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Colloidal Hydrodynamics and Interfacial Effects

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Book cover Soft Matter at Aqueous Interfaces

Part of the book series: Lecture Notes in Physics ((LNP,volume 917))

Abstract

Interfaces and boundaries play an important role in numerous soft matter and biological systems. Apart from direct interactions, the boundaries interact with suspended microparticles by altering the solvent flow field in their vicinity. Hydrodynamic interactions with walls and liquid interfaces may lead to a significant change in the particle dynamics in (partially) confined geometry. In these lecture notes we review the basic concepts related to colloidal hydrodynamics and discuss in more detail the effects of geometric confinement and the hydrodynamic boundary conditions which an interface imposes on a suspension of microparticles. We start with considering the general characteristic features of low-Reynolds-number flows, which are an inherent part of any colloidal system, and discuss the appropriate boundary conditions for various types of interfaces. We then proceed to develop a proper theoretical description of the friction-dominated, inertia-free dynamics of colloidal particles. To this end, we introduce the concept of hydrodynamic mobility, and analyse the solutions of the Stokes equations for a single spherical particle in the bulk and in the presence of a planar solid-fluid, and fluid-fluid interfaces. Both forced and phoretic motions are considered, with a particular emphasis on the principles of electrophoresis and the associated fluid flows. Moreover, we discuss the hydrodynamic interactions of self-propelling microswimmers, and the peculiar motion of bacteria attracted to slip and no-slip walls.

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References

  1. J.K.G. Dhont, An Introduction to Dynamics of Colloids. Elsevier, Amsterdam (1996)

    Google Scholar 

  2. P. Szymczak, M. Cieplak, J. Phys. Condens. Matter. 23, 033102 (2011)

    Article  ADS  Google Scholar 

  3. R.G. Larson, J.J. Magda, Macromolecules 22, 3004 (1989)

    Article  ADS  Google Scholar 

  4. H. Tanaka, J. Phys.: Condens. Matter 13, 4637 (2001)

    ADS  Google Scholar 

  5. P. Wojtaszczyk, J.B. Avalos, Phys. Rev. Lett. 80, 754 (1998)

    Article  ADS  Google Scholar 

  6. C. Korn, U.S. Schwarz, Phys. Rev. Lett. 97, 138103 (2006)

    Article  ADS  Google Scholar 

  7. O.B. Usta, J.E. Butler, A.J.C. Ladd, Phys. Fluids 18, 031703 (2006)

    Article  ADS  Google Scholar 

  8. E. Guazzelli, J.F. Morris, A Physical Introduction to Suspension Dynamics (Cambridge University Press, Cambridge, 2012)

    MATH  Google Scholar 

  9. G. Nägele, Colloidal Hydrodynamics, in Physics of Complex Colloids, ed. by C. Bechinger, F. Sciortino, P. Ziherl. Proceedings of the International School of Physics “Enrico Fermi”, vol. 184 (IOS Press, Amsterdam; SIF, Bologna, 2012), p. 451

    Google Scholar 

  10. G. Nägele, Dynamics of charged-particles dispersions, in Proceedings of the 5th Warsaw School of Statistical Physics (Warsaw University Press, 2014), p. 83

    Google Scholar 

  11. E.J. Hinch, Hydrodynamics at low Reynolds numbers: A brief and elementary introduction, in Disorder and Mixing, vol. 2, ed. by E. Guyon, J.-P. Nadal, Y. Pomeau (Springer, Dordrecht, 1988), pp. 43–55

    Google Scholar 

  12. P.N. Pusey, Colloidal suspensions, in Liquids, Freezing and Glass Transition, ed. by J.P. Hansen, D. Levesque, J. Zinn-Justin (Elsevier, Amsterdam, 1991), p. 763

    Google Scholar 

  13. R.B. Jones, P.N. Pusey, Annu. Rev. Phys. Chem. 42, 137 (1991)

    Article  ADS  Google Scholar 

  14. S. Kim, S.J. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworth-Heinemann, Boston, 1991)

    Google Scholar 

  15. J. Happel, H. Brenner, Low Reynolds Numbers Hydrodynamics (Kluwer, Dordrecht, 1991)

    MATH  Google Scholar 

  16. Z. Zapryanov, S. Tabakova, Dynamics of Bubbles, Drops and Rigid Particles, Fluid Mechanics and Its Applications (Springer, Dordrecht, 2011)

    MATH  Google Scholar 

  17. G.K. Batchelor, An Introduction to Fluid Dynamics. Cambridge Mathematical Library (Cambridge University Press, Cambridge, 2000)

    Google Scholar 

  18. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics (Pergamon Press, London, 1987)

    Google Scholar 

  19. E. Guyon, J.P. Hulin, L. Petit, Physical Hydrodynamics (Oxford University Press, Oxford, 2001)

    MATH  Google Scholar 

  20. G.I. Taylor, Low Reynolds Number Flows. National Committe For Fluid Mechanics Films (1996), http://web.mit.edu/hml/ncfmf.html

  21. W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 1989)

    Book  Google Scholar 

  22. E. Lauga, M.P. Brenner, H.A. Stone, The no-slip boundary condition, in Springer Handbook of Experimental Fluid Mechanics, ed. by C. Tropea, A. Yarin, J.F. Foss (Springer, Berlin, 2007

    Google Scholar 

  23. L.G. Leal, Laminar Flow and Convective Transport Processes (Butterworth-Heinemann, Boston, 1992

    Google Scholar 

  24. N. Lecoq, R. Anthore, B. Cichocki, P. Szymczak, F. Feuillebois, J. Fluid Mech. 513, 247 (2004)

    Article  ADS  Google Scholar 

  25. R. Tuinier, T. Taniguchi, J. Phys.: Condens. Matter 17, L9 (2005)

    ADS  Google Scholar 

  26. D. Lopez, E. Lauga, Phys. Fluids 26, 071902 (2014)

    Article  ADS  Google Scholar 

  27. K.H. Lan, N. Ostrowsky, D. Sornette, Phys. Rev. Lett. 57, 17 (1986)

    Article  ADS  Google Scholar 

  28. B. Cichocki, M.L. Ekiel-Jezewska, E. Wajnryb, J. Chem. Phys. 136, 071102 (2012)

    Article  ADS  Google Scholar 

  29. J.F. Brady, G. Bossis, Annu. Rev. Fluid Mech. 20, 111 (1988)

    Article  ADS  Google Scholar 

  30. I.M. Jánosi, T. Tél, D.E. Wolf, J.A.C. Gallas, Phys. Rev. E 56, 2858 (1997)

    Article  ADS  Google Scholar 

  31. M.L. Ekiel-Jeżewska, E. Wajnryb, Phys. Rev. E 83, 067301 (2011)

    Article  ADS  Google Scholar 

  32. D.L. Ermak, J.A. McCammon, J. Chem. Phys. 69, 1352 (1978)

    Article  ADS  Google Scholar 

  33. G. Nägele, Brownian Dynamics simulations, in Computational Condensed Matter Physics, vol. 32 (Forschungszentrum Jülich Publishing, 37th IFF Spring School edition, 2006)

    Google Scholar 

  34. A.T. Chwang, T. Wu, J. Fluid Mech. 67, 787 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  35. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, 1992)

    Book  MATH  Google Scholar 

  36. J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1998

    Google Scholar 

  37. B. Cichocki, B.U. Felderhof, K. Hinsen, J. Chem. Phys. 100, 3780 (1994)

    Article  ADS  Google Scholar 

  38. M.L. Ekiel-Jeżewska, E. Wajnryb, Precise multipole method for calculating hydrodynamic interactions between spherical particles in the stokes flow, in Theoretical Methods for Micro Scale Viscous Flows, ed. by F. Feuillebois, A. Sellier (2009), pp. 127–172

    Google Scholar 

  39. M. Lisicki, arXiv:1312.6231 [physics.flu-dyn] (2013)

    Google Scholar 

  40. L.G. Leal, Annu. Rev. Fluid Mech. 12, 435 (1980)

    Article  ADS  Google Scholar 

  41. S.E. Spagnolie, E. Lauga, J. Fluid Mech. 700, 105 (2012)

    Article  MathSciNet  Google Scholar 

  42. H. Luo, C. Pozrikidis, J. Eng. Math. 62, 1 (2007)

    Article  Google Scholar 

  43. G.K. Batchelor, J. Fluid Mech. 44, 419 (1970)

    Article  ADS  MathSciNet  Google Scholar 

  44. M.M. Tirado, C.L. Martinez, J.G. de la Torre, J. Chem. Phys. 81, 2047 (1984)

    Article  ADS  Google Scholar 

  45. R.G. Cox, J. Fluid Mech. 44, 791 (1970)

    Article  ADS  Google Scholar 

  46. J.B. Keller, S.I. Rubinow, J. Fluid Mech. 75, 705 (1976)

    Article  ADS  Google Scholar 

  47. G.G. Stokes, Trans. Camb. Philos. Soc. 9, 8 (1851)

    ADS  Google Scholar 

  48. J.L. Anderson, Annu. Rev. Fluid Mech. 21, 61 (1989)

    Article  ADS  Google Scholar 

  49. J.H. Masliyah, S. Bhattacharjee, Electrokinetic and Colloid Transport Phenomena (Wiley, New York, 2006

    Google Scholar 

  50. H.J. Keh, J.L. Anderson, J. Fluid Mech. 153, 417 (1985)

    Article  ADS  Google Scholar 

  51. A.S. Khair, T.M. Squires, Phys. Fluids 21, 042001 (2009)

    Article  ADS  Google Scholar 

  52. R. Golestanian, T.B. Liverpool, A. Ajdari, New J. Phys. 9, 126 (2007)

    Article  ADS  Google Scholar 

  53. H.A. Stone, A.D. Samuel, Phys. Rev. Lett. 77, 4102 (1996)

    Article  ADS  Google Scholar 

  54. C. Contreras-Aburto, G. Nägele, J. Chem. Phys. 139, 134110 (2013)

    Article  ADS  Google Scholar 

  55. F. Weinert, D. Braun, Phys. Rev. Lett. 101, 168301 (2008)

    Article  ADS  Google Scholar 

  56. J. Rotne, S. Prager, J. Chem. Phys. 50, 4831 (1969)

    Article  ADS  Google Scholar 

  57. H. Yamakawa, J. Chem. Phys. 53, 436 (1970)

    Article  ADS  Google Scholar 

  58. E. Wajnryb, K.A. Mizerski, P.J. Zuk, P. Szymczak, J. Fluid Mech. 731, R3 (2013)

    Article  ADS  Google Scholar 

  59. R. Courant, D. Hilbert, Methods of Mathematical Physics II (Interscience, New York, 1962)

    MATH  Google Scholar 

  60. F.M. Weinert, D. Braun, Phys. Rev. Lett. 101, 168301 (2008)

    Article  ADS  Google Scholar 

  61. P.J. Zuk, E. Wajnryb, K.A. Mizerski, P. Szymczak, J. Fluid Mech. 741, R5 (2014)

    Article  ADS  Google Scholar 

  62. B. Carrasco, J. Garcia de la Torre, Biophys. J. 76, 3044 (1999)

    Article  Google Scholar 

  63. B. Cichocki, R.B. Jones, R. Kutteh, E. Wajnryb, J. Chem. Phys. 112, 2548 (2000)

    Article  ADS  Google Scholar 

  64. S. Bhattacharya, J. Blawzdziewicz, E. Wajnryb, Physica A 356, 294 (2005)

    Google Scholar 

  65. M. Kedzierski, E. Wajnryb, J. Chem. Phys. 133, 154105 (2010)

    Article  ADS  Google Scholar 

  66. D.J. Acheson, Elementary Fluid Dynamics (Oxford University Press, Oxford, 1990)

    MATH  Google Scholar 

  67. D.J. Jeffrey, Y. Onishi, J. Fluid Mech. 139, 261 (1984)

    Article  ADS  Google Scholar 

  68. R. Tadmor, J. Phys.: Condens. Matter 13, L195 (2001)

    ADS  Google Scholar 

  69. M.L. Ekiel-Jeżewska, R. Boniecki, Stokes Flow generated by a point force in various geometries II. Velocity field, Technical report, IFTR. Polish Acad. Sci. (2010)

    Google Scholar 

  70. B. Cichocki, M.L. Ekiel-Jeżewska, G. Nägele, E. Wajnryb, J. Chem. Phys. 121, 2305 (2004)

    Article  ADS  Google Scholar 

  71. J. Blake, Proc. Camb. Philos. Soc. 70, 303 (1971)

    Article  ADS  Google Scholar 

  72. K. Aderogba, J.R. Blake, Bull. Aust. Math. Soc. 18, 345 (1978)

    Article  Google Scholar 

  73. J. Blake, A. Chwang, J. Eng. Math. 8, 23 (1974)

    Article  Google Scholar 

  74. E. Lauga, T.M. Squires, Phys. Fluids 17, 103102 (2005)

    Article  ADS  Google Scholar 

  75. M. Lisicki, B. Cichocki, S.A. Rogers, J.K.G. Dhont, P.R. Lang, Soft Matter 10, 4312 (2014)

    Article  ADS  Google Scholar 

  76. B. Cichocki, R.B. Jones, Phys. A 258, 273 (1998)

    Article  Google Scholar 

  77. H.A. Lorentz, Abhandlung über Theoretische Physik (B. G. Teubner, Leipzig, 1907)

    Google Scholar 

  78. H. Faxén, Ark. Mat. Astron. Fys. 17, 1 (1923)

    Google Scholar 

  79. H. Brenner, Chem. Eng. Sci. 16, 242 (1961)

    Article  Google Scholar 

  80. A.J. Goldman, R.G. Cox, H. Brenner, Chem. Eng. Sci. 22, 637 (1967)

    Article  Google Scholar 

  81. A.J. Goldman, R.G. Cox, H. Brenner, Chem. Eng. Sci. 22, 653 (1967)

    Article  Google Scholar 

  82. W. Dean, M. O’Neill, Mathematika 10, 13 (1963)

    Article  MathSciNet  Google Scholar 

  83. W. Dean, M. O’Neill, Mathematika 11, 67 (1964)

    Article  MathSciNet  Google Scholar 

  84. R.B. Jones, J. Chem. Phys. 123, 164705 (2005)

    Article  ADS  Google Scholar 

  85. B. Lin, J. Yu, S. Rice, Phys. Rev. E 62, 3909 (2000)

    Article  ADS  Google Scholar 

  86. R. Sadr, C. Hohenegger, H. Li, P.J. Mucha, M. Yoda, J. Fluid Mech. 577, 443 (2007)

    Article  ADS  Google Scholar 

  87. P. Huang, K. Breuer, Phys. Rev. E 76, 046307 (2007)

    Article  ADS  Google Scholar 

  88. L. Lobry, N. Ostrowsky, Phys. Rev. B 53, 12050 (1996)

    Article  ADS  Google Scholar 

  89. K. Ishii, T. Iwai, H. Xia, Opt. Express 18, 7390 (2010)

    Article  ADS  Google Scholar 

  90. M.A. Plum, W. Steffen, G. Fytas, W. Knoll, B. Menges, Opt. Express 17, 10364 (2009)

    Article  ADS  Google Scholar 

  91. M.A. Plum, J. Rička, H.-J. Butt, W. Steffen, New J. Phys. 12, 103022 (2010)

    Article  ADS  Google Scholar 

  92. P. Holmqvist, J.K.G. Dhont, P.R. Lang, Phys. Rev. E 74, 021402 (2006)

    Article  ADS  Google Scholar 

  93. P. Holmqvist, J.K.G. Dhont, P.R. Lang, J. Chem. Phys. 126, 044707 (2007)

    Article  ADS  Google Scholar 

  94. M. Hosoda, K. Sakai, K. Takagi, Phys. Rev. E 58, 6275 (1998)

    Article  ADS  Google Scholar 

  95. M. Lisicki, B. Cichocki, J.K.G. Dhont, P.R. Lang, J. Chem. Phys. 136, 204704 (2012)

    Article  ADS  Google Scholar 

  96. S.A. Rogers, M. Lisicki, B. Cichocki, J.K.G. Dhont, P.R. Lang, Phys. Rev. Lett. 109, 098305 (2012)

    Article  ADS  Google Scholar 

  97. B.J. Berne, R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics. Dover Books on Physics Series (Dover Publications, Mineola, 2000

    Google Scholar 

  98. R. Sigel, Curr. Opin. Colloid Interface Sci. 14, 426 (2009)

    Article  Google Scholar 

  99. G. Nägele, Phys. Rep. 272, 215 (1996)

    Article  ADS  Google Scholar 

  100. B. Cichocki, M.L. Ekiel-Jeżewska, E. Wajnryb, J. Chem. Phys. 140, 164902 (2014)

    Article  ADS  Google Scholar 

  101. W.B. Russel, E.J. Hinch, L.G. Leal, G. Tieffenbruck, J. Fluid Mech. 83, 273 (1977)

    Article  ADS  Google Scholar 

  102. S.-M. Yang, L.G. Leal, J. Fluid Mech. 136, 393 (1983)

    Article  ADS  Google Scholar 

  103. E.P. Ascoli, D.S. Dandy, L.G. Leal, J. Fluid Mech. 213, 287 (1990)

    Article  ADS  Google Scholar 

  104. I. Cantat, C. Misbah, Phys. Rev. Lett. 83, 880 (1999)

    Article  ADS  Google Scholar 

  105. U.S. Agarwal, A. Dutta, R.A. Mashelkar, Chem. Eng. Sci. 49, 1693 (1994)

    Article  Google Scholar 

  106. C. Berdan, L.G. Leal, J. Colloid Interface Sci. 87, 62 (1982)

    Article  Google Scholar 

  107. R. Trouilloud, T. Yu, A. Hosoi, E. Lauga, Phys. Rev. Lett. 101, 048102 (2008)

    Article  ADS  Google Scholar 

  108. E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)

    Article  ADS  Google Scholar 

  109. J. Elgeti, R.G. Winkler, G. Gompper, Rep. Prog. Phys. 78, 056601 (2015)

    Google Scholar 

  110. J. Lighthill, Mathematical Biofluiddynamics (SIAM, Philadelphia, 1975)

    Book  MATH  Google Scholar 

  111. E.M. Purcell, Am. J. Phys. 45, 3 (1977)

    Article  ADS  Google Scholar 

  112. J.W. Swan, J.F. Brady, R.S. Moore, Phys. Fluids 23, 071901 (2011)

    Article  ADS  Google Scholar 

  113. A.P. Berke, L. Turner, H.C. Berg, E. Lauga, Phys. Rev. Lett. 101, 038102 (2008)

    Article  ADS  Google Scholar 

  114. E. Lauga, W.R. DiLuzio, G.M. Whitesides, H.A. Stone, Biophys. J. 90, 400 (2006)

    Article  ADS  Google Scholar 

  115. R. Di Leonardo, D. Dell’Arciprete, L. Angelani, V. Iebba, Phys. Rev. Lett. 038101 (2011)

    Google Scholar 

  116. P.P. Lele, J.W. Swan, J.F. Brady, N.J. Wagner, E.M. Furst, Soft Matter 7, 6844 (2011)

    Article  ADS  Google Scholar 

  117. T. Squires, M. Brenner, Phys. Rev. Lett. 85, 4976 (2000)

    Article  ADS  Google Scholar 

  118. T.M. Squires, J. Fluid Mech. 443, 403 (2001)

    Article  ADS  Google Scholar 

  119. R. Di Leonardo, F. Ianni, G. Ruocco, Langmuir 25, 4247 (2009)

    Article  Google Scholar 

  120. J. Morthomas, A. Würger, Phys. Rev. E 81, 051405 (2010)

    Article  ADS  Google Scholar 

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Acknowledgments

These notes include and complement material which was presented in August 2014 at the SOMATAI summer school in Berlin, and in March 2014 at the SOMATAI workshop in Jülich. It is our pleasure to thank the organizers of these events, and here in particular Peter Lang (ICS-3, FZ Jülich), for having invited us to present a lecture on the colloidal hydrodynamics of microparticles and associated interfacial effects. We thank Maria Ekiel-Jeżewska (Polish Academy of Sciences, Warsaw) for having provided us with the streamlines figures of a point force near a planar interface, and Jonas Riest and Rafael Roa (ICS-3, FZ Jülich) and Roland Winkler (IAS-2, FZ Jülich) for helpful discussions. Moreover, we are grateful to Ulrike Nägele (FZ Jülich, ICS-3) for her help with travel and accommodation.

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Authors and Affiliations

  1. Faculty of Physics, Institute of Theoretical Physics, University of Warsaw, Warsaw, Poland

    Maciej Lisicki

  2. Institute for Complex Systems ICS-3, Forschungszentrum Jülich, and Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, Jülich, Germany

    Gerhard Nägele

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  1. Maciej Lisicki
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Correspondence to Maciej Lisicki .

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Editors and Affiliations

  1. Forschungszentrum Jülich, Juelich, Germany

    Peter Lang

  2. Forschungszentrum Juelich GmbH, Juelich, Germany

    Yi Liu

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Lisicki, M., Nägele, G. (2016). Colloidal Hydrodynamics and Interfacial Effects. In: Lang, P., Liu, Y. (eds) Soft Matter at Aqueous Interfaces. Lecture Notes in Physics, vol 917. Springer, Cham. https://doi.org/10.1007/978-3-319-24502-7_10

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