Skip to main content
Springer Nature Link
Log in

Axisymmetric lattice Boltzmann model for simulation of ternary fluid flows

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this paper, a lattice Boltzmann model based on the phase-field Cahn–Hilliard-based approach is proposed to deal with ternary fluid flows in the axisymmetric coordinate system. The present model can handle both high density and viscosity ratios for partial and total spreading scenarios. A variety of numerical tests, including a static droplet test, a breakup of a liquid thread test, a spreading of a liquid lens test, and a droplet collision test, were performed to verify the model. It is found that the proposed model produces accurate results which agree well with the available data.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. He, X., Doolen, G.D.: Thermodynamic foundations of kinetic theory and lattice Boltzmann models for multiphase flows. J. Stat. Phys. 107, 309–328 (2002)

    Article  Google Scholar 

  2. He, X., Luo, L.-S.: Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56, 6811–6817 (1997)

    Article  Google Scholar 

  3. Li, Q., Luo, K., Kang, Q., He, Y., Chen, Q., Liu, Q.: Lattice Boltzmann methods for multiphase flow and phase-change heat transfer. Prog. Energy Combust. Sci. 52, 62–105 (2016)

    Article  Google Scholar 

  4. Geier, M., Fakhari, A., Lee, T.: Conservative phase-field lattice Boltzmann model for interface tracking equation. Phys. Rev. E 91, 063309 (2015)

    Article  MathSciNet  Google Scholar 

  5. Fakhari, A., Mitchell, T., Leonardi, C., Bolster, D.: Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios. Phys. Rev. E 00, 003300 (2017)

    Google Scholar 

  6. Liang, H., Shi, B.C., Chai, Z.H.: Lattice Boltzmann modeling of three-phase incompressible flows. Phys. Rev. E 93, 013308 (2016)

    Article  MathSciNet  Google Scholar 

  7. Liang, H., Xu, J., Chen, J., Chai, Z., Shi, B.: Lattice Boltzmann modeling of wall-bounded ternary fluid flows. Appl. Math. Model. 73, 487–513 (2019)

    Article  MathSciNet  Google Scholar 

  8. Haghani-Hassan-Abadi, R., Fakhari, A., Rahimian, M.-H.: Numerical simulation of three-component multiphase flows at high density and viscosity ratios using lattice Boltzmann methods. Phys. Rev. E 97, 033312 (2018)

    Article  Google Scholar 

  9. Haghani-Hassan-Abadi, R., Rahimian, M.-H.: Hybrid lattice Boltzmann finite difference model for simulation of phase change in a ternary fluid. Int. J. Heat Mass Transf. 127, 704–716 (2018)

    Article  Google Scholar 

  10. Haghani-Hassan-Abadi, R., Rahimian, M.-H.: A lattice Boltzmann method for simulation of condensation on liquid-impregnated surfaces. Int. Commun. Heat Mass Transfer 103, 7–16 (2019)

    Article  Google Scholar 

  11. Haghani-Hassan-Abadi, R., Rahimian, M.-H., Fakhari, A.: Conservative phase-field lattice-Boltzmann model for ternary fluids. J. Comput. Phys. 374, 668–691 (2018)

    Article  MathSciNet  Google Scholar 

  12. Premnath, K.N., Abraham, J.: Lattice Boltzmann model for axisymmetric multiphase flows. Phys. Rev. E 71, 056706 (2005)

    Article  MathSciNet  Google Scholar 

  13. Sun, K., Jia, M., Wang, T.: Numerical investigation of head-on droplet collision with lattice Boltzmann method. Int. J. Heat Mass Transf. 58, 260–275 (2013)

    Article  Google Scholar 

  14. Liang, H., Chai, Z., Shi, B., Guo, Z., Zhang, T.: Phase-field-based lattice Boltzmann model for axisymmetric multiphase flows. Phys. Rev. E 90, 063311 (2014)

    Article  Google Scholar 

  15. Liu, H., Wu, L., Ba, Y., Xi, G., Zhang, Y.: A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio. J. Comput. Phys. 327, 873–893 (2016)

    Article  MathSciNet  Google Scholar 

  16. Liang, H., Li, Y., Chen, J., Xu, J.: Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio. Int. J. Heat Mass Transf. 130, 1189–1205 (2019)

    Article  Google Scholar 

  17. Boyer, F., Lapuerta, C.: Study of a three component Cahn-Hilliard flow model. ESAIM: Mathematical Modelling and Numerical Analysis 40, 653–687 (2006)

    Article  MathSciNet  Google Scholar 

  18. Lee, T., Liu, L.: Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces. J. Comput. Phys. 229, 8045–8063 (2010)

    Article  Google Scholar 

  19. He, X., Chen, S., Doolen, G.D.: A novel thermal model for the lattice Boltzmann method in incompressible limit. J. Comput. Phys. 146, 282–300 (1998)

    Article  MathSciNet  Google Scholar 

  20. He, X., Luo, L.-S.: A priori derivation of the lattice Boltzmann equation. Phys. Rev. E 55, R6333 (1997)

    Article  Google Scholar 

  21. Lee, T., Fischer, P.F.: Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gases. Phys. Rev. E 74, 046709 (2006)

    Article  Google Scholar 

  22. Plateau, M.: Experimental and theoretical statics of liquid fluids subject to molecular forces only. Smithsonian Report (1863)

  23. Rayleigh, L.: On the instability of jets. Proc. Lond. Math. Soc. 1(10), 4–13 (1878)

    Article  MathSciNet  Google Scholar 

  24. Ashgriz, N., Mashayek, F.: Temporal analysis of capillary jet breakup. J. Fluid Mech. 291, 163–190 (1995)

    Article  Google Scholar 

  25. Tjahjadi, M., Stone, H.A., Ottino, J.M.: Satellite and subsatellite formation in capillary breakup. J. Fluid Mech. 243, 297–317 (1992)

    Article  Google Scholar 

  26. Lafrance, P.: Nonlinear breakup of a laminar liquid jet. Phys. Fluids 18, 428–432 (1975)

    Article  Google Scholar 

  27. Rutland, D., Jameson, G.: Theoretical prediction of the sizes of drops formed in the breakup of capillary jets. Chem. Eng. Sci. 25, 1689–1698 (1970)

    Article  Google Scholar 

  28. Weil, K.G., Rowlinson, J.S., Widom, B.: Molecular Theory of Capillarity. Clarendon Press, Oxford (1982). Berichte der Bunsengesellschaft für physikalische Chemie 88: 586–586 (1984)

  29. Jiang, F., Tsuji, T.: Estimation of three-phase relative permeability by simulating fluid dynamics directly on rock-microstructure images. Water Resour. Res. 53, 11–32 (2017)

    Article  Google Scholar 

  30. Chen, R.-H., Chen, C.-T.: Collision between immiscible drops with large surface tension difference: diesel oil and water. Exp. Fluids 41, 453–461 (2006)

    Article  Google Scholar 

  31. Gao, T.-C., Chen, R.-H., Pu, J.-Y., Lin, T.-H.: Collision between an ethanol drop and a water drop. Exp. Fluids 38, 731–738 (2005)

    Article  Google Scholar 

  32. Planchette, C., Lorenceau, E., Brenn, G.: Liquid encapsulation by binary collisions of immiscible liquid drops. Colloids Surf. A Physicochem. Eng. Aspects 365, 89–94 (2010). (4th International Workshop)

    Article  Google Scholar 

  33. Roisman, I.V., Planchette, C., Lorenceau, E., Brenn, G.: Binary collisions of drops of immiscible liquids. J. Fluid Mech. 690, 512–535 (2012)

    Article  Google Scholar 

  34. Planchette, C., Lorenceau, E., Brenn, G.: The onset of fragmentation in binary liquid drop collisions. J. Fluid Mech. 702, 5–25 (2012)

    Article  Google Scholar 

  35. Wöhrwag, M., Semprebon, C., Mazloomi Moqaddam, A., Karlin, I., Kusumaatmaja, H.: Ternary free-energy entropic lattice Boltzmann model with a high density ratio. Phys. Rev. Lett. 120, 234501 (2018)

    Article  Google Scholar 

  36. Li, G., Lian, Y., Guo, Y., Jemison, M., Sussman, M., Helms, T., Arienti, M.: Incompressible multiphase flow and encapsulation simulations using the moment-of-fluid method. Int. J. Numer. Methods Fluids 79, 456–490 (2015)

    Article  MathSciNet  Google Scholar 

  37. Qian, J., Law, C.K.: Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 59–80 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Reza Haghani-Hassan-Abadi & Mohammad-Hassan Rahimian

Authors
  1. Reza Haghani-Hassan-Abadi
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Mohammad-Hassan Rahimian
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Mohammad-Hassan Rahimian.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Haghani-Hassan-Abadi, R., Rahimian, MH. Axisymmetric lattice Boltzmann model for simulation of ternary fluid flows. Acta Mech 231, 2323–2334 (2020). https://doi.org/10.1007/s00707-020-02663-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-020-02663-1