Nanodroplets pp 143-167 | Cite as

Dynamics of Nanodroplets on Structured Surfaces

Chapter
Part of the Lecture Notes in Nanoscale Science and Technology book series (LNNST, volume 18)

Abstract

Fluids on the nanoscale behave qualitatively different from macroscopic systems. This becomes particularly evident if a free liquid–liquid or liquid–gas interface is close to a solid surface such as in the case of nanodroplets. In contrast to macroscopic drops, hydrodynamic slip, thermal fluctuations, the molecular structure of the liquid, and the range of the intermolecular interactions are important for the structure and the dynamics of such open nanofluidic systems. After a review of the macroscopic modeling and behavior of nonvolatile droplets on structured substrates, we discuss the static and dynamic peculiarities on the nanoscale with special emphasis on theory. In particular we show that nanodroplets experience long-ranged lateral interactions with sharp surface features and that their free energy might be lower on a less wettable part of the substrate surface. A discussion of possible experiments for observing these phenomena is followed by a summary and an outlook.

Keywords

Migration Graphite Convection Silane Helium 

Notes

Acknowledgements

Markus Rauscher thanks S. Dietrich for supporting this research. The surface evolver calculations were performed by D. Maier and H. Bartsch in their bachelor thesis project.

References

  1. 1.
    Rauscher, M., Dietrich, S.: Ann. Rev. Mater. Res. 38, 143 (2008)Google Scholar
  2. 2.
    Rauscher, M., Dietrich, S.: Soft Matter 5(16), 2997 (2009)Google Scholar
  3. 3.
    Rauscher, M., Dietrich, S.: In: Sattler, K.D. (ed.) Handbook of Nanophysics, vol. I: Principles and Methods,  chap. 11, pp. 1–23. CRC, Boca Raton (2010)
  4. 4.
    Dietrich, S., Rauscher, M., Napiórkowski, M.: In: Ondarçuhu, T., Aimé, J.P. (eds.) Nanoscale Liquid Interfaces: Wetting, Patterning and Force Microscopy at Molecular Scale. Pan Stanford Publishing, Singapore (2012)Google Scholar
  5. 5.
    de Gennes, P.G.: Rev. Mod. Phys. 57(3), 827 (1985)Google Scholar
  6. 6.
    Dietrich, S.: In: Domb, C., Lebowitz, J.L. (eds.) Phase Transitions and Critical Phenomena, vol. 12,  Chap. 1, pp. 1–218. Academic, London (1988)
  7. 7.
    de Gennes, P.G., Brochard-Wyart, F., Quéré, D.: Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer, New York (2004)Google Scholar
  8. 8.
    Ondarçuhu, T., Veyssié, M.: J. Phys. II France 1(1), 75 (1991)Google Scholar
  9. 9.
    Ondarçuhu, T., Raphaël, E.: C. R. Acad. Sci. Paris II 314, 453 (1992)Google Scholar
  10. 10.
    Chaudhury, M.K., Whitesides, G.M.: Science 256(5063), 1539 (1992)Google Scholar
  11. 11.
    Pismen, L.M., Thiele, U.: Phys. Fluids 18(4), 042104 (2006)Google Scholar
  12. 12.
    Moosavi, A., Mohammadi, A.: J. Phys. Condens. Matter 23(11), 085004 (2011)Google Scholar
  13. 13.
    Brinkmann, M., Lipowsky, R.: J. Appl. Phys. 92(8), 4296 (2002)Google Scholar
  14. 14.
    Lipowsky, R., Brinkmann, M., Dimova, R., Franke, T., Kierfeld, J., Zhand, X.: J. Phys. Condens. Matter 17(9), S537 (2005)Google Scholar
  15. 15.
    Dietrich, S., Popescu, M.N., Rauscher, M.: J. Phys. Condens. Matter 17(9), S577 (2005)Google Scholar
  16. 16.
    Koplik, J., Lo, T.S., Rauscher, M., Dietrich, S.: Phys. Fluids 18(3), 032104 (2006)Google Scholar
  17. 17.
    Rauscher, M., Dietrich, S., Koplik, J.: Phys. Rev. Lett. 98(22), 224504 (2007)Google Scholar
  18. 18.
    Brakke, K.: Exp. Math. 1(2), 141 (1992)Google Scholar
  19. 19.
    Bico, J., Thiele, U., Quéré, D.: Colloids Surf. A Physicochem. Eng. Aspects 206(1–3), 41 (2002)Google Scholar
  20. 20.
    Lafuma, A., Quéré, D.: Nat. Mater. 2(7), 457 (2003)Google Scholar
  21. 21.
    Quéré, D.: Rep. Prog. Phys. 68, 2495 (2005)Google Scholar
  22. 22.
    Quéré, D.: Ann. Rev. Mater. Res. 38, 71 (2008)Google Scholar
  23. 23.
    Yao, Z., Bowick, M.J.: Soft Matter 8(4), 1142 (2012)Google Scholar
  24. 24.
    Seemann, M., Brinkmann, R., Kramer, F.F., Lange, E.J., Lipowsky, R.: Proc. Natl. Acad. Sci. USA 102(6), 1848 (2005)Google Scholar
  25. 25.
    Khare, K., Herminghaus, S., Baret, J.C., Law, B.M., Brinkmann, M., Seemann, R.: Langmuir 23(26), 12997 (2007)Google Scholar
  26. 26.
    Herminghaus, S., Brinkmann, M., Seemann, R.: Ann. Rev. Mater. Res. 38, 101 (2008)Google Scholar
  27. 27.
    Gibbs, J.W.: The Scientific Papers of J. Willard Gibbs, vol. I: Thermodynamics, chap. III, pp. 55–353. Longmans, Green, London (1906)Google Scholar
  28. 28.
    Oliver, J.F., Hu, C., Mason, S.G.: J. Colloid Interface Sci. 59(3), 568 (1977)Google Scholar
  29. 29.
    Morison, K.R., Sellier, M.: Int. J. Multiphase Flow 39, 245 (2012)Google Scholar
  30. 30.
    Delmas, M., Monthioux, M., Ondarçuhu, T.: Phys. Rev. Lett. 106(13), 136102 (2011)Google Scholar
  31. 31.
    Eral, H.B.B., de Ruiter, J., de Ruiter, R., Oh, J.M., Semprebon, C., Brinkman, M., Mugele, F.: Soft Matter 7(11), 5138 (2011)Google Scholar
  32. 32.
    Lauga, E., Brenner, M.P., Stone, H.A.: In: Tropea, C., Yarin, A.L., Foss, J.F. (eds.) Springer Handbook of Experimental Fluid Mechanics, chap. Part C, pp. 1219–1240. Springer, Berlin, (2007)Google Scholar
  33. 33.
    Oron, A., Davis, S.H., Bankoff, S.G.: Rev. Mod. Phys. 69(3), 931 (1997)Google Scholar
  34. 34.
    Ralston, J., Popescu, M., Sedev, R.: Ann. Rev. Mater. Res. 38, 23 (2008)Google Scholar
  35. 35.
    Hansen, J.P., McDonald, I.R.: Theory of Simple Liquids, 2nd edn. Academic, London (1990)Google Scholar
  36. 36.
    Evans, R.: Adv. Phys. 28(2), 143 (1979)Google Scholar
  37. 37.
    Percus, J.K.: J. Stat. Phys. 15(6), 505 (1976)Google Scholar
  38. 38.
    Roth, R., Evans, R., Lang, A., Kahl, G.: J. Phys. Condens. Matter 14(46), 12063 (2002)Google Scholar
  39. 39.
    Hansen-Goos, H., Roth, R.: J. Phys. Condens. Matter 18(37), 8413 (2006)Google Scholar
  40. 40.
    Napiórkowski, M., Dietrich, S.: Phys. Rev. E 47(3), 1836 (1993)Google Scholar
  41. 41.
    Robbins, M.O., Andelman, D., Joanny, J.F.: Phys. Rev. A 43(8), 4344 (1991)Google Scholar
  42. 42.
    Dietrich, S., Napiórkowski, M.: Phys. Rev. A 43(4), 1861 (1991)Google Scholar
  43. 43.
    Moosavi, A., Rauscher, M., Dietrich, S.: J. Phys. Condens. Matter 21(46), 464120 (2009)Google Scholar
  44. 44.
    Becker, J., Grün, G., Seemann, R., Mantz, H., Jacobs, K., Mecke, K.R., Blossey, R.: Nat. Mater. 2(1), 59 (2003)Google Scholar
  45. 45.
    Neto, C., Jacobs, K., Seemann, R., Blossey, R., Becker, J., Grün, G.: J. Phys. Condens. Matter 15(19), 3355 (2003)Google Scholar
  46. 46.
    Landau, L.D., Lifshitz, E.M.: Fluid Mechanics, Course of Theoretical Physics, vol. 6, 2nd edn. Elsevier, Amsterdam (2005)Google Scholar
  47. 47.
    Mashiyama, K.T., Mori, H.: J. Stat. Phys. 18(4), 385 (1978)Google Scholar
  48. 48.
    Forster, D., Nelson, D.R., Stephen, M.J.: Phys. Rev. Lett. 36(15), 867 (1976)Google Scholar
  49. 49.
    Forster, D., Nelson, D.R., Stephen, M.J.: Phys. Rev. A 16(2), 732 (1977)Google Scholar
  50. 50.
    Hohenberg, P.C., Swift, J.B.: Phys. Rev. A 46(8), 4773 (1992)Google Scholar
  51. 51.
    Swift, J.B., Babcock, K.L., Hohenberg, P.C.: Physica A 204(1–4), 625 (1994)Google Scholar
  52. 52.
    Fetzer, R., Rauscher, M., Seemann, R., Jacobs, K., Mecke, K.: Phys. Rev. Lett. 99(11), 114503 (2007)Google Scholar
  53. 53.
    Mecke, K., Falk, K., Rauscher, M.: In: Radons, G., Rumpf, B., Schuster, H.G. (eds.) Nonlinear Dynamics of Nanosystems, pp. 121–142. Wiley-VCH, Berlin (2010)Google Scholar
  54. 54.
    Blossey, R., Münch, A., Rauscher, M., Wagner, B.: Eur. Phys. J. E 20(3), 267 (2006)Google Scholar
  55. 55.
    Rauscher, M., Blossey, R., Münch, A., Wagner, B.: Langmuir 24(21), 12290 (2008)Google Scholar
  56. 56.
    Münch, A., Wagner, B.: J. Phys. Condens. Matter 23(18), 184101 (2011)Google Scholar
  57. 57.
    Kalliadasis, S., Homsy, G.M.: J. Fluid Mech. 448, 387 (2001)Google Scholar
  58. 58.
    Bielarz, C., Kalliadasis, S.: Phys. Fluids 15(9), 2512 (2003)Google Scholar
  59. 59.
    Savva, N., Kalliadasis, S.: Phys. Fluids 21(9), 092102 (2009)Google Scholar
  60. 60.
    Gaskell, P.H., Jimack, P.K., Sellier, M., Thompson, H.M., Wilson, M.C.T.: J. Fluid Mech. 509, 253 (2004)Google Scholar
  61. 61.
    Gaskell, P.H., Jimack, P.K., Sellier, M., Thompson, H.M.: Phys. Fluids 18(1), 013601 (2006)Google Scholar
  62. 62.
    Baxter, S.J., Power, H., Cliffe, K.A., Hibberd, S.: Phys. Fluids 21(3), 032102 (2009)Google Scholar
  63. 63.
    Kondic, L., Diez, J.A.: Colloids Surf. A Physicochem. Eng. Aspects 214(1–3), 1 (2003)Google Scholar
  64. 64.
    Kondic, L., Diez, J.: Phys. Fluids 16(9), 3341 (2004)Google Scholar
  65. 65.
    Mechkov, S., Rauscher, M., Dietrich, S.: Phys. Rev. E 77(6), 061605 (2008)Google Scholar
  66. 66.
    Shan, X., Chen, H.: Phys. Rev. E 47(3), 1815 (1993)Google Scholar
  67. 67.
    Shan, X., Chen, H.: Phys. Rev. E 49(4), 2941 (1994)Google Scholar
  68. 68.
    Swift, M.R., Osborn, W.R., Yeomans, J.M.: Phys. Rev. Lett. 75(5), 830 (1995)Google Scholar
  69. 69.
    Swift, M.R., Orlandini, E., Osborn, W.R., Yeomans, J.M.: Phys. Rev. E 54(5), 5041 (1996)Google Scholar
  70. 70.
    Langaas, K., Yeomans, J.M.: Eur. Phys. J. B 15, 133 (2000)Google Scholar
  71. 71.
    Léopoldès, J., Dupuis, A., Bucknall, D.G., Yeomans, J.M.: Langmuir 19(23), 9818 (2003)Google Scholar
  72. 72.
    Kuksenok, O., Jasnow, D., Yeomans, J., Balazs, A.C.: Phys. Rev. Lett. 91(10), 108303 (2003)Google Scholar
  73. 73.
    Dupuis, A., Yeomans, J.M.: In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds.) Computational Science - ICCS 2004. Lecture Notes in Computer Science, vol. 3039, pp. 556–563. Springer, Berlin (2004). dx.doi.org/10.1007/b98005. Cond-mat/0401150
  74. 74.
    Dupuis, A., Léopoldes, J., Bucknall, D.G., Yeomans, J.M.: Appl. Phys. Lett. 87(2), 024103 (2005)Google Scholar
  75. 75.
    Dupuis, A., Yeomans, J.M.: Langmuir 21(6), 2624 (2005)Google Scholar
  76. 76.
    Kusumaatmaja, H., Léopoldès, J., Dupuis, A., Yeomans, J.M.: Europhys. Lett. 73(5), 740 (2006)Google Scholar
  77. 77.
    Kusumaatmaja, H., Yeomans, J: Langmuir 23(2), 956 (2007)Google Scholar
  78. 78.
    Kusumaatmaja, H., Yeomans, J.M.: Langmuir 23(11), 6019 (2007)Google Scholar
  79. 79.
    Hyväluoma, J., Harting, J.: Phys. Rev. E 100(24), 246001 (2008)Google Scholar
  80. 80.
    Harting, J., Kunert, C., Hyväluoma, J.: Microfluid Nanofluid 8(1), 1 (2009)Google Scholar
  81. 81.
    Dörfler, F., Rauscher, M., Koplik, J., Harting, J., Dietrich, S.: Soft Matter 8(35), 9221 (2012)Google Scholar
  82. 82.
    Jacqmin, D.: J. Comp. Phys. 155, 96 (1999)Google Scholar
  83. 83.
    Ding, H., Spelt, P.D.M.: Phys. Rev. E 75(4), 046708 (2007)Google Scholar
  84. 84.
    Pismen, L.M., Pomeau, Y.: Phys. Rev. E 62(2), 2480 (2000)Google Scholar
  85. 85.
    Thiele, U., Velarde, M.G., Neuffer, K., Pomeau, Y.: Phys. Rev. E 64(3), 031602 (2001)Google Scholar
  86. 86.
    Thiele, U., Velarde, M.G., Neuffer, K., Bestehorn, M., Pomeau, Y.: Phys. Rev. E 64(6), 061601 (2001)Google Scholar
  87. 87.
    Pismen, L.M.: Phys. Rev. E 64(2), 021603 (2001)Google Scholar
  88. 88.
    Pismen, L.M.: Colloids Surf. A Physicochem. Eng. Aspects 206(1–3), 11 (2002)Google Scholar
  89. 89.
    Dimitrakopoulos, P., Higdon, J.J.L.: J. Fluid Mech. 336, 351 (1997)Google Scholar
  90. 90.
    Dimitrakopoulos, P., Higdon, J.J.L.: J. Fluid Mech. 377, 189 (1998)Google Scholar
  91. 91.
    Dimitrakopoulos, P., Higdon, J.J.L.: J. Fluid Mech. 435, 327 (2001)Google Scholar
  92. 92.
    Dimitrakopoulos, P.: J. Fluid Mech. 580, 451 (2007)Google Scholar
  93. 93.
    Kelmanson, M.A.: J. Comp. Phys. 51, 139 (1983)Google Scholar
  94. 94.
    Mazouchi, A., Gramlich, C.M., Homsy, G.M.: Phys. Fluids 16(5), 1647 (2004)Google Scholar
  95. 95.
    Marconi, U.M.B., Tarazona, P.: J. Chem. Phys. 110(16), 8032 (1999)Google Scholar
  96. 96.
    Marconi, U.M.B., Tarazona, P.: J. Phys. Condens. Matter 12(8A), A413 (2000)Google Scholar
  97. 97.
    Archer, A.J., Rauscher, M.: J. Phys. A Math. Gen. 37(40), 9325 (2004)Google Scholar
  98. 98.
    Archer, A.J.: J. Phys. Condens. Matter 18(24), 5617 (2006)Google Scholar
  99. 99.
    Marconi, U.M.B., Melchionna, S.: J. Chem. Phys. 131(1), 014105 (2009)Google Scholar
  100. 100.
    Green, H.S.: The Molecular Theory of Fluids. North-Holland, Amsterdam (1952)Google Scholar
  101. 101.
    Kreuzer, H.J.: Nonequilibrium Thermodynamics and Its Statistical Foundations. Clarendon, Oxford (1981)Google Scholar
  102. 102.
    Frenkel, D., Smit, B.: Understanding Molecular Simulation, 2nd edn. Academic, San Diego (2002)Google Scholar
  103. 103.
    Yaneva, J., Milchev, A., Binder, K.: J. Chem. Phys. 121(24), 12632 (2004)Google Scholar
  104. 104.
    Cieplak, M., Koplik, J., Banavar, J.R.: Phys. Rev. Lett. 96(11), 114502 (2006)Google Scholar
  105. 105.
    Cottin-Bizonne, C., Barrat, J.L., Bocquet, L., Charlaix, E.: Nat. Mater. 2(4), 237 (2003)Google Scholar
  106. 106.
    Cottin-Bizonne, C., Barentin, C., Charlaix, E., Bocquet, L., Barrat, J.L.: Eur. Phys. J. E 15, 427 (2004)Google Scholar
  107. 107.
    Cao, B.Y., Chen, M., Guo, Z.Y.: Phys. Rev. E 74(6), 066311 (2006)Google Scholar
  108. 108.
    Huang, D.M., Cottin-Bizonne, C., Ybert, C., Bocquet, L.: Phys. Rev. Lett. 06, 064503 (2008)Google Scholar
  109. 109.
    Moosavi, A., Rauscher, M., Dietrich, S.: Phys. Rev. Lett. 97(23), 236101 (2006)Google Scholar
  110. 110.
    Ehrlich, G., Hudda, F.G.: J. Chem. Phys. 44(3), 1039 (1966)Google Scholar
  111. 111.
    Schwoebel, R.L., Shipsey, E.J.: J. Appl. Phys. 37(10), 3682 (1966)Google Scholar
  112. 112.
    Dutka, F., Napiórkowski, M., Dietrich, S.: J. Chem. Phys. 136(6), 064702 (2012)Google Scholar
  113. 113.
    Ondarçuhu, T., Piednoir, A.: Nano Lett. 5(9), 1744 (2005)Google Scholar
  114. 114.
    Moosavi, A., Rauscher, M., Dietrich, S.: Langmuir 24(3), 734 (2008)Google Scholar
  115. 115.
    Moosavi, A., Rauscher, M., Dietrich, S.: J. Chem. Phys. 129(4), 044706 (2008)Google Scholar
  116. 116.
    Hu, J., Xiao, X.D., Salmeron, M.: Appl. Phys. Lett. 67(4), 476 (1995)Google Scholar
  117. 117.
    Hu, J., Carpick, R.W., Salmeron, M., Xiao, X.D.: J. Vac. Sci. Tech. B 14(2), 1341 (1996)Google Scholar
  118. 118.
    Checco, A., Gang, O., Ocko, B.M.: Phys. Rev. Lett. 96(5), 056104 (2006)Google Scholar
  119. 119.
    Checco, A., Schollmeyer, H., Daillant, J., Guenoun, P., Boukherroub, R.: Langmuir 22(1), 116 (2006)Google Scholar
  120. 120.
    Checco, A.: Phys. Rev. Lett. 102(10), 106103 (2009)Google Scholar
  121. 121.
    Fang, A., Dujardin, E., Ondarçuhu, T.: Nano Lett. 6(10), 2368 (2006)Google Scholar
  122. 122.
    Fabi/’e, L., Ondarçuhu, T.: Soft Matter 8(18), 4995 (2012)Google Scholar
  123. 123.
    Burmeister, F., Badowsky, W., Braun, T., Wieprich, S., Boneberg, J., Leiderer, P.: Appl. Surf. Sci. 144–145, 461 (1999)Google Scholar
  124. 124.
    Habenicht, A., Olapinski, M., Burmeister, F., Leiderer, P., Boneberg, J.: Science 309(5743), 2043 (2005)Google Scholar
  125. 125.
    Boneberg, J., Habenicht, A., Benner, D., Leiderer, P., Trautvetter, M., Pfahler, C., Plettl, A., Ziemann, P.: Appl. Phys. A 93(2), 415 (2008)Google Scholar
  126. 126.
    Stokes, D.J.: Adv. Eng. Mater. 3(2), 126 (2001)Google Scholar
  127. 127.
    Yoon, B., Luedtke, W.D., Gao, J., Landman, U.: J. Phys. Chem. B 107(24), 5882 (2003)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Max-Planck-Institut für Intelligente SystemeStuttgartGermany
  2. 2.Institut für Theoretische Physik IVStuttgartGermany

Personalised recommendations