- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Rolling and Sliding Modes of Nanodroplet Spreading: Molecular Simulations and a Continuum Approach

Sreehari Perumanath1,*, Mykyta V. Chubynsky1,2,†, Rohit Pillai3,‡, Matthew K. Borg3,§, and James E. Sprittles1,∥

  • 1Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 2Centre for Fluid and Complex Systems, Coventry University, Coventry, CV1 5FB, United Kingdom
  • 3School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, United Kingdom

  • *S.Perumanath@warwick.ac.uk
  • †ae2173@coventry.ac.uk
  • ‡R.Pillai@ed.ac.uk
  • §matthew.borg@ed.ac.uk
  • ∥j.e.sprittles@warwick.ac.uk
PDF

Phys. Rev. Lett. 131, 164001 – Published 19 October, 2023

DOI: https://doi.org/10.1103/PhysRevLett.131.164001

Abstract

Molecular simulations discover a new mode of dynamic wetting that manifests itself in the very earliest stages of spreading, after a droplet contacts a solid. The observed mode is a “rolling” type of motion, characterized by a contact angle lower than the classically assumed value of 180°, and precedes the conventional “sliding” mode of spreading. This motivates the development of a novel continuum framework that captures all modes of motion, allows the dominant physical mechanisms to be understood, and permits the study of larger droplets.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (61)

  1. S. J. Weinstein and K. J. Ruschak, Coating flows, Annu. Rev. Fluid Mech. 36, 29 (2004).
  2. P. Simpkins and V. Kuck, On air entrainment in coatings, J. Colloid Interface Sci. 263, 562 (2003).
  3. N. Patra, B. Wang, and P. Král, Nanodroplet activated and guided folding of graphene nanostructures, Nano Lett. 9, 3766 (2009).
  4. J. C. Fernández-Toledano, B. Braeckeveldt, M. Marengo, and J. De Coninck, How wettability controls nanoprinting, Phys. Rev. Lett. 124, 224503 (2020).
  5. Y. L. Kong, M. K. Gupta, B. N. Johnson, and M. C. McAlpine, 3D printed bionic nanodevices, Nano Today 11, 330 (2016).
  6. M. Rauscher and S. Dietrich, Wetting phenomena in nanofluidics, Annu. Rev. Mater. Res. 38, 143 (2008).
  7. D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, Wetting and spreading, Rev. Mod. Phys. 81, 739 (2009).
  8. N. Kavokine, R. R. Netz, and L. Bocquet, Fluids at the nanoscale: From continuum to subcontinuum transport, Annu. Rev. Fluid Mech. 53, 377 (2021).
  9. L. Xu, W. W. Zhang, and S. R. Nagel, Drop Splashing on a Dry Smooth Surface, Phys. Rev. Lett. 94, 184505 (2005).
  10. J. M. Kolinski, L. Mahadevan, and S. M. Rubinstein, Drops can bounce from perfectly hydrophilic surfaces, Europhys. Lett. 108, 24001 (2014).
  11. J. Qian and H. Gao, Scaling effects of wet adhesion in biological attachment systems, Acta Biomater. 2, 51 (2006).
  12. M. J. Vogel and P. H. Steen, Capillarity-based switchable adhesion, Proc. Natl. Acad. Sci. U.S.A. 107, 3377 (2010).
  13. J. C. Bird, S. Mandre, and H. A. Stone, Short-Time Dynamics of Partial Wetting, Phys. Rev. Lett. 100, 234501 (2008).
  14. A. Eddi, K. G. Winkels, and J. H. Snoeijer, Short time dynamics of viscous drop spreading, Phys. Fluids 25, 013102 (2013).
  15. K. G. Winkels, J. H. Weijs, A. Eddi, and J. H. Snoeijer, Initial spreading of low-viscosity drops on partially wetting surfaces, Phys. Rev. E 85, 055301(R) (2012).
  16. A.-L. Biance, C. Clanet, and D. Quéré, First steps in the spreading of a liquid droplet, Phys. Rev. E 69, 016301 (2004).
  17. Y. D. Shikhmurzaev, Reflections on reflections of Dieter Bothe on the ‘litmus test’ for mathematical models of dynamic wetting, Eur. Phys. J. Spec. Top. 229, 1989 (2020).
  18. J. Philippi, P.-Y. Lagrée, and A. Antkowiak, Drop impact on a solid surface: Short-time self-similarity, J. Fluid Mech. 795, 96 (2016).
  19. C. Huh and L. Scriven, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid Interface Sci. 35, 85 (1971).
  20. E. B. Dussan, On the spreading of liquids on solid surfaces: Static and dynamic contact lines, Annu. Rev. Fluid Mech. 11, 371 (1979).
  21. P. G. de Gennes, Wetting: Statics and dynamics, Rev. Mod. Phys. 57, 827 (1985).
  22. Y. D. Shikhmurzaev, Capillary Flows with Forming Interfaces (Chapman and Hall/CRC, London, 2007).
  23. E. B. Dussan V., The moving contact line: The slip boundary condition, J. Fluid Mech. 77, 665 (1976).
  24. L. M. Hocking, A moving fluid interface on a rough surface, J. Fluid Mech. 76, 801 (1976).
  25. Y. D. Shikhmurzaev, Moving contact lines in liquid/liquid/solid systems, J. Fluid Mech. 334, 211 (1997).
  26. C. G. Ngan and E. B. Dussan V, The moving contact line with a 180° advancing contact angle, Phys. Fluids 27, 2785 (1984).
  27. L. Mahadevan and Y. Pomeau, Rolling droplets, Phys. Fluids 11, 2449 (1999).
  28. E. S. Benilov and M. Vynnycky, Contact lines with a 180° contact angle, J. Fluid Mech. 718, 481 (2013).
  29. O. Schnitzer, A. M. J. Davis, and E. Yariv, Rolling of non-wetting droplets down a gently inclined plane, J. Fluid Mech. 903, A25 (2020).
  30. T. Blake and J. Haynes, Kinetics of liquid-liquid displacement, J. Colloid Interface Sci. 30, 421 (1969).
  31. T. D. Blake, The physics of moving wetting lines, J. Colloid Interface Sci. 299, 1 (2006).
  32. R. G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow, J. Fluid Mech. 168, 169 (1986).
  33. O. V. Voinov, Hydrodynamics of wetting, Fluid Dyn. 11, 714 (1977).
  34. J. H. Snoeijer and B. Andreotti, Moving contact lines: Scales, regimes, and dynamical transitions, Annu. Rev. Fluid Mech. 45, 269 (2013).
  35. D. Richard and D. Quéré, Viscous drops rolling on a tilted non-wettable solid, Europhys. Lett. 48, 286 (1999).
  36. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, 2nd ed. (Oxford University Press, New York, 2017).
  37. J. Koplik and J. R. Banavar, Continuum deductions from molecular hydrodynamics, Annu. Rev. Fluid Mech. 27, 257 (1995).
  38. J. De Coninck and T. D. Blake, Wetting and molecular dynamics simulations of simple liquids, Annu. Rev. Mater. Res. 38, 1 (2008).
  39. Y. Nakamura, A. Carlson, G. Amberg, and J. Shiomi, Dynamic wetting at the nanoscale, Phys. Rev. E 88, 033010 (2013).
  40. V. Molinero and E. B. Moore, Water modeled as an intermediate element between carbon and silicon, J. Phys. Chem. B 113, 4008 (2009).
  41. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.131.164001 which contains technical details that are complementary to this Letter. We discuss (I) the molecular dynamics simulation details, (II) the first contact and the following rolling regime in wetting, (III) the details of the novel continuum model for wetting, (IV) additional results from the new continuum model, and (V) some further exploration of the rolling mode using the continuum model. Readers are also invited to view the supplemental movie.
  42. J. L. Abascal and C. Vega, A general purpose model for the condensed phases of water: TIP4P/2005., J. Chem. Phys. 123, 234505 (2005).
  43. L. Bocquet and J.-L. Barrat, Hydrodynamic boundary conditions, correlation functions, and Kubo relations for confined fluids, Phys. Rev. E 49, 3079 (1994).
  44. Y. Zhang, J. E. Sprittles, and D. A. Lockerby, Nanoscale thin-film flows with thermal fluctuations and slip, Phys. Rev. E 102, 053105 (2020).
  45. G. J. Wang and N. G. Hadjiconstantinou, Universal molecular-kinetic scaling relation for slip of a simple fluid at a solid boundary, Phys. Rev. Fluids 4, 064201 (2019).
  46. N. G. Hadjiconstantinou and M. M. Swisher, On the equivalence of nonequilibrium and equilibrium measurements of slip in molecular dynamics simulations, Phys. Rev. Fluids 7, 114203 (2022).
  47. T. Young, III: An essay on the cohesion of fluids, Phil. Trans. R. Soc. London 95, 65 (1805).
  48. M. V. Chubynsky, K. I. Belousov, D. A. Lockerby, and J. E. Sprittles, Bouncing Off the Walls: The Influence of Gas-Kinetic and van der Waals Effects in Drop Impact, Phys. Rev. Lett. 124, 084501 (2020).
  49. I. Chakraborty, M. V. Chubynsky, and J. E. Sprittles, Computational modelling of Leidenfrost drops, J. Fluid Mech. 936 (2022).
  50. R. A. Cairncross, P. R. Schunk, T. A. Baer, R. R. Rao, and P. A. Sackinger, A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion, Int. J. Numer. Methods Fluids 33, 375 (2000).
  51. Y. D. Shikhmurzaev, Moving contact lines and dynamic contact angles: A ‘litmus test’ for mathematical models, accomplishments and new challenges, Eur. Phys. J. Spec. Top. 229, 1945 (2020).
  52. J. Zhang, P. Wang, M. K. Borg, J. M. Reese, and D. Wen, A critical assessment of the line tension determined by the modified Young’s equation, Phys. Fluids 30, 082003 (2018).
  53. D. G. A. L. Aarts, M. Schmidt, and H. N. W. Lekkerkerker, Direct visual observation of thermal capillary waves, Science 304, 847 (2004).
  54. S. Perumanath, M. K. Borg, M. V. Chubynsky, J. E. Sprittles, and J. M. Reese, Droplet Coalescence is Initiated by Thermal Motion, Phys. Rev. Lett. 122, 104501 (2019).
  55. A. Oron, S. H. Davis, and S. G. Bankoff, Long-scale evolution of thin liquid films, Rev. Mod. Phys. 69, 931 (1997).
  56. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  57. Y. Sui, H. Ding, and P. D. Spelt, Numerical simulations of flows with moving contact lines, Annu. Rev. Fluid Mech. 46, 97 (2014).
  58. P. Seppecher, Moving contact lines in the Cahn-Hilliard theory, Int. J. Eng. Sci. 34, 977 (1996).
  59. J. A. Diez and L. Kondic, Computing three-dimensional thin film flows including contact lines, J. Comput. Phys. 183, 274 (2002).

  60. COMSOL Ltd., Cambridge, United Kingdom.

  61. M. Chubynsky, S. Perumanath, R. Pillai, J. Sprittles, and M. Borg, Rolling and Sliding modes of Droplet Spreading: Molecular Simulations and a Continuum Approach (2023), 10.7488/ds/7516.

Outline

Information

Phys. Rev. Lett. 131, 164001– Published 19 October, 2023
  • Received 12 September 2022
  • Revised 11 May 2023
  • Accepted 15 August 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation