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Numerical simulations of complex fluid-fluid interface dynamics

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Abstract

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually deformable and their shapes are not known a priori. Since experiments do not provide access to all observables of interest, computer simulations pose attractive alternatives to gain insight into the physics of interfaces. In the present article, we restrict ourselves to systems with dimensions comparable to the lateral interface extensions. We provide a critical discussion of three numerical schemes coupled to the lattice Boltzmann method as a solver for the hydrodynamics of the problem: (a) the immersed boundary method for the simulation of vesicles and capsules, the Shan-Chen pseudopotential approach for multi-component fluids in combination with (b) an additional advection-diffusion component for surfactant modelling and (c) a molecular dynamics algorithm for the simulation of nanoparticles acting as emulsifiers.

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References

  1. U. Seifert, Adv. Phys. 46, 13 (1997)

    Article  ADS  Google Scholar 

  2. C. Pozrikidis (ed.), Modeling and Simulation of Capsules and Biological Cells (Chapman & Hall/CRC Mathematical Biology and Medicine Series, 2003)

  3. G. Gompper, M. Schick, Self-assembling amphiphilic systems, Vol. 16 (Academic Press, 1994)

  4. S. Suresh, J. Spatz, J. Mills, A. Micoulet, M. Dao, C. Lim, M. Beil, M. Seufferlein, Acta Biomaterialia 1, 15 (2005)

    Article  Google Scholar 

  5. L. Battaglia, M. Gallarate, Expert Opinion Drug Delivery 9, 497 (2012)

    Article  Google Scholar 

  6. D. Fedosov, W. Pan, B. Caswell, G. Gompper, G. Karniadakis, P. Natl. Acad. Sci. 108, 11772 (2011)

    Article  Google Scholar 

  7. H. Hou, A. Bhagat, A. Chong, P. Mao, K. Tan, J. Han, C. Lim, Lab Chip 10, 2605 (2010)

    Article  Google Scholar 

  8. H. Silva, M. Cerqueira, A. Vicente, Food Bioproc. Technol. 1 (2011)

  9. C. Puglia, F. Bonina, Exp. Opinion Drug Delivery 9, 429 (2012)

    Article  Google Scholar 

  10. G. Hirasaki, C. Miller, M. Puerto, SPE J. 16, 889 (2011)

    Google Scholar 

  11. S. Jafari, E. Assadpoor, Y. He, B. Bhandari, Food Hydrocoll. 22, 1191 (2008)

    Article  Google Scholar 

  12. J. Harting, M. Harvey, J. Chin, M. Venturoli, P. V. Coveney, Phil. Trans. R. Soc. Lond. A 363 1895 (2005)

    Article  ADS  Google Scholar 

  13. J. Harting, M. Harvey, J. Chin, P.V. Coveney, Comp. Phys. Comm. 165, 97 (2004)

    Article  ADS  Google Scholar 

  14. R. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, 1999)

  15. B. Binks, Cur. Opin. Colloid Interface Sci. 7, 21 (2002)

    Article  Google Scholar 

  16. S. Tcholakova, N. Denkov, A. Lips, Phys. Chem. Chem. Phys. 10, 1608 (2008)

    Article  Google Scholar 

  17. S. Frijters, F. Günther, J. Harting, Soft Matter 8, 6542 (2012)

    Article  Google Scholar 

  18. W. Ramsden, Proc. R. Soc. London 72, 156 (1903)

    Article  Google Scholar 

  19. S. Pickering, J. Chem. Soc., Trans. 91, 2001 (1907)

    Article  Google Scholar 

  20. K. Stratford, R. Adhikari, I. Pagonabarraga, J. Desplat, M. Cates, Science 309, 2198 (2005)

    Article  ADS  Google Scholar 

  21. E. Herzig, K. White, A. Schofield, W. Poon, P. Clegg, Nature Materials 6, 966 (2007)

    Article  ADS  Google Scholar 

  22. E. Kim, K. Stratford, M. Cates, Langmuir 26, 7928 (2010)

    Article  Google Scholar 

  23. B. Binks, P. Fletcher, Langmuir 17, 4708 (2001)

    Article  Google Scholar 

  24. L. Sagis, Rev. Mod. Phys. 83, 1367 (2011)

    Article  ADS  Google Scholar 

  25. D. Barthès-Biesel, J. Rallison, J. Fluid Mech. 113, 251 (1981)

    Article  ADS  MATH  Google Scholar 

  26. E. Wetzel, J. Fluid Mech. 426, 199 (2001)

    Article  ADS  MATH  Google Scholar 

  27. S. Succi, The Lattice Boltzmann Equation (Oxford University Press, Oxford, UK, 2001)

  28. R. Benzi, M. Bernaschi, M. Sbragaglia, S. Succi, Europhys. Lett. 91, 14003 (2010)

    Article  ADS  Google Scholar 

  29. R. Pal, Curr. Opin. Colloid In. 16, 41 (2011)

    Article  Google Scholar 

  30. M. Sukop, D. Thorne, Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers (Springer, Berlin, Germany, 2006)

  31. M. Sukop, D. Thorne, Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers (Springer, Berlin, Germany, 2006)

  32. C. Aidun, J. Clausen, Annu. Rev. Fluid Mech 42, 439 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  33. Y.-H. Qian, D. d’Humières, P. Lallemand, Europhys. Lett. 17, 479 (1992)

    Article  ADS  MATH  Google Scholar 

  34. X. Shan, H. Chen, Phys. Rev. E 47, 1815 (1993)

    Article  ADS  Google Scholar 

  35. X. Shan, H. Chen, Phys. Rev. E 49, 2941 (1994)

    Article  ADS  Google Scholar 

  36. E. Orlandini, M.R. Swift, J.M. Yeomans, Europhys. Lett. 32, 463 (1995)

    Article  ADS  Google Scholar 

  37. M.R. Swift, E. Orlandini, W.R. Osborn, J.M. Yeomans, Phys. Rev. E 54, 5041 (1996)

    Article  ADS  Google Scholar 

  38. M. Dupin, I. Halliday, C. Care, J. Phys. A: Math. Gen. 36, 8517 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. S. Lishchuk, C. Care, I. Halliday, Phys. Rev. E 67, 036701 (2003)

    Article  ADS  Google Scholar 

  40. C. Peskin, Acta Numerica 11, 479 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  41. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, Y.-J. Jan, J. Comput. Phys. 169, 708 (2001)

    Article  ADS  MATH  Google Scholar 

  42. T. Krüger, F. Varnik, D. Raabe, Comput. Math. Appl. 61, 3485 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  43. S. Chen, T. Lookman, J. Stat. Phys. 81, 223 (1995)

    Article  ADS  MATH  Google Scholar 

  44. H. Chen, B. Boghosian, P. Coveney, M. Nekovee, Proc. R. Soc. Lond. A 456, 2043 (2000)

    Article  ADS  MATH  Google Scholar 

  45. M. Nekovee, P. Coveney, H. Chen, B. Boghosian, Phys. Rev. E 62, 8282 (2000)

    Article  ADS  Google Scholar 

  46. K. Furtado, R. Skartlien, Phys. Rev. E 81, 066704 (2010)

    Article  ADS  Google Scholar 

  47. A. Lamura, G. Gonnella, J.M. Yeomans, Europhys. Lett. 45, 314 (1999)

    Article  ADS  Google Scholar 

  48. R. Benzi, S. Chibbaro, S. Succi, Phys. Rev. Lett. 102, 026002 (2009)

    Article  ADS  Google Scholar 

  49. R. Benzi, M. Sbragaglia, S. Succi, M. Bernaschi, S. Chibbaro, J. Chem. Phys. 131, 104903 (2009)

    Article  ADS  Google Scholar 

  50. F. Jansen, J. Harting, Phys. Rev. E 83, 046707 (2011)

    Article  ADS  Google Scholar 

  51. F. Günther, F. Janoschek, S. Frijters, J. Harting, Comput. Fluids (2012)

  52. A. Joshi, Y. Sun, Phys. Rev. E 82, 041401 (2010)

    Article  ADS  Google Scholar 

  53. A. Joshi, Y. Sun, Phys. Rev. E 79, 066703 (2009)

    Article  ADS  Google Scholar 

  54. A. Ladd, R. Verberg, J. Stat. Phys 104, 1191 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  55. N.-Q. Nguyen, A. Ladd, Phys. Rev. E 66, 046708 (2002)

    Article  ADS  Google Scholar 

  56. H. Hertz. Über die Berührung fester elastischer Körper, J. Reine Ang. Math. 92, 156 (1881)

    Google Scholar 

  57. B. Berne, P. Pechukas, J. Chem. Phys. 56, 4213 (1972)

    Article  ADS  Google Scholar 

  58. S. Keller, R. Skalak, J. Fluid Mech. 120, 27 (1982)

    Article  ADS  MATH  Google Scholar 

  59. M. Mader, V. Vitkova, M. Abkarian, A. Viallat, T. Podgorski, Eur. Phys. J. E. 19, 389397 (2006)

    Article  Google Scholar 

  60. V. Kantsler, V. Steinberg, Phys. Rev. Lett 96, 036001 (2006)

    Article  ADS  Google Scholar 

  61. B. Kaoui, J. Harting, C. Misbah, Phys. Rev. E 83, 066319 (2011)

    Article  ADS  Google Scholar 

  62. B. Kaoui, T. Krüger, J. Harting, Soft Matter, doi:10.1039/C2SM26289D (2012)

  63. B. Kaoui, G. Ristow, I. Cantat, C. Misbah, W. Zimmermann, Phys. Rev. E 77, 021903 (2008)

    Article  ADS  Google Scholar 

  64. T. Geislinger, B. Eggart, S. Braunmüller, L. Schmid, T. Franke, Appl. Phys. Lett. 100, 183701 (2012)

    Article  ADS  Google Scholar 

  65. T. Krüger, F. Varnik, D. Raabe, Phil. Trans. R. Soc. Lond. A 369, 2414 (2011)

    Article  ADS  MATH  Google Scholar 

  66. R.S. Saksena, P.V, J. Phys. Chem. B 112, 2950 (2008)

    Article  Google Scholar 

  67. N. González-Segredo, M. Nekovee, P.V. Coveney, Phys. Rev. E 67, 046304 (2003)

    Article  ADS  Google Scholar 

  68. G. Giupponi, J. Harting, P.V. Coveney, Europhys. Lett. 73, 533 (2006)

    Article  ADS  Google Scholar 

  69. A.N. Emerton, P.V. Coveney, B.M. Boghosian, Phys. Rev. E 56, 1286 (1997)

    Article  ADS  Google Scholar 

  70. N. González-Segredo, P.V. Coveney, Phys. Rev. E 69, 061501 (2004)

    Article  ADS  Google Scholar 

  71. J. Harting, G. Giupponi, P.V. Coveney, Phys. Rev. E 75, 041504 (2007)

    Article  ADS  Google Scholar 

  72. N. González-Segredo, P.V, Europhys. Lett. 65, 795 (2004)

    Article  ADS  Google Scholar 

  73. P.J.F. Gandy, J. Klinowski, Chem. Phys. Lett. 321, 363 (2000)

    Article  ADS  Google Scholar 

  74. K. Große-Brauckmann, Exp. Math. 6, 33 (1997)

    Article  MATH  Google Scholar 

  75. V.Z.H. Chan, J. Hoffman, V.Y. Lee, H. Iatrou, A. Avgeropoulos, N. Hadjichristidis, R.D. Miller, E.L. Thomas, Science 286, 1716 (1999)

    Article  Google Scholar 

  76. R.S. Saksena, P.V. Coveney, Soft Matter 5, 4446 (2009)

    Article  ADS  Google Scholar 

  77. A. Ghosh, J. Harting, M. van Hecke, A. Siemens, B. Kaoui, V. Koning, K. Langner, I. Niessen, J.P. Rojas, S. Stoyanov, M. Dijkstra, Proceedings of the Workshop Physics with Industry (Leiden, The Netherlands, October 17-21, 2011). Stichting FOM, 2011

  78. C. Zeng, F. Brau, B. Davidovitch, A.D. Dinsmore, Soft Matter 8, 8582 (2012)

    Article  ADS  Google Scholar 

  79. A. Lees, S. Edwards, J. Phys. C. 5, 1921 (1972)

    Article  ADS  Google Scholar 

  80. A. Wagner, I. Pagonabarraga, J. Stat. Phys. 107, 521 (2002)

    Article  MATH  Google Scholar 

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Correspondence to T. Krüger, S. Frijters, F. Günther, B. Kaoui or J. Harting.

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Krüger, T., Frijters, S., Günther, F. et al. Numerical simulations of complex fluid-fluid interface dynamics. Eur. Phys. J. Spec. Top. 222, 177–198 (2013). https://doi.org/10.1140/epjst/e2013-01834-y

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  • DOI: https://doi.org/10.1140/epjst/e2013-01834-y

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