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The European Physical Journal Special Topics

, Volume 225, Issue 8–9, pp 1551–1582 | Cite as

Multi-scale simulation method for electroosmotic flows

  • Lin Guo
  • Shiyi Chen
  • Mark O. RobbinsEmail author
Regular Article Hybrid and Adaptive Coarse Graining Methods
Part of the following topical collections:
  1. Modern Simulation Approaches in Soft Matter Science: From Fundamental Understanding to Industrial Applications

Abstract

Electroosmotic transport in micro-and nano- channels has important applications in biological and engineering systems but is difficult to model because nanoscale structure near surfaces impacts flow throughout the channel. We develop an efficient multi-scale simulation method that treats near-wall and bulk subdomains with different physical descriptions and couples them through a finite overlap region. Molecular dynamics is used in the near-wall subdomain where the ion density is inconsistent with continuum models and the discrete structure of solvent molecules is important. In the bulk region the solvent is treated as a continuum fluid described by the incompressible Navier-Stokes equations with thermal fluctuations. A discrete description of ions is retained because of the low density of ions and the long range of electrostatic interactions. A stochastic Euler-Lagrangian method is used to simulate the dynamics of these ions in the implicit continuum solvent. The overlap region allows free exchange of solvent and ions between the two subdomains. The hybrid approach is validated against full molecular dynamics simulations for different geometries and types of flows.

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References

  1. 1.
    K.A. Sharp, B. Honig, Annu. Rev. Biophys. Bio. 19, 301 (1990)CrossRefGoogle Scholar
  2. 2.
    B. Honig, A. Nicholls, Science 268, 1144 (1995)ADSCrossRefGoogle Scholar
  3. 3.
    D.J. Harrison, K. Fluri, K. Seiler, Z. Fan, C.S. Effenhauser, A. Manz, Science 261, 895 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    D.R. Reyes, D. Iossifidis, P.-A. Auroux, A. Manz, Anal. Chem. 74, 2623 (2002)CrossRefGoogle Scholar
  5. 5.
    P.J. Kemery, J.K. Steehler, P.W. Bohn, Langmuir 14, 2884 (1998)CrossRefGoogle Scholar
  6. 6.
    T.-C. Kuo, L.A. Sloan, J.V. Sweedler, P.W. Bohn, Langmuir 17, 6298 (2001)CrossRefGoogle Scholar
  7. 7.
    T.-C. Kuo, D.M. Cannon, Y. Chen, J.J. Tulock, M.A. Shannon, J.V. Sweedler, P.W. Bohn, Anal. Chem. 75, 1861 (2003)CrossRefGoogle Scholar
  8. 8.
    P.C. Hiemenz, R. Rajagopalan, Principles of Colloid and Surface Chemistry, Vol. 14 (CRC Press, 1997)Google Scholar
  9. 9.
    K. Seiler, Z.H. Fan, K. Fluri, D.J. Harrison, Anal. Chem. 66, 3485 (1994)CrossRefGoogle Scholar
  10. 10.
    D.Q. Li. Electrokinetics in Microfluidics, Vol. 2 (Academic Press, 2004)Google Scholar
  11. 11.
    R.J. Hunter, Zeta Potential in Colloid Science: Principles and Applications, Vol. 2 (Academic Press, 2013)Google Scholar
  12. 12.
    C. Yang, D. Li, Colloid Surf. A 143, 339 (1998)CrossRefGoogle Scholar
  13. 13.
    D. Li, Colloid Surf. A 195, 35 (2001)ADSCrossRefGoogle Scholar
  14. 14.
    Y. Hu, C. Werner, D. Li, Anal. Chem. 75, 5747 (2003)CrossRefGoogle Scholar
  15. 15.
    Y. Hu, C. Werner, D.Q. Li, J. Colloid Interf. Sci. 280, 527 (2004)CrossRefGoogle Scholar
  16. 16.
    J. Wang, M. Wang, Z. Li, Mod. Phys. Lett. B 19, 1515 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    Z. Guo, T.S. Zhao, Y. Shi, J. Chem. Phys. 122, 144907 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    J. Wang, M. Wang, Z. Li, J. Colloid Interf. Sci. 296, 729 (2006)CrossRefGoogle Scholar
  19. 19.
    N.A. Patankar, H.H. Hu, Anal. Chem. 70, 1870 (1998)CrossRefGoogle Scholar
  20. 20.
    S.V. Ermakov, S.C. Jacobson, J. Michael Ramsey, Anal. Chem. 70, 4494 (1998)CrossRefGoogle Scholar
  21. 21.
    M.J. Mitchell, R. Qiao, N.R. Aluru, J. MEMS. 9, 435 (2000)CrossRefGoogle Scholar
  22. 22.
    R. Qiao, N.R. Aluru, J. Chem. Phys. 118, 4692 (2003)ADSCrossRefGoogle Scholar
  23. 23.
    R. Qiao, N.R. Aluru, Colloid Surf. A 267, 103 (2005)CrossRefGoogle Scholar
  24. 24.
    R. Qiao, N.R. Aluru, Int. J. Multiscale Comput. Eng. 2 (2004)Google Scholar
  25. 25.
    M.S. Kilic, M.Z. Bazant, A. Ajdari, Phys. Rev. E. 75, 021502 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    M. Kilic, M.Z. Bazant, A. Ajdari, Phys. Rev. E. 75, 021503 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    I. Borukhov, D. Andelman, H. Orland, Phys. Rev. Lett. 79, 435 (1997)ADSCrossRefGoogle Scholar
  28. 28.
    P. Wu, R. Qiao, Phys. Fluids 23, 072005 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    D. Frenkel, B. Smit, Understanding Molecular Simulation: from Algorithms to Applications, Vol. 1 (Academic Press, 2001)Google Scholar
  30. 30.
    J.M. Haile, Comput. Phys. 7, 625 (1993)ADSCrossRefGoogle Scholar
  31. 31.
    M.P. Allen, D.J. Tildesley, Computer simulation of liquids (Oxford University Press, 1989)Google Scholar
  32. 32.
    J. Koplik, J.R. Banavar, J.F. Willemsen, Phys. Fluids A: Fluid 1, 781 (1989)ADSCrossRefGoogle Scholar
  33. 33.
    S.T. OConnell, P.A. Thompson, Phys. Rev. E 52, R5792 (1995)ADSCrossRefGoogle Scholar
  34. 34.
    X.B. Nie, S.Y. Chen, M.O. Robbins, W. E, J. Fluid Mech. 500, 55 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    X. Nie, S. Chen, M.O. Robbins, Phys. Fluids 16, 3579 (2004)ADSCrossRefGoogle Scholar
  36. 36.
    X. Nie, M.O. Robbins, S. Chen, Phys. Rev. Lett. 96, 134501 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    J. Liu, S. Chen, X. Nie, M.O. Robbins, J. Comput. Phys. 227, 279 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    J. Liu, S. Chen, X.B. Nie, M.O. Robbins, Commun. Comput. Phys. 4, 1279 (2008)ADSGoogle Scholar
  39. 39.
    N.G. Hadjiconstantinou, J. Comput. Phys. 154, 245 (1999)ADSCrossRefGoogle Scholar
  40. 40.
    N.G. Hadjiconstantinou, A.T. Patera, Int. J. Mod. Phys. C 8, 967 (1997)ADSCrossRefGoogle Scholar
  41. 41.
    G. Wagner, E.G. Flekkøy, Phil. Trans. Roy. Soc. London A 362, 1655 (2004)ADSCrossRefGoogle Scholar
  42. 42.
    G. Wagner, E. Flekkøy, J. Feder, T. Jøssang, Comput. Phys. Commun. 147, 670 (2002)ADSCrossRefGoogle Scholar
  43. 43.
    G.D. Fabritiis, R. Delgado-Buscalioni, P.V. Coveney, Phys. Rev. Lett. 97, 134501 (2006)ADSCrossRefGoogle Scholar
  44. 44.
    R. Delgado-Buscalioni, E.G. Flekkøy, P.V. Coveney, Europhys. Lett. 69, 59 (2005)CrossRefGoogle Scholar
  45. 45.
    R. Delgado-Buscalioni, G.D. Fabritiis, Phys. Rev. E 76, 036709 (2007)ADSCrossRefGoogle Scholar
  46. 46.
    R. Delgado-Buscalioni, K. Kremer, M. Praprotnik, J. Chem. Phys. 128, 114110 (2008)ADSCrossRefGoogle Scholar
  47. 47.
    R. Delgado-Buscalioni, A. Dejoan, Phys. Rev. E 78, 046708 (2008)ADSCrossRefGoogle Scholar
  48. 48.
    R. Delgado-Buscalioni, K. Kremer, M. Praprotnik, J. Chem. Phys. 131, 244107 (2009)ADSCrossRefGoogle Scholar
  49. 49.
    E.G. Flekkøy, G. Wagner, J. Feder, Europhys. Lett. 52, 271 (2000)ADSCrossRefGoogle Scholar
  50. 50.
    E.G. Flekkøy, R. Delgado-Buscalioni, P.V. Coveney, Phys. Rev. E 72, 026703 (2005)ADSCrossRefGoogle Scholar
  51. 51.
    E. Weinan, W. Ren, E. Vanden-Eijnden, J. Comput. Phys. 228, 5437 (2009)ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    E. Weinan, B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, Commun. Comput. Phys. 2, 367 (2007)MathSciNetGoogle Scholar
  53. 53.
    A. Donev, J.B. Bell, A.L. Garcia, B.J. Alder, Multiscale Model. Sim. 8, 871 (2010)MathSciNetCrossRefGoogle Scholar
  54. 54.
    O.B. Usta, A.J.C. Ladd, J.E. Butler, J. Chem. Phys. 122(9), 094902 (2005)ADSCrossRefGoogle Scholar
  55. 55.
    O.B. Usta, J.E. Butler, A.J.C. Ladd, Phys. Fluids 18, 031703 (2006)ADSCrossRefGoogle Scholar
  56. 56.
    G. Giupponi, G.D. Fabritiis, P.V. Coveney, Int. J. Mod. Phys. C 18, 520 (2007)ADSCrossRefGoogle Scholar
  57. 57.
    G. Giupponi, G.D. Fabritiis, P.V. Coveney, J. Chem. Phys. 126, 154903 (2007)ADSCrossRefGoogle Scholar
  58. 58.
    R. Kapral, Adv. Chem. Phys. 140, 89 (2008)CrossRefGoogle Scholar
  59. 59.
    C.S. Peskin, Acta numerica 11, 479 (2002)MathSciNetCrossRefGoogle Scholar
  60. 60.
    P. Ahlrichs, B. Dünweg, Int. J. Mod. Phys. C 9, 1429 (1998)ADSCrossRefGoogle Scholar
  61. 61.
    P. Ahlrichs, B. Dünweg, J. Chem. Phys. 111, 8225 (1999)ADSCrossRefGoogle Scholar
  62. 62.
    P. Ahlrichs, R. Everaers, B. Dünweg, Phys. Rev. E 64, 040501 (2001)ADSCrossRefGoogle Scholar
  63. 63.
    M.G. Fyta, S. Melchionna, E. Kaxiras, S. Succi, Multiscale Model. Sim. 5, 1156 (2006)MathSciNetCrossRefGoogle Scholar
  64. 64.
    T.T. Pham, U.D. Schiller, J.R. Prakash, B. Dünweg, J. Chem. Phys. 131, 164114 (2009)ADSCrossRefGoogle Scholar
  65. 65.
    V. Lobaskin, B. Dünweg, New J. Phys. 6, 54 (2004)ADSCrossRefGoogle Scholar
  66. 66.
    V. Lobaskin, B. Dünweg, C. Holm, J. Phys.: Condens. Mat. 16, S4063 (2004)ADSGoogle Scholar
  67. 67.
    V. Lobaskin, B. Dünweg, M. Medebach, T. Palberg, C. Holm. Phys. Rev. Lett. 98, 176105 (2007)ADSCrossRefGoogle Scholar
  68. 68.
    A. Chatterji, Jürgen Horbach, J. Chem. Phys. 122, 184903 (2005)ADSCrossRefGoogle Scholar
  69. 69.
    A. Chatterji, J. Horbach, J. Phys.: Condens. Mat. 22, 494102 (2010)Google Scholar
  70. 70.
    J. Smiatek, M. Sega, C. Holm, U.D. Schiller, F. Schmid, J. Chem. Phys. 130, 244702 (2009)ADSCrossRefGoogle Scholar
  71. 71.
    S. Kohlhoff, P. Gumbsch, H.F. Fischmeister, Philos. Mag. A 64, 851 (1991)ADSCrossRefGoogle Scholar
  72. 72.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, 1959)Google Scholar
  73. 73.
    R.F. Fox, G.E. Uhlenbeck, Phys. Fluids 13, 1893 (1970)ADSMathSciNetCrossRefGoogle Scholar
  74. 74.
    J.-P. Hansen, I.R. McDonald, Theory of Simple Liquids (Elsevier, 1990)Google Scholar
  75. 75.
    J.M. Ortiz, D. Zarate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, 2006)Google Scholar
  76. 76.
    A. Donev, J.B. Bell, A. De la Fuente, A.L. Garcia, J. Stat. Mech.: Theory E 2011, P06014 (2011)CrossRefGoogle Scholar
  77. 77.
    D. Bedeaux, I. Pagonabarraga, J.M. Ortiz De Zárate, J.V. Sengers, S. Kjelstrup, Phys. Chem. Chem. Phys. 12, 12780 (2010)CrossRefGoogle Scholar
  78. 78.
    J. Howard, et al., Mechanics of motor proteins and the cytoskeleton (Sinauer Associates Sunderland, MA, 2001)Google Scholar
  79. 79.
    A. Evilevitch, L. Lavelle, C.M. Knobler, E. Raspaud, W.M. Gelbart, P. Natl. A. Sci. 100, 9292 (2003)ADSCrossRefGoogle Scholar
  80. 80.
    F. Balboa, J.B. Bell, R. Delgado-Buscalioni, A. Donev, T.G. Fai, B.E. Griffith, C.S. Peskin, Multiscale Model. Sim. 10, 1369 (2012)CrossRefGoogle Scholar
  81. 81.
    F.B. Usabiaga, I. Pagonabarraga, R. Delgado-Buscalioni, J. Comput. Phys. 235, 701 (2013)ADSMathSciNetCrossRefGoogle Scholar
  82. 82.
    F.B. Usabiaga, R. Delgado-Buscalioni, B.E. Griffith, A. Donev, Comput. Method. Appl. M. 269, 139 (2014)CrossRefGoogle Scholar
  83. 83.
    P.J. Atzberger, Phys. Lett. A, 351, 225 (2006)ADSCrossRefGoogle Scholar
  84. 84.
    P.J. Atzberger, P.R. Kramer, C.S. Peskin, J. Comput. Phys. 224, 1255 (2007)ADSMathSciNetCrossRefGoogle Scholar
  85. 85.
    P.J. Atzberger, J. Comput. Phys. 230, 2821 (2011)ADSMathSciNetCrossRefGoogle Scholar
  86. 86.
    Y. Wang, J.K. Sigurdsson, E. Brandt, P.J. Atzberger, Phys. Rev. E 88, 023301 (2013)ADSCrossRefGoogle Scholar
  87. 87.
    G.S. Grest, K. Kremer, Phys. Rev. A 33, 3628 (1986)ADSCrossRefGoogle Scholar
  88. 88.
    P.A. Thompson, M.O. Robbins, Phys. Rev. A 41, 6830 (1990)ADSCrossRefGoogle Scholar
  89. 89.
    P.A. Thompson, S.M. Troian, Nature 389, 360 (1997)ADSCrossRefGoogle Scholar
  90. 90.
    N.V. Priezjev, S.M. Troian, J. Fluid Mech. 554, 25 (2006)ADSCrossRefGoogle Scholar
  91. 91.
    J. Liu, M. Wang, S. Chen, M.O. Robbins, J. Comput. Phys. 229, 7834 (2010)ADSCrossRefGoogle Scholar
  92. 92.
    I.-C. Yeh, M.L. Berkowitz, J. Chem. Phys. 111, 3155 (1999)ADSCrossRefGoogle Scholar
  93. 93.
    W.T. Coffey, Y.P. Kalmykov, The Langevin Equation (World Scientific, 2012)Google Scholar
  94. 94.
    C.W. Gardiner, Handbook of stochastic methods for physics, chemistry and the natural sciences, Vol. 13 Springer Series Syne (Springer, 1985)Google Scholar
  95. 95.
    N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, Vol. 1 (Elsevier, 1992)Google Scholar
  96. 96.
    M.O. Robbins, M.H. Müser, Computer simulations of friction, lubrication and wear, edited by B. Bhushan, Handbook of Modern Tribology (CRC Press, Boca Raton, 2000), p. 717 (cond-mat/0001056)Google Scholar
  97. 97.
    A.J.C. Ladd, R. Kekre, J.E. Butler, Phys. Rev. E 80, 036704 (2009)ADSCrossRefGoogle Scholar
  98. 98.
    N.K. Voulgarakis, B.Z. Shang, J.-W. Chu, Phys. Rev. E 88, 023305 (2013)ADSCrossRefGoogle Scholar
  99. 99.
    A.M. Roma, C.S. Peskin, M.J. Berger, J. Comput. Phys. 153, 509 (1999)ADSMathSciNetCrossRefGoogle Scholar
  100. 100.
    B. Dünweg, A.J.C. Ladd, Adv. Polym. Sci. 221, 89 (2009)Google Scholar
  101. 101.
    A. Chatterji, J. Horbach, Math. Comput. Sim. 72, 98 (2006)MathSciNetCrossRefGoogle Scholar
  102. 102.
    A. Brünger, C.L. Brooks, M. Karplus, Chem. Phys. Lett. 105, 495 (1984)ADSCrossRefGoogle Scholar
  103. 103.
    L.E. Reichl, A Modern Course in Statistical Physics (Wiley, 1998)Google Scholar
  104. 104.
    K.M. Mohamed, A.A. Mohamad, Microfluid. Nanofluid. 8, 283 (2010)CrossRefGoogle Scholar
  105. 105.
    R. Delgado-Buscalioni, Numerical Analysis of Multiscale Computations (Springer, 2012), p. 145Google Scholar
  106. 106.
    W. Ren, J. Comput. Phys. 227, 1353 (2007)ADSMathSciNetCrossRefGoogle Scholar
  107. 107.
    R. Delgado-Buscalioni, P.V. Coveney, J. Chem. Phys. 119, 978 (2003)ADSCrossRefGoogle Scholar
  108. 108.
    X. Yong, L.T. Zhang, J. Chem. Phys. 138, 084503 (2013)ADSCrossRefGoogle Scholar
  109. 109.
    C. Pastorino, T. Kreer, M. Müller, K. Binder, Phys. Rev. E 76, 026706 (2007)ADSCrossRefGoogle Scholar
  110. 110.
    R. Khare, J.J. de Pablo, A. Yethiraj, Macromolecules 29, 7910 (1996)ADSCrossRefGoogle Scholar
  111. 111.
    B. Dünweg, K. Kremer, J. Chem. Phys. 99, 6983 (1993)ADSCrossRefGoogle Scholar
  112. 112.
    R.M. Jendrejack, D.C. Schwartz, M.D. Graham, J.J. de Pablo, J. Chem. Phys. 119, 1165 (2003)ADSCrossRefGoogle Scholar
  113. 113.
    H. Hasimoto, J. Fluid Mech. 5, 317 (1959)ADSMathSciNetCrossRefGoogle Scholar
  114. 114.
    I.-C. Yeh, G. Hummer, J. Phys. Chem. B 108, 15873 (2004)CrossRefGoogle Scholar
  115. 115.
    J. Lyklema, S. Rovillard, J.D. Coninck, Langmuir 14, 5659 (1998)CrossRefGoogle Scholar
  116. 116.
    J.B. Freund, J. Chem. Phys. 116, 2194 (2002)ADSCrossRefGoogle Scholar
  117. 117.
    A. Beskok, G.E. Karniadakism, Microscale Therm. Eng. 3, 43 (1999)CrossRefGoogle Scholar
  118. 118.
    E. Spohr, J. Phys. Chem. 93, 6171 (1989)CrossRefGoogle Scholar
  119. 119.
    R.G. Horn, J.N. Israelachvili, J. Chem. Phys. 75, 1400 (1981)ADSCrossRefGoogle Scholar
  120. 120.
    F.F. Abraham, J. Chem. Phys. 68, 3713 (1978)ADSCrossRefGoogle Scholar
  121. 121.
    S. Toxvaerd, J. Chem. Phys. 74, 1998 (1981)ADSCrossRefGoogle Scholar
  122. 122.
    M. Plischke, D. Henderson, J. Chem. Phys. 84, 2846 (1986)ADSCrossRefGoogle Scholar
  123. 123.
    I. Bitsanis, S.A. Somers, H.T. Davis, M. Tirrell, J. Chem. Phys. 93, 3427 (1990)ADSCrossRefGoogle Scholar
  124. 124.
    I. Bitsanis, G. Hadziioannou, J. Chem. Phys. 92, 3827 (1990)ADSCrossRefGoogle Scholar
  125. 125.
    P.A. Thompson, M.O. Robbins, G.S. Grest, Isr. J. Chem. 35, 93 (1995)CrossRefGoogle Scholar
  126. 126.
    J.-L. Barrat, L. Bocquet, Faraday Discuss. 112, 119 (1999)ADSCrossRefGoogle Scholar
  127. 127.
    J. Koplik, J.R. Banavar, Annu. Rev. Fluid Mech. 27, 257 (1995)ADSCrossRefGoogle Scholar
  128. 128.
    J. Gao, W.D. Luedtke, U. Landman, Phys. Rev. Lett. 79, 705 (1997)ADSCrossRefGoogle Scholar
  129. 129.
    T.-M. Galea, P. Attard, Langmuir 20, 3477 (2004)CrossRefGoogle Scholar
  130. 130.
    R.R. Netz, Eur. Phys. J. E 5, 557 (2001)CrossRefGoogle Scholar
  131. 131.
    J.N. Israelachvili, Intermolecular And Surface Forces (Academic Press, 1991)Google Scholar
  132. 132.
    N. Cuvillier, F. Rondelez, Thin Solid Films 327, 19 (1998)ADSCrossRefGoogle Scholar
  133. 133.
    S.T. Cui, H.D. Cochran, J. Chem. Phys. 117, 5850 (2002)ADSCrossRefGoogle Scholar
  134. 134.
    M.J. Stevens, M.O. Robbins, Europhys. Lett. 12, 81 (1990)ADSCrossRefGoogle Scholar
  135. 135.
    T. Das, D. Bratko, L.B. Bhuiyan, C.W. Outhwaite, J. Phys. Chem. 99, 410 (1995)CrossRefGoogle Scholar
  136. 136.
    M. Deserno, C. Holm, S. May, Macromolecules 33, 199 (2000)ADSCrossRefGoogle Scholar
  137. 137.
    R. Messina, J. Phys.: Condens. Mat. 21, 113102 (2009)ADSGoogle Scholar
  138. 138.
    M. Gouy, J. Phys. Theor. Appl. 9, 457 (1910)CrossRefGoogle Scholar
  139. 139.
    D.L. Chapman, Philos. Mag. 25, 475 (1913)CrossRefGoogle Scholar
  140. 140.
    R.R. Netz, H. Orland, Eur. Phys. J. E 1, 67 (2000)CrossRefGoogle Scholar
  141. 141.
    A.G. Moreira, R.R. Netz, Phys. Rev. Lett. 87, 078301 (2001)ADSCrossRefGoogle Scholar
  142. 142.
    A.G. Moreira, R. Netz, Europhys. Lett. 52, 705 (2000)ADSCrossRefGoogle Scholar
  143. 143.
    C. Navier, Mémoires de l'Académie Royale des Sciences de l'Institut de France 6, 389 (1823)Google Scholar
  144. 144.
    L. Joly, C. Ybert, E. Trizac, L. Bocquet, Phys. Rev. Lett. 93, 257805 (2004)ADSCrossRefGoogle Scholar
  145. 145.
    L. Bocquet, J.-L. Barrat, Phys. Rev. E 49, 3079 (1994)ADSCrossRefGoogle Scholar
  146. 146.
    N.V. Priezjev, S.M. Troian, Phys. Rev. Lett. 92, 018302 (2004)ADSCrossRefGoogle Scholar
  147. 147.
    N. Priezjev, Phys. Rev. E 75, 051605 (2007)ADSCrossRefGoogle Scholar
  148. 148.
    L. Guo, S. Chen, M.O. Robbins, Phys. Rev. E 93, 013105 (2016)ADSCrossRefGoogle Scholar
  149. 149.
    C. Denniston, M.O. Robbins, J. Chem. Phys. 125, 214102 (2006)ADSCrossRefGoogle Scholar
  150. 150.
    J. Smiatek, M.P. Allen, F. Schmid, Eur. Phys. J. E 26, 115 (2008)CrossRefGoogle Scholar
  151. 151.
    G. He, Ph.D. thesis Johns Hopkins University, Baltimore, 2001Google Scholar
  152. 152.
    T. Nishimura, Y. Ohori, Y. Kawamura, J. Chem. Eng. Jpn. 17, 466 (1984)CrossRefGoogle Scholar
  153. 153.
    P. Panzer, M. Liu, D. Einzel, Int. J. Mod. Phys. B 6, 3251 (1992)ADSCrossRefGoogle Scholar
  154. 154.
    K. Kamrin, M.Z. Bazant, H.A. Stone, J. Fluid Mech. 658, 409 (2010)ADSMathSciNetCrossRefGoogle Scholar
  155. 155.
    L.M. Hocking, J. Fluid Mech. 76, 801 (1976)ADSCrossRefGoogle Scholar
  156. 156.
    S. Richardson, J. Fluid Mech. 59, 707 (1973)ADSCrossRefGoogle Scholar
  157. 157.
    E.O. Tuck, A. Kouzoubov, J. Fluid Mech. 300, 59 (1995)ADSMathSciNetCrossRefGoogle Scholar
  158. 158.
    A. Niavarani, N.V. Priezjev, Phys. Fluids 21, 052105 (2009)ADSCrossRefGoogle Scholar
  159. 159.
    C. Kunert, J. Harting, Phys. Rev. Lett. 99, 176001 (2007)ADSCrossRefGoogle Scholar
  160. 160.
    P.J. Atzberger, arXiv preprint [arXiv:1003.2680] (2010)

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringJohns Hopkins UniversityMarylandUSA
  2. 2.South University of Science and TechnologyShenzhenChina
  3. 3.Department of Physics and AstronomyJohns Hopkins UniversityMarylandUSA

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