Skip to main content
SpringerLink
Log in

Simulation of droplet spreading on surfaces with asymmetrical wettability using multiphase Smoothed Particle Hydrodynamics (SPH)

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Maneuvering the droplet spreading by changing the wettability of solid surface with surface treatment technology has attracted much attention. Smoothed Particle Hydrodynamics (SPH) is a meshfree Lagrangian particle method and has special advantages in coping with large deformations and interfaces problems. In this paper, a multiphase SPH model was proposed which is associated with number density to approximate density, color function to calculate stress at the interface between different phases, and particle shifting technique to regularize particle distribution. The multiphase SPH model was first validated and then applied to numerically study droplet spreading on surfaces with asymmetrical wettability (different surface tension coefficients on two sides). The simulation results demonstrated that the spreading characteristic is closely dependent on the ratio of the surface tension on the two sides of the asymmetric surface. According to different spreading forms, the Contact angle maps were obtained which clearly described the relationship of the surface tension ratio, the contact angles on two sides and the spreading modes. Furthermore, through analyzing the evolution of velocity at four modes (Bi-directional spreading (Left deviation), Bi-directional spreading (Right deviation), Uni-directional spreading (Left) and Uni-directional spreading (Right)), a general law of the change and the distribution of velocity is formulated. Finally, the mode of uni-directional spreading is theoretically studied and theoretical solutions which can quantitatively describe the evolution of the droplet on the substrate, while the theoretical solution is associated with two dimensionless numbers, which respectively determine the displacement and speed of the droplet, are proposed. All these results provide solid theoretical basis and profound insights for the spreading of droplets on surfaces with asymmetrical wettability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Data availability

This manuscript has associated data in a data repository. [Authors’ comment: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.]

Code availability

Not applicable.

References

  1. N.-R. Chiou, C. Lu, J. Guan, L.J. Lee, A.J. Epstein, Nat. Nanotechnol. 2, 354 (2007)

    Article  Google Scholar 

  2. R.B. Fair, Microfluid. Nanofluid. 3, 245 (2007)

    Article  Google Scholar 

  3. S. Nishimotoab, B. Bhushan, RSC. Adv. 3, 671 (2012)

    Article  Google Scholar 

  4. K. Yin, H. Du, X. Dong, C. Wang, J.-A. Duan, J. He, Nanoscale 9, 14620 (2017)

    Article  Google Scholar 

  5. E.B. Secor, P.L. Prabhumirashi, K. Puntambekar, M.L. Geier, M.C. Hersam, J. Phys. Chem. Lett. 4, 1347 (2013)

    Article  Google Scholar 

  6. D. Gropper, L. Wang, T.J. Harvey, Tribol. Int. 94, 509 (2016)

    Article  Google Scholar 

  7. D. Tian, Y. Song, L. Jiang, Chem. Soc. Rev. 42, 5184 (2013)

    Article  Google Scholar 

  8. Y. Lai, J. Huang, Z. Cui, M. Ge, K.-Q. Zhang, Z. Chen, L. Chi, Small 12, 2203 (2016)

    Article  Google Scholar 

  9. Y. Sun, Z. Guo, Nanoscale. Horiz. 4, 52 (2018)

    Article  Google Scholar 

  10. R. Seemann, M. Brinkmann, E.J. Kramer, F.F. Lange, R. Lipowsky, P. Natl, Acad. Sci. USA 102, 1848 (2005)

    Article  Google Scholar 

  11. B. Lim, M. Jiang, J. Tao, P.H.C. Camargo, Y. Zhu, Adv. Funct. Mater. 19, 189 (2009)

    Article  Google Scholar 

  12. R. Xiao, K.-H. Chu, E. N. Wang, Appl. Phys. Lett. 94, 193104 (2009).

  13. M.O. Robbins, D. Andelman, J.-F. Joanny, Phys. Rev. A. 43, 4344 (1991)

    Article  Google Scholar 

  14. L. Xu, X. Li, Y. Chen, F. Xu, Appl. Surf. Sci. 257, 4031 (2011)

    Article  Google Scholar 

  15. F. Zhang, H.Y. Low, Langmuir 23, 7793 (2007)

    Article  Google Scholar 

  16. H. Kusumaatmaja, R.J. Vrancken, C.W.M. Bastiaansen, J.M. Yeomans, Langmuir 24, 7299 (2008)

    Article  Google Scholar 

  17. D. Murakami, H. Jinnai, A. Takahara, Langmuir 30, 2061 (2014)

    Article  Google Scholar 

  18. L. Chen, E. Bonaccurso, Adv. Colloid. Interfac. 210, 2 (2014)

    Article  Google Scholar 

  19. J.H. Li, X.X. Ni, D.B. Zhang, H. Zheng, J.B. Wang, Q.Q. Zhang, Appl. Surf. Sci. 444, 672 (2018)

    Article  Google Scholar 

  20. C. Yang, L. Wu, G. Li, Acs. Appl. Mater. Inter. 10, 20150 (2018)

    Article  Google Scholar 

  21. K.-H. Chu, R. Xiao, E.N. Wang, Nat. Mater. 9, 413 (2010)

    Article  Google Scholar 

  22. M.J. Hancock, K. Sekeroglu, M.C. Demirel, Adv. Funct. Mater. 22, 2223 (2012)

    Article  Google Scholar 

  23. A.M. Aly, M. Asai, Y. Sonda, Int. J. Numer. Method. H. 23, 479 (2013)

    Article  Google Scholar 

  24. L.D.G. Sigalotti, A.D.J. Daza, Condens. Matter. Phys. 9, 359 (2006)

    Article  Google Scholar 

  25. S. Nugent, H.A. Posch, Phys. Rev. E. 62, 4968 (2000)

    Article  Google Scholar 

  26. Y. Melean, L. Sigalotti, Int. J. Heat. Mass. Tran. 48, 4041 (2005)

    Article  Google Scholar 

  27. A. Tartakovsky, P. Meakin, Phys. Rev. E. 72, 6301 (2005)

    Article  Google Scholar 

  28. L.Q. Ma, M.B. Liu, J.Z. Chang, T.X. Su, H.T. Liu, Acta. Phys. Sin-CH. Ed. 61, 244701 (2012)

    Google Scholar 

  29. L. Li, L. Shen, G.D. Nguyen, A. El-Zein, F. Maggi, Comput. Mech. 62, 1071 (2018)

    Article  MathSciNet  Google Scholar 

  30. M.Y. Zhang, H. Zhang, L.L. Zhang, Int. J. Heat. Mass. Tran. 51, 3410 (2008)

    Article  Google Scholar 

  31. E. Arai, A. Tartakovsky, R.G. Holt, S. Grace, E. Ryan, Computers and Fluids 203, 104540 (2020)

    Article  MathSciNet  Google Scholar 

  32. T. Breinlinger, P. Polfer, A. Hashibon, T. Kraft, J. Comput. Phys. 243, 14 (2013)

    Article  Google Scholar 

  33. J.U. Brackbill, D.B. Kothe, C. Zemach, J. Comput. Phys. 100, 335 (1992)

    Article  MathSciNet  Google Scholar 

  34. M. Huber, F. Keller, W. Säckel, M. Hirschler, P. Kunz, S.M. Hassanizadeh, U. Nieken, J. Comput. Phys. 310, 459 (2016)

    Article  MathSciNet  Google Scholar 

  35. X.Y. Hu, N.A. Adams, J. Comput. Phys. 227, 264 (2007)

    Article  Google Scholar 

  36. X.Y. Hu, N.A. Adams, J. Comput. Phys. 228, 2082 (2009)

    Article  Google Scholar 

  37. A. Krimi, M. Rezoug, S. Khelladi, X. Nogueira, M. Deligant, L. Ramirez, J. Comput. Phys. 358, 53 (2018)

    Article  MathSciNet  Google Scholar 

  38. B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti, J. Comput. Phys. 113, 134 (1994)

    Article  MathSciNet  Google Scholar 

  39. S.J. Neethling, D.J. Barker, Miner. Eng. 90, 17 (2016)

    Article  Google Scholar 

  40. M. Zhang, H. Zhang, L. Zheng, Numer. Heat. Tr. A-Appl. 52, 299 (2007)

    Article  Google Scholar 

  41. A.K. Das, P.K. Das, Langmuir 25, 11459 (2009)

    Article  Google Scholar 

  42. A.M. Tartakovsky, A. Panchenko, J. Comput. Phys. 305, 1119 (2016)

    Article  MathSciNet  Google Scholar 

  43. M. Olejnik, J. Pozorski, Flow. Turbul. Combust. 104, 115 (2020)

    Article  Google Scholar 

  44. J.P. Morris, Publ. Astron. Soc. Aust. 13, 97 (1996)

    Article  Google Scholar 

  45. X.Y. Hu, N.A. Adams, J. Comput. Phys. 213, 844 (2006)

    Article  MathSciNet  Google Scholar 

  46. J.J. Monaghan, J. Comput. Phys. 110, 339 (1994)

    Article  Google Scholar 

  47. R. Xu, P. Stansby, D. Laurence, J. Comput. Phys. 228, 6703 (2009)

    Article  MathSciNet  Google Scholar 

  48. C. Huang, D.H. Zhang, Y.X. Shi, Y.L. Si, B. Huang, Int. J. Numer. Meth. Eng. 113, 179 (2018)

    Article  Google Scholar 

  49. J.R. Shao, H.Q. Li, G.R. Liu, M.B. Liu, Comput. Struct. 100–101, 18 (2012)

    Article  Google Scholar 

  50. Z. Chen, Z. Zong, M.B. Liu, H.T. Li, Int. J. Numer. Meth. Fl. 73, 813 (2013)

    Article  Google Scholar 

  51. Z. Lin, X. Wang, X. Peng, J. Eng. Thermophys. 5, 847 (2005)

    Google Scholar 

  52. K. Guo, R. Chen, C. Wang, S. Qiu, W. Tian, G. Su, Nuclear Eng. Des. 369, 110855 (2020)

    Article  Google Scholar 

  53. B. Lavi, A. Marmur, Colloids and Surfaces A-Physicochemical and Engineering Aspects 250, 409 (2004)

    Google Scholar 

  54. R. Rioboo, M. Marengo, C. Tropea, Exp. Fluids 33, 112 (2002)

    Article  Google Scholar 

  55. J.W.M. Bush, D.L. Hu, Annu. Rev. Fluid Mech. 38, 339 (2006)

    Article  Google Scholar 

  56. V.G. Levich, V.S. Krylov, Annu. Rev. Fluid Mech. 1, 293 (1969)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 51976203 and 51476150), and Applied Basic Research Programs of Shanxi Province in China (Grant No. 201801D221370).

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 51976203 and 51476150), and Applied Basic Research Programs of Shanxi Province in China (Grant No. 201801D221370).

Author information

Authors and Affiliations

  1. College of Mechatronics Engineering, North University of China, Taiyuan, 030051, China

    Chao Li

  2. Research Center of Shanxi Province for Solar Energy Engineering and Technology, North University of China, Taiyuan, 030051, China

    Chao Li, Hantao Liu, Haiqiao Li & Jianzhong Chang

  3. BIC-ESAT, College of Engineering, Peking University, Beijing, 100871, China

    Zekun Wang

  4. State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing, 100871, China

    Zekun Wang

Authors
  1. Chao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hantao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zekun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Haiqiao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jianzhong Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hantao Liu.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Ethics approval

Not applicable.

Consent for publication

We agree to publish.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, C., Liu, H., Wang, Z. et al. Simulation of droplet spreading on surfaces with asymmetrical wettability using multiphase Smoothed Particle Hydrodynamics (SPH). Eur. Phys. J. Plus 136, 692 (2021). https://doi.org/10.1140/epjp/s13360-021-01677-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01677-5

Search

Navigation