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Journal of Engineering Mathematics

, Volume 94, Issue 1, pp 5–18 | Cite as

On the dewetting of liquefied metal nanostructures

  • Shahriar AfkhamiEmail author
  • Lou Kondic
Article

Abstract

Direct numerical simulations of liquefied metal nanostructures dewetting a substrate are carried out. Full three-dimensional Navier–Stokes equations are solved and a volume-of-fluid method is used for tracking and locating the interface. Substrate wettability is varied to study the influence of the solid–liquid interaction. The effects of initial geometry on the retraction dynamics is numerically investigated. It is shown that the dewetting velocity increases with increases in the contact angle and that the retraction dynamics is governed by an elaborate interplay of initial geometry, inertial and capillary forces, and the dewetting phenomena. Numerical results are presented for the dewetting of nanoscale Cu and Au liquefied structures on a substrate.

Keywords

Dewetting Liquefied metal nanostructures Navier–Stokes Surface tension Volume-of-fluid 

Notes

Acknowledgments

The results presented here are a part of a larger research project involving Kyle Mahady (New Jersey Institute of Technology), Javier Diez and Alejandro Gonzalez from Universidad Nacional del Centro de la Provincia de Buenos Aires (Argentina), and Jason Fowlkes, Miguel Fuentes-Cabrera, and Philip Rack from Oak Ridge National Laboratory and the University of Tennessee. We acknowledge the extensive discussions with all members of the research team. This work was supported in part by National Science Foundation Grants DMS-1320037 (S.A.) and CBET-1235710 (L.K.).

References

  1. 1.
    Habenicht A, Olapinski M, Burmeister F, Leiderer P, Boneberg J (2005) Jumping nanodroplets. Science 309:2043CrossRefADSGoogle Scholar
  2. 2.
    Boneberg J, Habenicht A, Benner D, Leiderer P, Trautvetter M, Pfahler C, Plettl A, Ziemann P (2008) Jumping nanodroplets: a new route towards metallic nano-particles. Appl Phys A 93:415CrossRefADSGoogle Scholar
  3. 3.
    Roberts NA, Fowlkes JD, Mahady K, Afkhami S, Kondic L, Rack PD (2013) Directed assembly of one- and two-dimensional nanoparticle arrays from pulsed laser induced dewetting of square waveforms. ACS Appl Mater Interfaces 5:4450Google Scholar
  4. 4.
    Fuentes-Cabrera M, Rhodes BH, Fowlkes JD, López-Benzanilla A, Terrones H, Simpson ML, Rack PD (2011) Molecular dynamics study of the dewetting of copper on graphite and graphene: implications for nanoscale self-assembly. Phys Rev E 83:041603CrossRefADSGoogle Scholar
  5. 5.
    Fuentes-Cabrera M, Rhodes BH, Baskes MI, Terrones H, Fowlkes JD, Simpson ML, Rack PD (2011) Controlling the velocity of jumping nanodroplets via their initial shape and temperature. ACS Nano 5:7130Google Scholar
  6. 6.
    de Gennes PG (1985) Wetting: statics and dynamics. Rev Mod Phys 57:827CrossRefADSGoogle Scholar
  7. 7.
    Haley PJ, Miksis MJ (1991) The effect of the contact line on droplet spreading. J Fluid Mech 223:57zbMATHMathSciNetCrossRefADSGoogle Scholar
  8. 8.
    Trice J, Thomas D, Favazza C, Sureshkumar R, Kalyanaraman R (2007) Pulsed-laser-induced dewetting in nanoscopic metal films: theory and experiments. Phys Rev B 75:235439CrossRefADSGoogle Scholar
  9. 9.
    Ajaev VS, Willis DA (2003) Thermocapillary flow and rupture in films of molten metal on a substrate. Phys Fluids 15:3144CrossRefADSGoogle Scholar
  10. 10.
    Kondic L, Diez J, Rack P, Guan Y, Fowlkes J (2009) Nanoparticle assembly via the dewetting of patterned thin metal lines: understanding the instability mechanism. Phys Rev E 79:026302CrossRefADSGoogle Scholar
  11. 11.
    Afkhami S, Bussmann M (2008) Height functions for applying contact angles to 2D VOF simulations. Int J Numer Method Fluids 57:453zbMATHCrossRefGoogle Scholar
  12. 12.
    Afkhami S, Bussmann M (2009) Height functions for applying contact angles to 3D VOF simulations. Int J Numer Method Fluids 61:827zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Afkhami S, Zaleski S, Bussmann M (2009) A mesh-dependent model for applying dynamic contact angles to VOF simulations. J Comput Phys 228:5370Google Scholar
  14. 14.
    Hirt CW, Nichols BD (1981) Volume of fluid VOF method for the dynamics of free boundaries. J Comput Phys 39:201zbMATHCrossRefADSGoogle Scholar
  15. 15.
    Gueyffier D, Li J, Nadim A, Scardovelli R, Zaleski S (1999) Volume-of-fluid interface tracking and smoothed surface stress methods for three-dimensional flows. J Comput Phys 152:423zbMATHCrossRefADSGoogle Scholar
  16. 16.
    Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100:335zbMATHMathSciNetCrossRefADSGoogle Scholar
  17. 17.
    Sussman M (2003) A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. J Comput Phys 187:110zbMATHMathSciNetCrossRefADSGoogle Scholar
  18. 18.
    Cummins SJ, Francois MM, Kothe DB (2005) Estimating curvature from volume fractions. Comput Struct 83:425CrossRefGoogle Scholar
  19. 19.
    Francois MM, Cummins SJ, Dendy ED, Kothe DB, Sicilian JM, Williams MW (2006) A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J Comput Phys 213:141zbMATHCrossRefADSGoogle Scholar
  20. 20.
    Popinet S (2003) Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J Comput Phys 190:572zbMATHMathSciNetCrossRefADSGoogle Scholar
  21. 21.
    Bell JB, Colella P, Glaz HM (1989) A second-order projection method for the incompressible Navier–Stokes equations. J Comput Phys 85:257zbMATHMathSciNetCrossRefADSGoogle Scholar
  22. 22.
    Young T (1805) An essay on the cohesion of fluids. Philos Trans R Soc Lond 95:65–87CrossRefGoogle Scholar
  23. 23.
    Afkhami S, Kondic L (2013) Numerical simulation of ejected molten metal nanoparticles liquified by laser irradiation: interplay of geometry and dewetting. Phys Rev Lett 111:034501CrossRefADSGoogle Scholar
  24. 24.
    González AG, Diez JA, Kondic L (2013) Stability of a liquid ring on a substrate. J Fluid Mech 718:246zbMATHMathSciNetCrossRefADSGoogle Scholar
  25. 25.
    Mahady K, Afkhami S, Diez J, Kondic L (2013) Comparison of Navier–Stokes simulations with long-wave theory: study of wetting and dewetting. Phys Fluids 25:112103CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA

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