1995)

    Article  Google Scholar 

  59. J. Baudry, E. Charlaix, A. Tonck, D. Mazuyer: Experimental evidence for a large slip effect at a nonwetting fluid-solid interface, Langmuir 17, 5232–5236 (2001)

    Article  Google Scholar 

  60. U.C. Boehnke, T. Remmler, H. Motschmann, S. Wurlitzer, J. Hauwede, M.Th. Fischer: Partial air wetting on solvophobic surfaces in polar liquids, J. Colloid Int. Sci. 211, 243–251 (1999)

    Article  Google Scholar 

  61. E. Bonaccurso, H.S. Butt, V.S.J. Craig: Surface roughness and hydrodynamic boundary slip of a Newtonian fluid in a completely wetting system, Phys. Rev. Lett. 90, 144501 (2003)

    Article  Google Scholar 

  62. E. Bonaccurso, M. Kappl, H.S. Butt: Hydrodynamic force measurements: Boundary slip of water on hydrophilic surfaces and electrokinetics effects, Phys. Rev. Lett. 88, 076103 (2002)

    Article  Google Scholar 

  63. C. Cheikh, G. Koper: Stick-slip transition at the nanometer scale, Phys. Rev. Lett. 91, 156102 (2003)

    Article  Google Scholar 

  64. J.T. Cheng, N. Giordano: Fluid flow through nanometer-scale channels, Phys. Rev. E 65, 031206 (2002)

    Article  Google Scholar 

  65. C.-H. Choi, K. Johan, A. Westin, K.S. Breuer: Apparent slip flows in hydrophilic and hydrophobic microchannels, Phys. Fluids 15, 2897–2902 (2003)

    Article  Google Scholar 

  66. N.V. Churaev, J. Ralston, I.P. Sergeeva, V.D. Sobolev: Electrokinetic properties of methylated quartz capillaries, Adv. Colloid Int. Sci. 96, 265–278 (2002)

    Article  Google Scholar 

  67. C. Cottin-Bizonne, B. Cross, A. Steinberger, E. Charlaix: Boundary slip on smooth hydrophobic surfaces: Intrinsic effects and possible artifacts, Phys. Rev. Lett. 94, 056102 (2005)

    Article  Google Scholar 

  68. C. Cottin-Bizonne, S. Jurine, J. Baudry, J. Crassous, F. Restagno, É. Charlaix: Nanorheology: An investigation of the boundary condition at hydrophobic and hydrophilic interfaces, Eur. Phys. J. E 9, 47–53 (2002)

    Google Scholar 

  69. V.S.J. Craig, C. Neto, D.R.M. Williams: Shear-dependent boundary slip in an aqueous Newtonian liquid, Phys. Rev. Lett. 87, 054504 (2001)

    Article  Google Scholar 

  70. C.L. Henry, C. Neto, D.R. Evans, S. Biggs, V.S.J. Craig: The effect of surfactant adsorption on liquid boundary slippage, Physica A 339, 60–65 (2004)

    Article  Google Scholar 

  71. H. Hervet, L. Léger: Flow with slip at the wall: From simple to complex fluids, C. R. Physique 4, 241–249 (2003)

    Article  Google Scholar 

  72. P. Joseph, P. Tabeling: Direct measurement of the apparent slip length, Phys. Rev. E 71, 035303 (2005)

    Article  Google Scholar 

  73. O.A. Kiseleva, V.D. Sobolev, N.V. Chuarev: Slippage of the aqueous solutions of cetyltrimethylammonium bromide during flow in thin quartz capillaries, Colloid J. 61, 263–264 (1999)

    Google Scholar 

  74. D. Lumma, A. Best, A. Gansen, F. Feuillebois, J.O. Rädler, O.I. Vinogradova: Flow profile near a wall measured by double-focus fluorescence cross-correlation, Phys. Rev. E 67, 056313 (2003)

    Article  Google Scholar 

  75. C. Neto, V.S.J. Craig, D.R.M. Williams: Evidence of shear-dependent boundary slip in Newtonian liquids, Eur. Phys. J. E 12, S71–S74 (2003)

    Article  Google Scholar 

  76. R. Pit, H. Hervert, L. Léger: Friction and slip of a simple liquid at a solid surface, Trib. Lett. 7, 147–152 (1999)

    Article  Google Scholar 

  77. R. Pit, H. Hervert, L. Léger: Direct experimental evidence of slip in hexadecane: Solid interfaces, Phys. Rev. Lett. 85, 980–983 (2000)

    Article  Google Scholar 

  78. G. Sun, E. Bonaccurso, V. Franz, H.S. Butt: Confined liquid: Simultaneous observation of a molecularly layered structure and hydrodynamic slip, J. Chem. Phys. 117, 10311–10314 (2002)

    Article  Google Scholar 

  79. D.C. Tretheway, C.D. Meinhart: Apparent fluid slip at hydrophobic microchannel walls, Phys. Fluids 14, L9–L12 (2002)

    Article  Google Scholar 

  80. D.C. Tretheway, C.D. Meinhart: A generating mechanism for apparent fluid slip in hydrophobic microchannels, Phys. Fluids 16, 1509–1515 (2004)

    Article  Google Scholar 

  81. O.I. Vinogradova, G.E. Yakubov: Dynamic effects on force measurements, 2. Lubrication and the atomic force microscope, Langmuir 19, 1227–1234 (2003)

    Article  Google Scholar 

  82. Y. Zhu, S. Granick: Rate-dependent slip of Newtonian liquid at smooth surfaces, Phys. Rev. Lett. 87, 096105 (2001)

    Article  Google Scholar 

  83. Y. Zhu, S. Granick: Apparent slip of Newtonian fluids past adsorbed polymer layers, Macromolecules 35, 4658–4663 (2002)

    Article  Google Scholar 

  84. Y. Zhu, S. Granick: Limits of the hydrodynamic no-slip boundary condition, Phys. Rev. Lett. 88, 106102 (2002)

    Article  Google Scholar 

  85. Y. Zhu, S. Granick: No-slip boundary condition switches to partial slip when fluid contains surfactant, Langmuir 18, 10058–10063 (2002)

    Article  Google Scholar 

  86. R. Bulkley: Viscous flow and surface films, Bur. Stand. J. Res. 6, 89–112 (1931)

    Google Scholar 

  87. N.V. Churaev, V.D. Sobolev, A.N. Somov: Slippage of liquids over lyophobic solid surfaces, J. Colloid Int. Sci. 97, 574–581 (1984)

    Article  Google Scholar 

  88. P. Debye, R.L. Cleland: Flow of liquid hydrocarbons in porous Vycor, J. Appl. Phys. 30, 843–849 (1959)

    Article  Google Scholar 

  89. E. Schnell: Slippage of water over nonwettable surfaces, J. Appl. Phys. 27, 1149–1152 (1956)

    Article  Google Scholar 

  90. J. Traube, S.-H. Whang: Über Reibungskonstante und Wandschicht, Z. Physikal. Chem. A 138, 102–122 (1928)

    Google Scholar 

  91. E. Lauga, H.A. Stone: Effective slip in pressure-driven Stokes flow, J. Fluid Mech. 489, 55–77 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  92. J. Pfahler, J. Harley, H. Bau, J. Zemel: Liquid transport in micron and submicron channels, Sensors Actuators A21-A23, 431–434 (1990)

    Google Scholar 

  93. T. Hasegawa, M. Suganuma, H. Watanabe: Anomaly of excess pressure drops of the flow through very small orifices, Phys. Fluids 9, 1–3 (1997)

    Article  Google Scholar 

  94. J. Happel, H. Brenner: Low Reynolds Number Hydrodynamics (Prentice Hall, Englewood Cliffs 1965)

    Google Scholar 

  95. B.N.J. Perrson, F. Mugele: Squeeze-out and wear: Fundamental principles and applications, J. Phys.: Condens. Mat. 16, R295–R355 (2004)

    Article  Google Scholar 

  96. O. Reynolds: On the theory of lubrication and its application to Mr Beauchamp Towerʼs experiments, including an experimental determination of the viscosity of olive oil, Phil. Trans. R. Soc. Lond. 177, 157–234 (1886)

    Article  Google Scholar 

  97. O.I. Vinogradova: Drainage of a thin liquid-film confined between hydrophobic surfaces, Langmuir 11, 2213–2220 (1995)

    Article  Google Scholar 

  98. O.I. Vinogradova: Hydrodynamic interaction of curved bodies allowing slip on their surfaces, Langmuir 12, 5963–5968 (1996)

    Article  Google Scholar 

  99. A.J. Goldman, R.G. Cox, H. Brenner: Slow viscous motion of a sphere parallel to a plane wall, I. Motion through a quiescent fluid, Chem. Eng. Sci. 22, 637–651 (1967)

    Article  Google Scholar 

  100. G. Binnig, C.F. Quate, C. Gerber: Atomic force microscope, Phys. Rev. Lett. 56, 930–933 (1986)

    Article  Google Scholar 

  101. D. Burgeen, F.R. Nakache: Electrokinetic flow in ultrafine capillary slits, J. Phys. Chem. 68, 1084–1091 (1964)

    Article  Google Scholar 

  102. R.J. Hunter: Zeta Potential in Colloid Science: Principles and Applications (Academic, New York 1982)

    Google Scholar 

  103. C.L. Rice, R. Whitehead: Electrokinetic flow in a narrow cylindrical capillary, J. Phys. Chem. 69, 4017–4023 (1965)

    Article  Google Scholar 

  104. S. Jin, P. Huang, J. Park, J.Y. Yoo, K.S. Breuer: Near-surface velocimetry using evanescent wave illumination, Exp. Fluids 37, 825–833 (2004)

    Article  Google Scholar 

  105. J. Yamada: Evanescent wave Doppler velocimetry for a wallʼs near field, Appl. Phys. Lett. 75, 1805–1806 (1999)

    Article  Google Scholar 

  106. C.M. Zettner, M. Yoda: Particle velocity field measurements in a near-wall flow using evanescent wave illumination, Exp. Fluids 34, 115–121 (2003)

    Google Scholar 

  107. J.H. Cho, B.M. Law, F. Rieutord: Dipole-dependent slip on Newtonian liquids at smooth solid hydrophobic surfaces, Phys. Rev. Lett. 92, 166102 (2004)

    Article  Google Scholar 

  108. M.P. Allen, D.J. Tildesley: Computer Simulation of Liquids (Clarendon, Oxford 1987)

    MATH  Google Scholar 

  109. J. Koplik, J.R. Banavar: Continuum deductions from molecular hydrodynamics, Annu. Rev. Fluid Mech. 27, 257–292 (1995)

    Article  Google Scholar 

  110. U. Heinbuch, J. Fischer: Liquid flow in pores – Slip, no-slip, or multilayer sticking, Phys. Rev. A 40, 1144–1146 (1989)

    Article  Google Scholar 

  111. P.A. Thompson, M.O. Robbins: Simulations of contact line motion – Slip and the dynamic contact-angle, Phys. Rev. Lett. 63, 766–769 (1989)

    Article  Google Scholar 

  112. J. Koplik, J.R. Banavar, J.F. Willemsen: Molecular dynamics of fluid flow at solid-surfaces, Phys. Fluids 1, 781–794 (1989)

    Article  Google Scholar 

  113. P.A. Thompson, M.O. Robbins: Shear flow near solids – Epitaxial order and flow boundary conditions, Phys. Rev. A 41, 6830–6837 (1990)

    Article  Google Scholar 

  114. M. Sun, C. Ebner: Molecular dynamics study of flow at a fluid-wall interface, Phys. Rev. Lett. 69, 3491–3494 (1992)

    Article  Google Scholar 

  115. P.A. Thompson, S.M. Troian: A general boundary condition for liquid flow at solid surfaces, Nature 389, 360–362 (1997)

    Article  Google Scholar 

  116. J.L. Barrat, L. Bocquet: Large slip effect at a nonwetting fluid-solid interface, Phys. Rev. Lett. 82, 4671–4674 (1999)

    Article  Google Scholar 

  117. A. Jabbarzadeh, J.D. Atkinson, R.I. Tanner: Effect of the wall roughness on slip and rheological properties of hexadecane in molecular dynamics simulation of Couette shear flow between two sinusoidal walls, Phys. Rev. E 61, 690–699 (2000)

    Article  Google Scholar 

  118. M. Cieplak, J. Koplik, J.R. Banavar: Boundary conditions at a fluid-solid interface, Phys. Rev. Lett. 86, 803–806 (2001)

    Article  Google Scholar 

  119. X.J. Fan, N. Phan-Thien, N.T. Yong, X. Diao: Molecular dynamics simulation of a liquid in a complex nano channel flow, Phys. Fluids 14, 1146–1153 (2002)

    Article  Google Scholar 

  120. V.P. Sokhan, D. Nicholson, N. Quirke: Fluid flow in nanopores: Accurate boundary conditions for carbon nanotubes, J. Chem. Phys. 117, 8531–8539 (2002)

    Article  Google Scholar 

  121. C. Cottin-Bizonne, J.L. Barrat, L. Bocquet, E. Charlaix: Low-friction flows of liquid at nanopatterned interfaces, Nature Mat. 2, 237–240 (2003)

    Article  Google Scholar 

  122. T.M. Galea, P. Attard: Molecular dynamics study of the effect of atomic roughness on the slip length at the fluid-solid boundary during shear flow, Langmuir 20, 3477–3482 (2004)

    Article  Google Scholar 

  123. G. Nagayama, P. Cheng: Effects of interface wettability on microscale flow by molecular dynamics simulation, Int. J. Heat Mass Transfer 47, 501–513 (2004)

    Article  MATH  Google Scholar 

  124. C. Cottin-Bizonne, C. Barentin, E. Charlaix, L. Boequet, J.L. Barrat: Dynamics of simple liquids at heterogeneous surfaces: Molecular dynamics simulations and hydrodynamic description, Eur. Phys. J. E 15, 427–438 (2004)

    Article  Google Scholar 

  125. J.N. Israelachvili: Intermolecular and Surface Forces (Academic, London 1992)

    Google Scholar 

  126. L. Bocquet, J.L. Barrat: Hydrodynamic boundary conditions and correlation functions of confined fluids, Phys. Rev. Lett. 70, 2726–2729 (1993)

    Article  Google Scholar 

  127. J.B. Freund: The atomic detail of a wetting/de-wetting flow, Phys. Fluids 15, L33–L36 (2003)

    Article  Google Scholar 

  128. J. Koplik, J.R. Banavar: Corner flow in the sliding plate problem, Phys. Fluids 7, 3118–3125 (1995)

    Article  MATH  Google Scholar 

  129. M. Vergeles, P. Keblinski, J. Koplik, J.R. Banavar: Stokes drag and lubrication flows: A molecular dynamics study, Phys. Rev. E 53, 4852–4864 (1996)

    Article  Google Scholar 

  130. L. Bocquet, J.L. Barrat: Hydrodynamic boundary conditions, correlation functions, and Kubo relations for confined fluids, Phys. Rev. E 49, 3079–3092 (1994)

    Article  Google Scholar 

  131. H. Brenner, V. Ganesan: Molecular wall effects: Are conditions at a boundary “boundary conditions”?, Phys. Rev. E 61, 6879–6897 (2000)

    Article  Google Scholar 

  132. S. Richardson: On the no-slip boundary condition, J. Fluid Mech. 59, 707–719 (1973)

    Article  MATH  Google Scholar 

  133. J.F. Nye: A calculation on sliding of ice over a wavy surface using a Newtonian viscous approximation, Proc. R. Soc. Lond. A 311, 445–467 (1969)

    Article  Google Scholar 

  134. J.F. Nye: Glacier sliding without cavitation in a linear viscous approximation, Proc. R. Soc. Lond. A 315, 381–403 (1970)

    Article  Google Scholar 

  135. K.M. Jansons: Determination of the macroscopic (partial) slip boundary condition for a viscous flow over a randomly rough-surface with a perfect slip microscopic boundary condition, Phys. Fluids 31, 15–17 (1988)

    Article  MathSciNet  Google Scholar 

  136. J. Casado-Diaz, E. Fernandez-Cara, J. Simon: Why viscous fluids adhere to rugose walls: A mathematical explanation, J. Diff. Eq. 189, 526–537 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  137. M.J. Miksis, S.H. Davis: Slip over rough and coated surfaces, J. Fluid Mech. 273, 125–139 (1994)

    Article  MATH  Google Scholar 

  138. I.V. Ponomarev, A.E. Meyerovich: Surface roughness and effective stick-slip motion, Phys. Rev. E 67, 026302 (2003)

    Article  Google Scholar 

  139. K. Sarkar, A. Prosperetti: Effective boundary conditions for Stokes flow over a rough surface, J. Fluid Mech. 316, 223–240 (1996)

    Article  MATH  Google Scholar 

  140. E.O. Tuck, A. Kouzoubov: A laminar roughness boundary condition, J. Fluid Mech. 300, 59–70 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  141. S. Richardson: Model for boundary condition of a porous material, Part 2., J. Fluid Mech. 49, 327–336 (1971)

    Article  MATH  Google Scholar 

  142. G.I. Taylor: Model for boundary condition of a porous material, Part 1., J. Fluid Mech. 49, 319–326 (1971)

    Article  Google Scholar 

  143. K. Sarkar, A. Prosperetti: Effective boundary conditions for the Laplace equation with a rough boundary, Proc. R. Soc. Lond. A 451, 425–452 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  144. J. Bico, C. Marzolin, D. Quere: Pearl drops, Europhys. Lett. 47, 220–226 (1999)

    Article  Google Scholar 

  145. A.B.D. Cassie, S. Baxter: Wettability of porous surfaces, Trans. Faraday Soc. 40, 546–551 (1944)

    Article  Google Scholar 

  146. T. Onda, S. Shibuichi, N. Satoh, K. Tsujii: Super-water-repellent fractal surfaces, Langmuir 12, 2125–2127 (1996)

    Article  Google Scholar 

  147. R.N. Wenzel: Resistance of solid surfaces to wetting by water, Ind. Eng. Chem. 28, 988–994 (1936)

    Article  Google Scholar 

  148. D.M. Buschnell: Drag reduction in nature, Ann. Rev. Fluid Mech. 23, 65–79 (1991)

    Article  Google Scholar 

  149. K. Watanabe, S. Ogata: Drag reduction for a rotating disk with highly water-repellent wall, JSME Int. J. Ser. B 44, 556–560 (1998)

    Google Scholar 

  150. K. Watanabe, Y. Udagawa, H. Udagawa: Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall, J. Fluid Mech. 381, 225–238 (1999)

    Article  MATH  Google Scholar 

  151. K. Watanabe, Yanuar, H. Mizunuma: Slip of Newtonian fluids at solid boundary, JSME Int. J. Ser. B 44, 525–529 (1998)

    Google Scholar 

  152. J. Ou, B. Perot, J.P. Rothstein: Laminar drag reduction in microchannels using ultrahydrophobic surfaces, Phys. Fluids 16, 4635–4643 (2004)

    Article  Google Scholar 

  153. C.Y. Wang: Flow over a surface with parallel grooves, Phys. Fluids 15, 1114–1121 (2003)

    Article  Google Scholar 

  154. T.G. Min, J. Kim: Effects of hydrophobic surface on skin-friction drag, Phys. Fluids 16, L55–L58 (2004)

    Article  Google Scholar 

  155. D. Tretheway, S. Stone, C. Meinhart: Effects of absolute pressure and dissolved gases on apparent fluid slip in hydrophobic microchannels, Bull. Am. Phys. Soc. 49, 215 (2004)

    Google Scholar 

  156. Z.Q. Lin, S. Granick: Platinum nanoparticles at mica surfaces, Langmuir 19, 7061–7070 (2003)

    Article  Google Scholar 

  157. E. Ruckenstein, P. Rajora: On the no-slip boundary condition of hydrodynamics, J. Colloid Int. Sci. 96, 488–491 (1983)

    Article  Google Scholar 

  158. E. Ruckenstein, N. Churaev: A possible hydrodynamic origin of the forces of hydrophobic attraction, J. Colloid Int. Sci. 147, 535–538 (1991)

    Article  Google Scholar 

  159. K. Lum, D. Chandler, J.D. Weeks: Hydrophobicity at small and large length scales, J. Phys. Chem. B 103, 4570–4577 (1999)

    Article  Google Scholar 

  160. D. Andrienko, B. Dunweg, O.I. Vinogradova: Boundary slip as a result of a prewetting transition, J. Chem. Phys. 119, 13106–13112 (2003)

    Article  Google Scholar 

  161. J.R. Philip: Flows satisfying mixed no-slip and no-shear conditions, Z.A.M.P. 23, 353–372 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  162. J.R. Philip: Integral properties of flows satisfying mixed no-slip and no-shear conditions, Z.A.M.P. 23, 960–968 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  163. A.A. Alexeyev, O.I. Vinogradova: Flow of a liquid in a nonuniformly hydrophobized capillary, Colloids Surf. A 108, 173–179 (1996)

    Article  Google Scholar 

  164. P.G. de Gennes: On fluid/wall slippage, Langmuir 18, 3413–3414 (2002)

    Article  Google Scholar 

  165. P. Attard, M.P. Moody, J.W.G. Tyrrell: Nanobubbles: The big picture, Physica A 314, 696–705 (2002)

    Article  Google Scholar 

  166. M. Holmberg, A. Kuhle, J. Garnaes, K.A. Morch, A. Boisen: Nanobubble trouble on gold surfaces, Langmuir 19, 10510–10513 (2003)

    Article  Google Scholar 

  167. N. Ishida, T. Inoue, M. Miyahara, K. Higashitani: Nano bubbles on a hydrophobic surface in water observed by tapping-mode atomic force microscopy, Langmuir 16, 6377–6380 (2000)

    Article  Google Scholar 

  168. S.T. Lou, J.X. Gao, X.D. Xiao, X.J. Li, G.L. Li, Y. Zhang, M.Q. Li, J.L. Sun, X.H. Li, J. Hu: Studies of nanobubbles produced at liquid/solid interfaces, Mat. Charac. 48, 211–214 (2002)

    Article  Google Scholar 

  169. A.C. Simonsen, P.L. Hansen, B. Klosgen: Nanobubbles give evidence of incomplete wetting at a hydrophobic interface, J. Colloid Int. Sci. 273, 291–299 (2004)

    Article  Google Scholar 

  170. R. Steitz, T. Gutberlet, T. Hauss, B. Klösgen, R. Krastev, S. Schemmel, A.C. Simonsen, G.H. Findenegg: Nanobubbles and their precursor layer at the interface of water against a hydrophobic substrate, Langmuir 19, 2409–2418 (2003)

    Article  Google Scholar 

  171. M. Switkes, J.W. Ruberti: Rapid cryofixation/freeze fracture for the study of nanobubbles at solid-liquid interfaces, Appl. Phys. Lett. 84, 4759–4761 (2004)

    Article  Google Scholar 

  172. J.W.G. Tyrrell, P. Attard: Images of nanobubbles on hydrophobic surfaces and their interactions, Phys. Rev. Lett. 87, 176104 (2001)

    Article  Google Scholar 

  173. J.W.G. Tyrrell, P. Attard: Atomic force microscope images of nanobubbles on a hydrophobic surface and corresponding force-separation data, Langmuir 18, 160–167 (2002)

    Article  Google Scholar 

  174. X.H. Zhang, X.D. Zhang, S.T. Lou, Z.X. Zhang, J.L. Sun, J. Hu: Degassing and temperature effects on the formation of nanobubbles at the mica/water interface, Langmuir 20, 3813–3815 (2004)

    Article  Google Scholar 

  175. X.H. Zhang, H. Jun: Nanobubbles at the solid/water interface, Prog. Chem. 16, 673–681 (2004)

    Google Scholar 

  176. T.R. Jensen, M.O. Jensen, N. Reitzel, K. Balashev, G.H. Peters, K. Kjaer, T. Bjornholm: Water in contact with extended hydrophobic surfaces: Direct evidence of weak dewetting, Phys. Rev. Lett. 90, 086101 (2003)

    Article  Google Scholar 

  177. D. Schwendel, T. Hayashi, R. Dahint, A. Pertsin, M. Grunze, R. Steitz, F. Schreiber: Interaction of water with self-assembled monolayers: Neutron reflectivity measurements of the water density in the interface region, Langmuir 19, 2284–2293 (2003)

    Article  Google Scholar 

  178. O.I. Vinogradova, G.E. Yakubov, H.J. Butt: Forces between polystyrene surfaces in water-electrolyte solutions: Long-range attraction of two types?, J. Chem. Phys. 114, 8124–8131 (2001)

    Article  Google Scholar 

  179. G.E. Yakubov, H.J. Butt, O.I. Vinogradova: Interaction forces between hydrophobic surfaces. Attractive jump as an indication of formation of “stable” submicrocavities, J. Phys. Chem. B 104, 3407–3410 (2000)

    Article  Google Scholar 

  180. P.S. Epstein, M.S. Plesset: On the stability of gas bubbles in liquid-gas solutions, J. Chem. Phys. 18, 1505–1509 (1950)

    Article  Google Scholar 

  181. S. Ljunggren, J.C. Eriksson: The lifetime of a colloid-sized gas bubble in water and the cause of the hydrophobic attraction, Colloids Surf. A 130, 151–155 (1997)

    Article  Google Scholar 

  182. R.A. Wentzell: Van der Waals stabilization of bubbles, Phys. Rev. Lett. 56, 732–733 (1986)

    Article  Google Scholar 

  183. P.-G.F. de Gennes Brochard-Wyart, D. Quéré: Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer, Berlin, Heidelberg 2004)

    MATH  Google Scholar 

  184. T.D. Blake: Slip between a liquid and a solid – D.M. Tolstoi (1952) theory reconsidered, Colloids Surf. 47, 135–145 (1990)

    Article  Google Scholar 

  185. J. Frenkel: Kinetic Theory of Liquids (Dover, New York 1955)

    Google Scholar 

  186. D.M. Tolstoi: Molecular theory for slippage of liquids over solid surfaces, Doklady Akad. Nauk SSSR 85, 1089 (1952), in Russian

    Google Scholar 

  187. J.L. Barrat, L. Bocquet: Influence of wetting properties on hydrodynamic boundary conditions at a fluid/solid interface, Faraday Disc. 112, 119–127 (1999)

    Article  Google Scholar 

  188. N.V. Priezjev, S.M. Troian: Molecular origin and dynamic behavior of slip in sheared polymer films, Phys. Rev. Lett. 92, 018302 (2004)

    Article  Google Scholar 

  189. S. Lichter, A. Roxin, S. Mandre: Mechanisms for liquid slip at solid surfaces, Phys. Rev. Lett. 93, 086001 (2004)

    Article  Google Scholar 

  190. E. Lauga, M.P. Brenner: Dynamic mechanisms for apparent slip on hydrophobic surfaces, Phys. Rev. E 70, 026311 (2004)

    Article  Google Scholar 

  191. H. Spikes, S. Granick: Equation for slip of simple liquids at smooth solid surfaces, Langmuir 19, 5065–5071 (2003)

    Article  Google Scholar 

  192. J. Gavis, R.L. Laurence: Viscous heating in plane and circular flow between moving surfaces, I&EC Fundamentals 7, 232–239 (1968)

    Article  Google Scholar 

  193. W. Urbanek, J.N. Zemel, H.H. Bau: An investigation of the temperature dependence of Poiseuille numbers in microchannel flow, J. Micromech. Microeng. 3, 206–208 (1993)

    Article  Google Scholar 

  194. N.F. Bunkin, O.A. Kiseleva, A.V. Lobeyev, T.G. Movchan, B.W. Ninham, O.I. Vinogradova: Effect of salts and dissolved gas on optical cavitation near hydrophobic and hydrophilic surfaces, Langmuir 13, 3024–3028 (1997)

    Article  Google Scholar 

  195. E. Lauga: Apparent slip due to the motion of suspended particles in flow of electrolyte solutions, Langmuir 20, 8924–8930 (2004)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139-4307, Cambridge, MA, USA

    Eric Lauga Prof.

  2. School of Engineering and Applied Science, Harvard University, 29 Oxford Street, 02139, Cambridge, MA, USA

    Michael Brenner Prof.

  3. Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Howard Stone Prof.

Authors
  1. Eric Lauga Prof.
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  2. Michael Brenner Prof.
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  3. Howard Stone Prof.
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Correspondence to Eric Lauga Prof. , Michael Brenner Prof. or Howard Stone Prof. .

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Editors and Affiliations

  1. Fachgebiet Strömungslehre und Aerodynamik, Technische Universität Darmstadt, Petersenstraße 30, 64287, Darmstadt, Germany

    Cameron Tropea Dr.

  2. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor St., 60607-7022, Chicago, IL, USA

    Alexander L. Yarin Dr.

  3. Mechanical Engineering, Michigan State University, A118 Engineering Research Complex, 48824-1326, East Lansing, MI, USA

    John F. Foss Dr.

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Lauga, E., Brenner, M., Stone, H. (2007). Microfluidics: The No-Slip Boundary Condition. In: Tropea, C., Yarin, A.L., Foss, J.F. (eds) Springer Handbook of Experimental Fluid Mechanics. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30299-5_19

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