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Multiphase and Multicomponent Flows

  • Timm Krüger
  • Halim Kusumaatmaja
  • Alexandr Kuzmin
  • Orest Shardt
  • Goncalo Silva
  • Erlend Magnus Viggen
Chapter
Part of the Graduate Texts in Physics book series (GTP)

Abstract

After reading this chapter, you will be able to expand lattice Boltzmann simulations by including non-ideal fluids, using either the free-energy or the Shan-Chen pseudopotential method. This will allow you to simulate fluids consisting of multiple phases (e.g. liquid water and water vapour) and multiple components (e.g. oil and water). You will also learn how the surface tension between fluid phases/components and the contact angle at solid surfaces can be varied and controlled.

References

  1. 1.
    A.K. Gunstensen, D.H. Rothman, S. Zaleski, G. Zanetti, Phys. Rev. A 43 (8), 4320 (1991)ADSCrossRefGoogle Scholar
  2. 2.
    D. Grunau, S. Chen, K. Eggert, Phys. Fluids A 5 (10), 2557 (1993)ADSCrossRefGoogle Scholar
  3. 3.
    M.M. Dupin, I. Halliday, C.M. Care, J. Phys. A: Math. Gen. 36 (31), 8517 (2003)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Latva-Kokko, D.H. Rothman, Phys. Rev. E 71 (5), 056702 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    H. Liu, A.J. Valocchi, Q. Kang, Phys. Rev. E 85 (4), 046309 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    S. Leclaire, M. Reggio, J.Y. Trépanier, J. Comput. Phys. 246, 318 (2013)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    P. Asinari, Phys. Rev. E 73 (5), 056705 (2006)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    S. Arcidiacono, I.V. Karlin, J. Mantzaras, C.E. Frouzakis, Phys. Rev. E 76 (4), 046703 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    T.J. Spencer, I. Halliday, Phys. Rev. E 88 (6), 063305 (2013)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    J. Tölke, G.D. Prisco, Y. Mu, Comput. Math. Appl. 65 (6), 864 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    L. Scarbolo, D. Molin, P. Perlekar, M. Sbragaglia, A. Soldati, F. Toschi, J. Comput. Phys. 234, 263 (2013)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    L. Chen, Q. Kang, Y. Mu, Y.L. He, W.Q. Tao, Int. J. Heat Mass Transfer 76, 210 (2014)CrossRefGoogle Scholar
  13. 13.
    H. Liu, Q. Kang, C.R. Leonardi, S. Schmieschek, A. Narváez, B.D. Jones, J.R. Williams, A.J. Valocchi, J. Harting, Comput. Geosci. pp. 1–29 (2015)Google Scholar
  14. 14.
    H. Huang, M.C. Sukop, X.Y. Lu, Multiphase Lattice Boltzmann Methods: Theory and Applications (Wiley-Blackwell, Hoboken, 2015)CrossRefGoogle Scholar
  15. 15.
    C.E. Brennen, Fundamentals of Multiphase Flows (Cambridge University Press, Cambridge, 2005)zbMATHCrossRefGoogle Scholar
  16. 16.
    J. Bibette, F.L. Calderon, P. Poulin, Reports Progress Phys. 62 (6), 969 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    M.J. Blunt, Current Opinion Colloid Interface Sci. 6 (3), 197 (2001)CrossRefGoogle Scholar
  18. 18.
    A. Faghri, Y. Zhang, Transport Phenomena in Multiphase Systems (Elsevier, Amsterdam, 2006)Google Scholar
  19. 19.
    C.D. Han, Multiphase Flow in Polymer Processing (Academic Press, New York, 1981)Google Scholar
  20. 20.
    A. Gunther, K.F. Jensen, Lab Chip 6, 1487 (2006)CrossRefGoogle Scholar
  21. 21.
    C. Wang, P. Cheng, Int. J. Heat Mass Transfer 39 (17), 3607 (1996)CrossRefGoogle Scholar
  22. 22.
    S. Blundell, K.M. Blundell, Concepts in Thermal Physics (Oxford University Press, Oxford, 2006)zbMATHGoogle Scholar
  23. 23.
    M. Doi, T. Ohta, J. Chem. Phys. 95 (2), 1242 (1991)ADSCrossRefGoogle Scholar
  24. 24.
    T.G. Mason, Current Opinion Colloid Interface Sci. 4 (3), 231 (1999)CrossRefGoogle Scholar
  25. 25.
    R. Osserman, A Survey of Minimal Surfaces (Dover Publications, New York, 1986)zbMATHGoogle Scholar
  26. 26.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1987)zbMATHGoogle Scholar
  27. 27.
    P.G. de Gennes, F. Brochard-Wyart, D. Quéré, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer, New York, 2004)zbMATHCrossRefGoogle Scholar
  28. 28.
    J.S. Rowlinson, B. Widom, Molecular Theory of Capillarity (Oxford University Press, Oxford, 1989)Google Scholar
  29. 29.
    J.L. Barrat, L. Bocquet, Phys. Rev. Lett. 82, 4671 (1999)ADSCrossRefGoogle Scholar
  30. 30.
    D.M. Huang, C. Sendner, D. Horinek, R.R. Netz, L. Bocquet, Phys. Rev. Lett. 101, 226101 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    A. Lafuma, Quéré, Nat. Mat. 2, 457–460 (2003)Google Scholar
  32. 32.
    J. Léopoldés, A. Dupuis, D.G. Bucknall, J.M. Yeomans, Langmuir 19 (23), 9818 (2003)CrossRefGoogle Scholar
  33. 33.
    Z. Wang, J. Yang, B. Koo, F. Stern, Int. J. Multiphase Flow 35 (3), 227 (2009)CrossRefGoogle Scholar
  34. 34.
    G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, Y.J. Jan, J. Comput. Phys. 169 (2), 708 (2001)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    C.S. Peskin, Acta Numerica 11, 479–517 (2002)MathSciNetCrossRefGoogle Scholar
  36. 36.
    J. van der Walls, J. Stat. Phys. 20 (2), 197 (1979)CrossRefGoogle Scholar
  37. 37.
    D. Anderson, G. McFadden, A. Wheeler, Annu. Rev. Fluid Mech. 30, 139 (1998)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    J.G. Kirkwood, F.P. Buff, J. Chem. Phys. 17 (3), 338 (1949)ADSCrossRefGoogle Scholar
  39. 39.
    M.R. Swift, W.R. Osborn, J.M. Yeomans, Phys. Rev. Lett. 75, 830 (1995)ADSCrossRefGoogle Scholar
  40. 40.
    M.R. Swift, E. Orlandini, W.R. Osborn, J.M. Yeomans, Phys. Rev. E 54, 5041 (1996)ADSCrossRefGoogle Scholar
  41. 41.
    A.J. Briant, A.J. Wagner, J.M. Yeomans, Phys. Rev. E 69, 031602 (2004)ADSCrossRefGoogle Scholar
  42. 42.
    A.J. Briant, J.M. Yeomans, Phys. Rev. E 69, 031603 (2004)ADSCrossRefGoogle Scholar
  43. 43.
    C. Semprebon, T. Krüger, H. Kusumaatmaja, Phys. Rev. E 93 (3), 033305 (2016)ADSCrossRefGoogle Scholar
  44. 44.
    T. Lee, C.L. Lin, J. Comput. Phys. 206 (1), 16 (2005)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    A. Mazloomi M., S.S. Chikatamarla, I.V. Karlin, Phys. Rev. E 92 (2), 023308 (2015)Google Scholar
  46. 46.
    G. Gompper, S. Zschocke, Europhys. Lett. 16 (8), 731 (1991)ADSCrossRefGoogle Scholar
  47. 47.
    V.M. Kendon, M.E. Cates, I. Pagonabarraga, J.C. Desplat, P. Bladon, J. Fluid Mech. 440, 147 (2001)ADSCrossRefGoogle Scholar
  48. 48.
    A. Wagner, Q. Li, Physica A Stat. Mech. Appl. 362 (1), 105 (2006)ADSCrossRefGoogle Scholar
  49. 49.
    T. Lee, P.F. Fischer, Phys. Rev. E 74, 046709 (2006)ADSCrossRefGoogle Scholar
  50. 50.
    T. Seta, K. Okui, JFST 2 (1), 139 (2007)ADSCrossRefGoogle Scholar
  51. 51.
    C.M. Pooley, K. Furtado, Phys. Rev. E 77, 046702 (2008)ADSCrossRefGoogle Scholar
  52. 52.
    Z. Guo, C. Zheng, B. Shi, Phys. Rev. E 65, 46308 (2002)ADSCrossRefGoogle Scholar
  53. 53.
    K. Connington, T. Lee, J. Mech. Sci. Technol. 26 (12), 3857 (2012)CrossRefGoogle Scholar
  54. 54.
    D. Jamet, D. Torres, J. Brackbill, J. Comput. Phys. 182 (1), 262 (2002)ADSCrossRefGoogle Scholar
  55. 55.
    A.J. Wagner, Int. J. Modern Phys. B 17 (01n02), 193 (2003)Google Scholar
  56. 56.
    T. Inamuro, N. Konishi, F. Ogino, Comput. Phys. Commun. 129 (1), 32 (2000)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    D.J. Holdych, D. Rovas, J.G. Georgiadis, R.O. Buckius, Int. J. Modern Phys. C 09 (08), 1393 (1998)ADSCrossRefGoogle Scholar
  58. 58.
    H. Kusumaatmaja, J. Léopoldés, A. Dupuis, J. M. Yeomans, Europhys. Lett. 73 (5), 740 (2006)ADSCrossRefGoogle Scholar
  59. 59.
    J.W. Cahn, J. Chem. Phys. 66 (8), 3667 (1977)ADSCrossRefGoogle Scholar
  60. 60.
    K.F. Riley, M.P. Hobson, S.J. Bence, Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (CUP, Cambridge, 2006)zbMATHCrossRefGoogle Scholar
  61. 61.
    H. Kusumaatmaja, J.M. Yeomans, in Simulating Complex Systems by Cellular Automata, ed. by J. Kroc, P.M. Sloot, A.G. Hoekstra, Understanding Complex Systems (Springer, New York, 2010), chap. 11, pp. 241–274Google Scholar
  62. 62.
    A. Lamura, G. Gonnella, J.M. Yeomans, Europhys. Lett. 45 (3), 314 (1999)ADSCrossRefGoogle Scholar
  63. 63.
    Q. Li, A.J. Wagner, Phys. Rev. E 76 (3), 036701 (2007)ADSCrossRefGoogle Scholar
  64. 64.
    J.W. Cahn, C.M. Elliott, A. Novick-Cohen, Eur. J. Appl. Math. 7, 287 (1996)MathSciNetCrossRefGoogle Scholar
  65. 65.
    J. Zhu, L.Q. Chen, J. Shen, V. Tikare, Phys. Rev. E 60, 3564 (1999)ADSCrossRefGoogle Scholar
  66. 66.
    H. Kusumaatmaja, E.J. Hemingway, S.M. Fielding, J. Fluid Mech. 788, 209 (2016)ADSMathSciNetCrossRefGoogle Scholar
  67. 67.
    J.J. Huang, C. Shu, Y.T. Chew, Phys. Fluids 21 (2) (2009)Google Scholar
  68. 68.
    X. Shan, H. Chen, Phys. Rev. E 47 (3), 1815 (1993)ADSCrossRefGoogle Scholar
  69. 69.
    X. Shan, G. Doolen, J. Stat. Phys. 81 (1), 379 (1995)ADSMathSciNetCrossRefGoogle Scholar
  70. 70.
    J. Zhang, F. Tian, Europhys. Lett. 81 (6), 66005 (2008)ADSCrossRefGoogle Scholar
  71. 71.
    N.S. Martys, H. Chen, Phys. Rev. E 53 (1), 743 (1996)ADSCrossRefGoogle Scholar
  72. 72.
    X. Shan, H. Chen, Phys. Rev. E 49 (4), 2941 (1994)ADSCrossRefGoogle Scholar
  73. 73.
    M.C. Sukop, D.T. Thorne, Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers (Springer, New York, 2006)Google Scholar
  74. 74.
    M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, K. Sugiyama, F. Toschi, Phys. Rev. E 75 (026702), 1 (2007)MathSciNetGoogle Scholar
  75. 75.
    M. Sbragaglia, H. Chen, X. Shan, S. Succi, Europhys. Lett. 86 (2), 24005 (2009)ADSCrossRefGoogle Scholar
  76. 76.
    J. Bao, L. Schaefer, Appl. Math. Model. 37 (4), 1860 (2013)MathSciNetCrossRefGoogle Scholar
  77. 77.
    D. Lycett-Brown, K.H. Luo, Phys. Rev. E 91, 023305 (2015)ADSCrossRefGoogle Scholar
  78. 78.
    P. Yuan, L. Schaefer, Phys. Fluids 18 (042101), 1 (2006)MathSciNetGoogle Scholar
  79. 79.
    A. Kuzmin, A. Mohamad, S. Succi, Int. J. Mod. Phys. C 19 (6), 875 (2008)ADSMathSciNetCrossRefGoogle Scholar
  80. 80.
    R. Benzi, L. Biferale, M. Sbragaglia, S. Succi, F. Toschi, Phys. Rev. E 74 (2), 021509 (2006)ADSMathSciNetCrossRefGoogle Scholar
  81. 81.
    Z. Yu, L.S. Fan, Phys. Rev. E 82 (4), 046708 (2010)ADSCrossRefGoogle Scholar
  82. 82.
    X. Shan, Phys. Rev. E 81 (4), 045701 (2010)ADSCrossRefGoogle Scholar
  83. 83.
    M. Sega, M. Sbragaglia, S.S. Kantorovich, A.O. Ivanov, Soft Matter 9 (42), 10092 (2013)ADSCrossRefGoogle Scholar
  84. 84.
    X. Shan, G. Doolen, Phys. Rev. E 54 (4), 3614 (1996)ADSCrossRefGoogle Scholar
  85. 85.
    J. Yang, E.S. Boek, Comput. Math. Appl. 65 (6), 882 (2013)MathSciNetCrossRefGoogle Scholar
  86. 86.
    H. Liu, Y. Zhang, A.J. Valocchi, Phys. Fluids 27 (5), 052103 (2015)ADSCrossRefGoogle Scholar
  87. 87.
    H. Huang, D.T. Thorne, M.G. Schaap, M.C. Sukop, Phys. Rev. E 76 (6), 066701 (2007)ADSCrossRefGoogle Scholar
  88. 88.
    S. Chibbaro, Eur. Phys. J. E 27 (1), 99 (2008)CrossRefGoogle Scholar
  89. 89.
    F. Jansen, J. Harting, Phys. Rev. E 83 (4), 046707 (2011)ADSCrossRefGoogle Scholar
  90. 90.
    I. Ginzburg, G. Wittum, J. Comp. Phys. 166 (2), 302 (2001)ADSCrossRefGoogle Scholar
  91. 91.
    A. Kupershtokh, D. Medvedev, D. Karpov, Comput. Math. Appl. 58 (5), 965 (2009)MathSciNetCrossRefGoogle Scholar
  92. 92.
    R. Benzi, M. Sbragaglia, S. Succi, M. Bernaschi, S. Chibbaro, J. Chem. Phys. 131 (10), 104903 (2009)ADSCrossRefGoogle Scholar
  93. 93.
    R. Benzi, M. Bernaschi, M. Sbragaglia, S. Succi, Europhys. Lett. 91 (1), 14003 (2010)ADSCrossRefGoogle Scholar
  94. 94.
    S. Chibbaro, G. Falcucci, G. Chiatti, H. Chen, X. Shan, S. Succi, Phys. Rev. E 77 (036705), 1 (2008)Google Scholar
  95. 95.
    Z. Guo, C. Zheng, B. Shi, Phys. Rev. E 83, 036707 (2011)ADSCrossRefGoogle Scholar
  96. 96.
    D. Chiappini, G. Bella, S. Succi, F. Toschi, S. Ubertini, Commun. Comput. Phys. 7, 423 (2010)Google Scholar
  97. 97.
    A. Kuzmin, A. Mohamad, Comp. Math. Appl. 59, 2260 (2010)MathSciNetCrossRefGoogle Scholar
  98. 98.
    T. Inamuro, T. Ogato, S. Tajima, N. Konishi, J. Comp. Phys. 198, 628 (2004)ADSCrossRefGoogle Scholar
  99. 99.
    H. Zheng, C. Shu, Y. Chew, J. Comput. Phys. 218 (1), 353 (2006)ADSMathSciNetCrossRefGoogle Scholar
  100. 100.
    A. Mazloomi M, S.S. Chikatamarla, I.V. Karlin, Phys. Rev. Lett. 114, 174502 (2015)Google Scholar
  101. 101.
    A. Kuzmin, M. Januszewski, D. Eskin, F. Mostowfi, J. Derksen, Chem. Eng. J. 171, 646 (2011)CrossRefGoogle Scholar
  102. 102.
    A. Kuzmin, M. Januszewski, D. Eskin, F. Mostowfi, J. Derksen, Chem. Eng. J. 178, 306 (2011)CrossRefGoogle Scholar
  103. 103.
    A. Kuzmin, Multiphase simulations with lattice Boltzmann scheme. Ph.D. thesis, University of Calgary (2010)Google Scholar
  104. 104.
    M.L. Porter, E.T. Coon, Q. Kang, J.D. Moulton, J.W. Carey, Phys. Rev. E 86 (3), 036701 (2012)ADSCrossRefGoogle Scholar
  105. 105.
    Q. Kang, D. Zhang, S. Chen, Adv. Water Resour. 27 (1), 13 (2004)ADSCrossRefGoogle Scholar
  106. 106.
    Z. Yu, H. Yang, L.S. Fan, Chem. Eng. Sci. 66 (14), 3441 (2011)CrossRefGoogle Scholar
  107. 107.
    M. Monteferrante, S. Melchionna, U.M.B. Marconi, J. Chem. Phys. 141 (1), 014102 (2014)ADSCrossRefGoogle Scholar
  108. 108.
    K. Premnath, J. Abraham, J. Comput. Phys. 224, 539 (2007)ADSMathSciNetCrossRefGoogle Scholar
  109. 109.
    Z.H. Chai, T.S. Zhao, Acta. Mech. Sin. 28 (4), 983 (2012)ADSMathSciNetCrossRefGoogle Scholar
  110. 110.
    D. Zhang, K. Papadikis, S. Gu, Int. J. Multiphas. Flow 64, 11 (2014)MathSciNetCrossRefGoogle Scholar
  111. 111.
    K. Yang, Z. Guo, Sci. Bull. 60 (6), 634 (2015)CrossRefGoogle Scholar
  112. 112.
    Y.Q. Zu, S. He, Phys. Rev. E 87 (4), 043301 (2013)ADSCrossRefGoogle Scholar
  113. 113.
    H. Liang, B.C. Shi, Z.H. Chai, Phys. Rev. E 93 (1), 013308 (2016)ADSCrossRefGoogle Scholar
  114. 114.
    Y. Fu, S. Zhao, L. Bai, Y. Jin, Y. Cheng, Chem. Eng. Sci. 146, 126 (2016)CrossRefGoogle Scholar
  115. 115.
    H. Chen, B.M. Boghosian, P.V. Coveney, M. Nekovee, Proc. R. Soc. Lond. A 456, 2043 (2000)ADSCrossRefGoogle Scholar
  116. 116.
    M. Nekovee, P.V. Coveney, H. Chen, B.M. Boghosian, Phys. Rev. E 62 (6), 8282 (2000)ADSCrossRefGoogle Scholar
  117. 117.
    S. Bogner, U. Rüde, Comput. Math. Appl. 65 (6), 901 (2013)MathSciNetCrossRefGoogle Scholar
  118. 118.
    D. Anderl, S. Bogner, C. Rauh, U. Rüde, A. Delgado, Comput. Math. Appl. 67 (2), 331 (2014)MathSciNetCrossRefGoogle Scholar
  119. 119.
    S. Bogner, R. Ammer, U. Rüde, J. Comput. Phys. 297, 1 (2015)ADSMathSciNetCrossRefGoogle Scholar
  120. 120.
    M. Gross, F. Varnik, Int. J. Mod. Phys. C 25 (01), 1340019 (2013)ADSCrossRefGoogle Scholar
  121. 121.
    X. Frank, P. Perré, H.Z. Li, Phys. Rev. E 91 (5), 052405 (2015)ADSMathSciNetCrossRefGoogle Scholar
  122. 122.
    Q. Li, Q.J. Kang, M.M. Francois, A.J. Hu, Soft Matter 12 (1), 302 (2015)ADSCrossRefGoogle Scholar
  123. 123.
    C. Pan, M. Hilpert, C.T. Miller, Water Resour. Res. 40 (1), W01501 (2004)ADSCrossRefGoogle Scholar
  124. 124.
    E.S. Boek, M. Venturoli, Comput. Math. Appl. 59 (7), 2305 (2010)MathSciNetCrossRefGoogle Scholar
  125. 125.
    J. Onishi, A. Kawasaki, Y. Chen, H. Ohashi, Comput. Math. Appl. 55 (7), 1541 (2008)MathSciNetCrossRefGoogle Scholar
  126. 126.
    A.S. Joshi, Y. Sun, Phys. Rev. E 79 (6), 066703 (2009)ADSCrossRefGoogle Scholar
  127. 127.
    T. Krüger, S. Frijters, F. Günther, B. Kaoui, J. Harting, Eur. Phys. J. Spec. Top. 222 (1), 177 (2013)CrossRefGoogle Scholar
  128. 128.
    K.W. Connington, T. Lee, J.F. Morris, J. Comput. Phys. 283, 453 (2015)ADSMathSciNetCrossRefGoogle Scholar
  129. 129.
    Q. Luo, Z. Guo, B. Shi, Phys. Rev. E 87 (063301), 1 (2013)Google Scholar
  130. 130.
    Z. Yu, O. Hemminger, L.S. Fan, Chem. Eng. Sci. 62, 7172 (2007)CrossRefGoogle Scholar
  131. 131.
    H. Liu, Y. Zhang, J. Appl. Phys. 106 (3), 1 (2009)Google Scholar
  132. 132.
    T. Munekata, T. Suzuki, S. Yamakawa, R. Asahi, Phys. Rev. E 88 (5), 052314 (2013)ADSCrossRefGoogle Scholar
  133. 133.
    R. Ledesma-Aguilar, D. Vella, J.M. Yeomans, Soft Matter 10 (41), 8267 (2014)ADSCrossRefGoogle Scholar
  134. 134.
    D. Sun, M. Zhu, S. Pan, D. Raabe, Acta Mater. 57 (6), 1755 (2009)CrossRefGoogle Scholar
  135. 135.
    R. Rojas, T. Takaki, M. Ohno, J. Comput. Phys. 298, 29 (2015)ADSMathSciNetCrossRefGoogle Scholar
  136. 136.
    P.R. Di Palma, C. Huber, P. Viotti, Adv. Water Resour. 82, 139 (2015)ADSCrossRefGoogle Scholar
  137. 137.
    G. Gonnella, E. Orlandini, J.M. Yeomans, Phys. Rev. E 58, 480 (1998)ADSCrossRefGoogle Scholar
  138. 138.
    Q. Du, C. Liu, X. Wang, J. Comput. Phys. 198 (2), 450 (2004)ADSMathSciNetCrossRefGoogle Scholar
  139. 139.
    J.S. Lowengrub, A. Rätz, A. Voigt, Phys. Rev. E 79, 031926 (2009)ADSCrossRefGoogle Scholar
  140. 140.
    C. Denniston, E. Orlandini, J.M. Yeomans, Phys. Rev. E 63, 056702 (2001)ADSCrossRefGoogle Scholar
  141. 141.
    J. Qian, C. Law, J. Fluid Mech. 331, 59 (1997)ADSCrossRefGoogle Scholar
  142. 142.
    N. Ashgriz, J. Poo, J. Fluid Mech. 221, 183 (1990)ADSCrossRefGoogle Scholar
  143. 143.
    C. Rabe, J. Malet, F. Feuillebois, Phys. Fluids 22 (047101), 1 (2010)Google Scholar
  144. 144.
    D. Lycett-Brown, K. Luo, R. Liu, P. Lv, Phys. Fluids 26 (023303), 1 (2014)Google Scholar
  145. 145.
    T. Inamuro, S. Tajima, F. Ogino, Int. J. Heat Mass Trans. 47, 4649 (2004)CrossRefGoogle Scholar
  146. 146.
    A. Moqaddam, S. Chikatamarla, I. Karlin, Phys. Fluids 28 (022106), 1 (2016)Google Scholar
  147. 147.
    A.E. Komrakova, D. Eskin, J.J. Derksen, Phys. Fluids 25 (4), 042102 (2013)ADSCrossRefGoogle Scholar
  148. 148.
    O. Shardt, J.J. Derksen, S.K. Mitra, Langmuir 29, 6201 (2013)CrossRefGoogle Scholar
  149. 149.
    O. Shardt, S.K. Mitra, J.J. Derksen, Langmuir 30, 14416 (2014)CrossRefGoogle Scholar
  150. 150.
    H. Kusumaatmaja, C.M. Pooley, S. Girardo, D. Pisignano, J.M. Yeomans, Phys. Rev. E 77, 067301 (2008)ADSCrossRefGoogle Scholar
  151. 151.
    J. Murison, B. Semin, J.C. Baret, S. Herminghaus, M. Schröter, M. Brinkmann, Phys. Rev. Appl. 2, 034002 (2014)ADSCrossRefGoogle Scholar
  152. 152.
    A.A. Darhuber, S.M. Troian, Annu. Rev. Fluid Mech. 37 (1), 425 (2005)ADSMathSciNetCrossRefGoogle Scholar
  153. 153.
    H. Gau, S. Herminghaus, P. Lenz, R. Lipowsky, Science 283 (5398), 46 (1999)ADSCrossRefGoogle Scholar
  154. 154.
    M. Brinkmann, R. Lipowsky, J. Appl. Phys. 92 (8), 4296 (2002)ADSCrossRefGoogle Scholar
  155. 155.
    H.P. Jansen, K. Sotthewes, J. van Swigchem, H.J.W. Zandvliet, E.S. Kooij, Phys. Rev. E 88, 013008 (2013)ADSCrossRefGoogle Scholar
  156. 156.
    A. Dupuis, J. Léopoldés, D.G. Bucknall, J.M. Yeomans, Appl. Phys. Lett. 87 (2), 024103 (2005)ADSCrossRefGoogle Scholar
  157. 157.
    S. Wang, T. Wang, P. Ge, P. Xue, S. Ye, H. Chen, Z. Li, J. Zhang, B. Yang, Langmuir 31 (13), 4032 (2015)CrossRefGoogle Scholar
  158. 158.
    D. Quéré, Annu. Rev. Mater. Res. 38 (1), 71 (2008)ADSCrossRefGoogle Scholar
  159. 159.
    W. Barthlott, C. Neinhuis, Planta 202 (1), 1 (1997)CrossRefGoogle Scholar
  160. 160.
    J. Bico, C. Marzolin, D. Quéré, Europhys. Lett. 47 (2), 220 (1999)ADSCrossRefGoogle Scholar
  161. 161.
    A. Tuteja, W. Choi, M. Ma, J.M. Mabry, S.A. Mazzella, G.C. Rutledge, G.H. McKinley, R.E. Cohen, Science 318 (5856), 1618 (2007)ADSCrossRefGoogle Scholar
  162. 162.
    A.B.D. Cassie, S. Baxter, Trans. Faraday Soc. 40, 546 (1944)CrossRefGoogle Scholar
  163. 163.
    C.H. Choi, C.J. Kim, Phys. Rev. Lett. 96, 066001 (2006)ADSCrossRefGoogle Scholar
  164. 164.
    R.N. Wenzel, J. Phys. Colloid Chem. 53 (9), 1466 (1949)CrossRefGoogle Scholar
  165. 165.
    F. Diotallevi, L. Biferale, S. Chibbaro, G. Pontrelli, F. Toschi, S. Succi, Euro. Phys. J. Special Topics 171 (1), 237 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Timm Krüger
    • 1
  • Halim Kusumaatmaja
    • 2
  • Alexandr Kuzmin
    • 3
  • Orest Shardt
    • 4
  • Goncalo Silva
    • 5
  • Erlend Magnus Viggen
    • 6
  1. 1.School of Engineering University of EdinburghEdinburghUK
  2. 2.Department of PhysicsDurham UniversityDurhamUK
  3. 3.Maya Heat Transfer TechnologiesWestmountCanada
  4. 4.Department of Mechanical and Aerospace EngineeringPrinceton UniversityPrincetonUSA
  5. 5.IDMEC/IST, University of LisbonLisbonPortugal
  6. 6.Acoustics Research Centre, SINTEF ICTTrondheimNorway

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