Advertisement

Breakup of finite-size liquid filaments: Transition from no-breakup to breakup including substrate effects

  • A. Dziedzic
  • M. Nakrani
  • B. Ezra
  • M. Syed
  • S. Popinet
  • S. AfkhamiEmail author
Regular Article
Part of the following topical collections:
  1. Flowing Matter, Problems and Applications

Abstract.

This work studies the breakup of finite-size liquid filaments, when also including substrate effects, using direct numerical simulations. The study focuses on the effects of three parameters: Ohnesorge number, the ratio of the viscous forces to inertial and surface tension forces, the liquid filament aspect ratio, and where there is a substrate, a measure of the fluid slip on the substrate, i.e. slip length. Through these parameters, it is determined whether a liquid filament breaks up during the evolution toward its final equilibrium state. Three scenarios are identified: a collapse into a single droplet, the breakup into one or multiple droplets, and recoalescence into a single droplet after the breakup (or even possibly another breakup after recoalescence). The results are compared with the ones available in the literature for free-standing liquid filaments. The findings show that the presence of the substrate promotes the breakup of the filament. The effect of the degree of slip on the breakup is also discussed. The parameter domain regions are comprehensively explored when including the slip effects. An experimental case is also carried out to illustrate the collapse and breakup of a finite-size silicon oil filament supported on a substrate, showcasing a critical length of the breakup in a physical configuration. Finally, direct numerical simulations reveal striking new details into the breakup pattern for low Ohnesorge numbers, where the dynamics are fast and the experimental imaging is not available; our results therefore significantly extend the range of Ohnesorge number over which filament breakup has been considered.

Graphical abstract

Keywords

Topical issue: Flowing Matter, Problems and Applications 

References

  1. 1.
    J.R. Lister, H.A. Stone, Phys. Fluids 11, 2758 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    J. Eggers, Phys. Rev. Lett. 71, 3458 (1993)ADSCrossRefGoogle Scholar
  3. 3.
    J. Eggers, Rev. Mod. Phy. 69, 865 (1997)ADSCrossRefGoogle Scholar
  4. 4.
    O.A. Basaran, AIChE J. 49, 1842 (2002)CrossRefGoogle Scholar
  5. 5.
    P.K. Notz, O.A. Basaran, J. Fluid Mech. 512, 223 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    J.R. Castrejón-Pita, N.F. Morrison, O.G. Harlen, G.D. Martin, I.M. Hutchings, Phys. Rev. E 83, 036306 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    A.A. Castrejón-Pita, J.R. Castrejón-Pita, I.M. Hutchings, Phys. Rev. Lett. 108, 074506 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    T. Driessen, R. Jeurissen, H. Wijshoff, F. Toschi, D. Lohse, Phys. Fluids 25, 062109 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    C.A. Hartnett, K. Mahady, J.D. Fowlkes, S. Afkhami, L. Kondic, P.D. Rack, Langmuir 31, 13609 (2015)CrossRefGoogle Scholar
  10. 10.
    G. Ghigliotti, C. Zhou, J.J. Feng, Phys. Fluids 25, 072102 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    I. Cuellar, P.D. Ravazzoli, J.A. Diez, A.G. González, Phys. Fluids 29, 102103 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    S. Popinet, The Gerris flow solver (2012) 1.3.2, https://doi.org/gfs.sourceforge.net/ gfs.sourceforge.net/
  13. 13.
    J. Diez, A.G. Gonzá, Physica D 209, 49 (2005)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    L. Rayleigh, Proc. London Math. Soc. 1, 4 (1878)MathSciNetCrossRefGoogle Scholar
  15. 15.
    S. Popinet, Savart-Plateau-Rayleigh instability of a water column, https://gfs.sourceforge.net/examples/examples/plateau.html
  16. 16.
    S. Afkhami, S. Zaleski, M. Bussmann, J. Comput. Phys. 228, 5370 (2009)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    S. Afkhami, J. Buongiorno, A. Guion, S. Popinet, Y. Saade, R. Scardovelli, S. Zaleski, J. Comput. Phys. 374, 1061 (2018)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    S. Popinet, J. Comput. Phys. 190, 572 (2003)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    S. Popinet, J. Comput. Phys. 228, 5838 (2009)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    S. Popinet, Annu. Rev. Fluid Mech. 50, 49 (2018)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    K. Mahady, S. Afkhami, L. Kondic, Phys. Fluids 27, 092104 (2015)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • A. Dziedzic
    • 1
  • M. Nakrani
    • 1
  • B. Ezra
    • 1
  • M. Syed
    • 1
  • S. Popinet
    • 2
  • S. Afkhami
    • 1
    Email author
  1. 1.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA
  2. 2.Sorbonne Université, Centre National de la Recherche Scientifique, Institut Jean le Rond ∂’AlembertParisFrance

Personalised recommendations