Steady moving contact line of water over a no-slip substrate

Challenges in benchmarking phase-field and volume-of-fluid methods against molecular dynamics simulations

Abstract

The movement of the triple contact line plays a crucial role in many applications such as ink-jet printing, liquid coating and drainage (imbibition) in porous media. To design accurate computational tools for these applications, predictive models of the moving contact line are needed. However, the basic mechanisms responsible for movement of the triple contact line are not well understood but still debated. We investigate the movement of the contact line between water, vapour and a silica-like solid surface under steady conditions in low capillary number regime. We use molecular dynamics (MD) with an atomistic water model to simulate a nanoscopic drop between two moving plates. We include hydrogen bonding between the water molecules and the solid substrate, which leads to a sub-molecular slip length. We benchmark two continuum methods, the Cahn–Hilliard phase-field (PF) model and a volume-of-fluid (VOF) model, against MD results. We show that both continuum models reproduce the statistical measures obtained from MD reasonably well, with a trade-off in accuracy. We demonstrate the importance of the phase-field mobility parameter and the local slip length in accurately modelling the moving contact line.

References

  1. 1.

    C. Huh, L.E. Scriven, J. Colloid Interf. Sci. 35, 85 (1971)

    ADS  Google Scholar 

  2. 2.

    D. Bonn, J. Eggers, J. Indekeu, J. Meunier, E. Rolley, Rev. Mod. Phys. 81, 739 (2009)

    ADS  Google Scholar 

  3. 3.

    J.H. Snoeijer, B. Andreotti, Annu. Rev. Fluid Mech. 45, 269 (2013)

    ADS  Google Scholar 

  4. 4.

    Y. Sui, H. Ding, P.D.M. Spelt, Annu. Rev. Fluid Mech. 46, 97 (2014)

    ADS  Google Scholar 

  5. 5.

    C.-L. Navier, Mémoires de l’Académie Royale des Sciences de l’Institut de France 6, 389 (1823)

    Google Scholar 

  6. 6.

    O. Voinov, Fluid Dyn. 11, 714 (1976)

    ADS  Google Scholar 

  7. 7.

    R.G. Cox, J. Fluid Mech. 168, 169 (1986)

    ADS  Google Scholar 

  8. 8.

    Y.D. Shikhmurzaev, Fluid Dyn. Res. 13, 45 (1994)

    ADS  Google Scholar 

  9. 9.

    Y.D. Shikhmurzaev, J. Fluid Mech. 334, 211 (1997)

    ADS  MathSciNet  Google Scholar 

  10. 10.

    S. Kalliadasis, C. Bielarz, G.M. Homsy, Phys. Fluids 12, 1889 (2000)

    ADS  MathSciNet  Google Scholar 

  11. 11.

    J. Eggers, Phys. Rev. Lett. 93, 094502 (2004)

    ADS  Google Scholar 

  12. 12.

    J.C. Flitton, J.R. King. J. Eng. Math. 50, 241 (2004)

    ADS  MathSciNet  Google Scholar 

  13. 13.

    J.H. Snoeijer, Phys. Fluids 18, 021701 (2006)

    ADS  Google Scholar 

  14. 14.

    L.M. Pismen, J. Eggers, Phys. Rev. E 78, 056304 (2008)

    ADS  MathSciNet  Google Scholar 

  15. 15.

    J.H. Snoeijer, J. Eggers, Phys. Rev. E 82, 056314 (2010)

    ADS  Google Scholar 

  16. 16.

    T.S. Chan, J.H. Snoeijer, J. Eggers, Phys. Fluids 24, 072104 (2012)

    ADS  Google Scholar 

  17. 17.

    A. Nold, L. González MacDowell, D.N. Sibley, B.D. Goddard, S. Kalliadasis, Mol. Phys. 116, 2239 (2018)

    ADS  Google Scholar 

  18. 18.

    T.D. Blake, J.-C. Fernandez-Toledano, G. Doyen, J. De Coninck, Phys. Fluids 27, 112101 (2015)

    ADS  Google Scholar 

  19. 19.

    Y. Deng, L. Chen, Q. Liu, J. Yu, H. Wang, J. Phys. Chem. Lett. 7, 1763 (2016)

    Google Scholar 

  20. 20.

    M. Fricke, M. Köhne, D. Bothe, Proc. Appl. Math. Mech. 18, e201800451 (2018)

    Google Scholar 

  21. 21.

    M. Fricke, M. Köhne, D. Bothe, Physica D 394, 26 (2019)

    ADS  MathSciNet  Google Scholar 

  22. 22.

    P. Johansson, A. Carlson, B. Hess, J. Fluid Mech. 781, 695 (2015)

    ADS  MathSciNet  Google Scholar 

  23. 23.

    P. Johansson, B. Hess, Phys. Rev. Fluids 3, 074201 (2018)

    ADS  Google Scholar 

  24. 24.

    N.G. Hadjiconstantinou, J. Comput. Phys. 154, 245 (1999)

    ADS  Google Scholar 

  25. 25.

    J. Zhang, M.K. Borg, J.M. Reese, Int. J. Heat Mass Transf. 115, 886 (2017)

    Google Scholar 

  26. 26.

    E.R. Smith, P.E. Theodorakis, R.V. Craster, O.K. Matar, Langmuir 34, 12501 (2018)

    Google Scholar 

  27. 27.

    M.K. Borg, D.A. Lockerby, K. Ritos, J.M. Reese, J. Membrane Sci. 567, 115 (2018)

    Google Scholar 

  28. 28.

    L.M. Pismen, Eur. Phys. J. Special Topics 197, 63 (2011)

    ADS  Google Scholar 

  29. 29.

    T.D. Blake, in Dynamic contact angles and wetting kinetics, Vol. 49. Surfactant Science Series, chap. 5 (Marcel Dekker, Inc., 1993), pp. 251–309

  30. 30.

    T. Qian, X.-P. Wang, P. Sheng, Phys. Rev. E 68, 016306 (2003)

    ADS  Google Scholar 

  31. 31.

    T. Qian, X.-P. Wang, P. Sheng, J. Fluid Mech. 564, 333 (2006)

    ADS  MathSciNet  Google Scholar 

  32. 32.

    A. Carlson, M. Do-Quang, G. Amberg, J. Fluid Mech. 682, 213 (2011)

    ADS  Google Scholar 

  33. 33.

    D. Jacqmin, J. Fluid Mech. 402, 57 (2000)

    ADS  MathSciNet  Google Scholar 

  34. 34.

    T. Laurila, A. Carlson, M. Do-Quang, T. Ala-Nissila, G. Amberg, Phys. Rev. E 85, 026320 (2012)

    ADS  Google Scholar 

  35. 35.

    J.J. Eggleston, G.B. McFadden, P.W. Voorhees, Physica D 150, 91 (2001)

    ADS  Google Scholar 

  36. 36.

    A. Carlson, M. Do-Quang, G. Amberg, Phys. Fluids 21, 121701 (2009)

    ADS  Google Scholar 

  37. 37.

    W. Villanueva, G. Amberg, Int. J. Multiphas. Flow 32, 1072 (2006)

    Google Scholar 

  38. 38.

    D. Jacqmin, J. Fluid Mech. 517, 209 (2004)

    ADS  MathSciNet  Google Scholar 

  39. 39.

    M. Sbragaglia, K. Sugiyama, L. Biferale, J. Fluid Mech. 614, 471 (2008)

    ADS  MathSciNet  Google Scholar 

  40. 40.

    W. Ren, W. E, Phys. Fluids 19, 022101 (2007)

    ADS  Google Scholar 

  41. 41.

    P.L. Barclay, J.R. Lukes, Phys. Fluids 31, 092107 (2019)

    ADS  Google Scholar 

  42. 42.

    H.S.H. Mohand, H. Hoang, G. Galliero, D. Legendre, J. Comput. Phys. 393, 29 (2019)

    ADS  MathSciNet  Google Scholar 

  43. 43.

    A. Carlson, Capillarity and dynamic wetting, PhD thesis, KTH Royal Institute of Technology, 2012

  44. 44.

    D. Jacqmin, J. Comput. Phys. 155, 96 (1999)

    ADS  MathSciNet  Google Scholar 

  45. 45.

    Engineering ToolBox, Water Vapor and Saturation Pressure in Humid Air, 2004. [online] Available at: https://www.engineeringtoolbox.com/water-vapor-saturation-pressure-air-d_689.html [Accessed5th of February, 2020]

  46. 46.

    Engineering ToolBox, Gases – Dynamic Viscosity, 2014. [online] Available at: https://www.engineeringtoolbox.com/gases-absolute-dynamic-viscosity-d_1888.html [Accessed 5th of February, 2020]

  47. 47.

    S. Afkhami, J. Buongiorno, A. Guion, S. Popinet, R. Scardovelli, S. Zaleski, J. Comput. Phys. 374, 1061 (2017)

    ADS  Google Scholar 

  48. 48.

    I. Bitsanis, T.K. Vanderlick, M. Tirrell, H.T. Davis, J. Chem. Phys. 89, 3152 (1988)

    ADS  Google Scholar 

  49. 49.

    H. Hoang, G. Galliero, Phys. Rev. E 86, 021202 (2012)

    ADS  Google Scholar 

  50. 50.

    M. Kronbichler, G. Kreiss, J. Comput. Multiphas. Flows 9, 114 (2017)

    Google Scholar 

  51. 51.

    H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, J. Phys. Chem. 91, 6269 (1987)

    Google Scholar 

  52. 52.

    M.J. Abraham, T. Murtola, R. Schulz, S. Páll, J.C. Smith, B. Hess, E. Lindahl, SoftwareX 1-2, 19 (2015)

    ADS  Google Scholar 

  53. 53.

    G. Amberg, R. Tönhardt, C. Winkler, Math. Comput. Simulat. 49, 257 (1999)

    Google Scholar 

  54. 54.

    M. Do-Quang, W. Villanueva, I. Singer-Loginova, G. Amberg, Bulletin of the Polish Academy of Sciences: Technical Sciences 55, 229 (2007)

    Google Scholar 

  55. 55.

    S. Afkhami, M. Bussmann, Int. J. Numer. Meth. Fl. 57, 453 (2008)

    Google Scholar 

  56. 56.

    S. Popinet, Annu. Rev. Fluid Mech. 50, 49 (2018)

    ADS  MathSciNet  Google Scholar 

  57. 57.

    S. Afkhami, M. Bussmann, Int. J. Numer. Meth. Fl. 61, 827 (2009)

    Google Scholar 

  58. 58.

    J.B. Bell, P. Colella, H.M. Glaz, J. Comput. Phys. 85, 257 (1989)

    ADS  MathSciNet  Google Scholar 

Download references

Acknowledgments

Open access funding provided by Royal Institute of Technology.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Uǧis Lācis.

Additional information

Publisher's Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lācis, U., Johansson, P., Fullana, T. et al. Steady moving contact line of water over a no-slip substrate. Eur. Phys. J. Spec. Top. 229, 1897–1921 (2020). https://doi.org/10.1140/epjst/e2020-900280-9

Download citation