Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

Abstract.

We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are available in the literature, which assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech 78, 227 (1998); M. Minale, Rheol. Acta 47, 667 (2008)). Beyond the practical importance of using a mesoscale simulation to assess “ab initio” the robustness and limitations of such theoretical models, our simulations are also key to discuss --in controlled situations-- some relevant phenomenology related to the interplay between the flow time scales and the droplet time scales regarding the “transparency” transition for high enough shear frequencies for an external oscillating flow. This work may be regarded as a step forward to discuss extensions towards a novel DNS approach, describing the mesoscale physics of small droplets subjected to a generic hydrodynamical strain field, possibly mimicking the effect of a realistic turbulent flow on dilute droplet suspensions.

Graphical abstract

This is a preview of subscription content, access via your institution.

References

  1. 1

    R. Benzi, S. Succi, M. Vergassola, Phys. Rep. 222, 145 (1992)

    ADS  Article  Google Scholar 

  2. 2

    S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, 2001).

  3. 3

    M. Sbragaglia, R. Benzi, M. Bernaschi, S. Succi, Soft Matter 8, 10773 (2012)

    ADS  Article  Google Scholar 

  4. 4

    J. Onishi, Y. Chen, H. Ohashi, Prog. Comput. Fluid Dyn. 5, 75 (2005)

    Article  Google Scholar 

  5. 5

    M. Gross, M.E. Cates, F. Varnik, R. Adhikari, J. Stat. Mech.: Theor. Exp. 2011, P03030 (2011)

    Article  Google Scholar 

  6. 6

    R.W. Flumerfelt, Ind. Eng. Chem. Fundam. 11, 312 (1972)

    Article  Google Scholar 

  7. 7

    G.I. Taylor, Proc. R. Soc. A 138, 41 (1932)

    ADS  Article  Google Scholar 

  8. 8

    F. Greco, J. Non-Newton. Fluid Mech. 107, 111 (2002)

    Article  Google Scholar 

  9. 9

    S. Guido, F. Greco, Rheol. Rev. 2, 99 (2004)

    Google Scholar 

  10. 10

    S. Guido, M. Simeone, F. Greco, J. Non-Newton. Fluid Mech. 114, 65 (2003)

    Article  Google Scholar 

  11. 11

    V. Sibillo, M. Simeone, S. Guido, F. Greco, P.L. Maffettone, J. Non-Newton. Fluid Mech. 134, 27 (2006)

    Article  Google Scholar 

  12. 12

    K. Premnath, J. Abraham, J. Comput. Phys. 224, 539 (2007)

    ADS  MathSciNet  Article  Google Scholar 

  13. 13

    M. Tomé, L. Grossi, A. Castelo, J. Cuminato, S. McKee, K. Walters, J. Non-Newton. Fluid Mech. 141, 148 (2007)

    Article  Google Scholar 

  14. 14

    M. Minale, Rheol. Acta 47, 667 (2008)

    Article  Google Scholar 

  15. 15

    M. Shapira, S. Haber, Int. J. Multiphase Flow 16, 305 (1990)

    Article  Google Scholar 

  16. 16

    P.L. Maffettone, F. Greco, J. Rheol. 48, 83 (2003)

    Article  Google Scholar 

  17. 17

    P.L. Maffettone, F. Greco, M. Simeone, S. Guido, J. Non-Newton. Fluid Mech. 126, 145 (2005)

    Article  Google Scholar 

  18. 18

    A. Gupta, M. Sbragaglia, Phys. Rev. E 90, 023305 (2014)

    ADS  Article  Google Scholar 

  19. 19

    F. Greco, Phys. Fluids 14, 946 (2002)

    ADS  MathSciNet  Article  Google Scholar 

  20. 20

    P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech. 78, 227 (1998)

    Article  Google Scholar 

  21. 21

    S. Guido, M. Villone, J. Rheol. 42, 395 (1998)

    ADS  Article  Google Scholar 

  22. 22

    H.A. Stone, Annu. Rev. Fluid Mech. 26, 65 (1994)

    ADS  Article  Google Scholar 

  23. 23

    K. Verhulst, R. Cardinaels, P. Moldenaers, Y. Renardy, S. Afkhami, J. Non-Newton. Fluid Mech. 156, 29 (2009)

    Article  Google Scholar 

  24. 24

    K. Verhulst, R. Cardinaels, P. Moldenaers, S. Afkhami, Y. Renardy, J. Non-Newton. Fluid Mech. 156, 44 (2009)

    Article  Google Scholar 

  25. 25

    N. Aggarwal, K. Sarkar, J. Fluid Mech. 601, 63 (2008)

    ADS  Article  Google Scholar 

  26. 26

    S. Mukherjee, K. Sarkar, J. Non-Newton. Fluid Mech. 165, 340 (2010)

    Article  Google Scholar 

  27. 27

    R. Cardinaels, P. Moldenaers, Microfluid Nanofluid 10, 1153 (2011)

    Article  Google Scholar 

  28. 28

    S. Guido, Curr. Opin. Colloid Interface Sci. 16, 61 (2011)

    Article  Google Scholar 

  29. 29

    R. Cardinaels, K. Verhulst, P. Moldenaers, J. Rheol. 53, 1403 (2009)

    ADS  Article  Google Scholar 

  30. 30

    R. Cardinaels, P. Moldenaers, Rheol. Acta 49, 941 (2010)

    Article  Google Scholar 

  31. 31

    R. Cardinaels, A. Vananroye, P. Van Puyvelde, P. Moldenaers, Macromol. Mater. Eng. 296, 214 (2011)

    Article  Google Scholar 

  32. 32

    A. Gupta, M. Sbragaglia, A. Scagliarini, J. Comput. Phys. 291, 177 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  33. 33

    R. Cardinaels, P. Moldenaers, J. Polym. Sci. Part B 48, 1372 (2010)

    Article  Google Scholar 

  34. 34

    P. Yue, J.J. Feng, C. Liu, J. Shen, J. Fluid Mech. 515, 293 (2004)

    ADS  MathSciNet  Article  Google Scholar 

  35. 35

    M. Minale, Rheol. Acta 49, 789 (2010)

    Article  Google Scholar 

  36. 36

    D.O. Njobuenwu, M. Fairweather, Chem. Eng. Sci. 123, 265 (2015)

    Article  Google Scholar 

  37. 37

    L. Biferale, C. Meneveau, R. Verzicco, J. Fluid Mech. 754, 184 (2014)

    ADS  Article  Google Scholar 

  38. 38

    V. Spandan, D. Lohse, R. Verzicco, J. Fluid Mech. 809, 480 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  39. 39

    M. Minale, J. Non-Newton. Fluid Mech. 123, 151 (2004)

    Article  Google Scholar 

  40. 40

    M. Minale, S. Caserta, S. Guido, Langmuir 26, 126 (2010)

    Article  Google Scholar 

  41. 41

    P. Yue, J.J. Feng, C. Liu, J. Shen, J. Fluid Mech. 540, 427 (2005)

    ADS  Article  Google Scholar 

  42. 42

    R.G.M. van der Sman, S. van der Graaf, Comput. Phys. Commun. 178, 492 (2008)

    ADS  Article  Google Scholar 

  43. 43

    A.E. Komrakovaa, O. Shardt, D. Eskinb, J.J. Derksen, Int. J. Multiphase Flow 59, 23 (2014)

    Article  Google Scholar 

  44. 44

    H. Xi, C. Duncan, Phys. Rev. E 59, 3022 (1999)

    ADS  Article  Google Scholar 

  45. 45

    V. Sibillo, G. Pasquariello, M. Simeone, V. Cristini, S. Guido, Phys. Rev. Lett. 97, 054502 (2006)

    ADS  Article  Google Scholar 

  46. 46

    C.E. Chaffey, H. Brenner, J. Colloid Interface Sci. 24, 258 (1967)

    ADS  Article  Google Scholar 

  47. 47

    Y.Y. Renardy, V. Cristini, Phys. Fluids 13, 7 (2001)

    ADS  MathSciNet  Article  Google Scholar 

  48. 48

    K. Verhulst, P. Moldenaers, M. Minale, J. Rheol. 51, 261 (2007)

    ADS  Article  Google Scholar 

  49. 49

    A. Vananroye, R. Cardinaels, P. Van Puyvelde, P. Moldenaers, J. Rheol. 52, 1459 (2008)

    ADS  Article  Google Scholar 

  50. 50

    X. Shan, H. Chen, Phys. Rev. E 47, 1815 (1993)

    ADS  Article  Google Scholar 

  51. 51

    X. Shan, H. Chen, Phys. Rev. E 49, 2941 (1994)

    ADS  Article  Google Scholar 

  52. 52

    M. Sbragaglia, D. Belardinellli, Phys. Rev. E 88, 013306 (2013)

    ADS  Article  Google Scholar 

  53. 53

    M. Sega, M. Sbragaglia, S. Kantorovich, A. Ivanov, Soft Matter 9, 10092 (2013)

    ADS  Article  Google Scholar 

  54. 54

    D. d'Humières, I. Ginzburg, M. Krafczyk, P. Lallemand, L. Luo, Philos. Trans. R. Soc. A 360, 437 (2002)

    ADS  Article  Google Scholar 

  55. 55

    K. Mattila et al., J. Stat. Mech.: Theor. Exp. 2009, 1742 (2009)

    Article  Google Scholar 

  56. 56

    M. Hecht, J. Harting, J. Stat. Mech.: Theor. Exp. 2010, 1742 (2010)

    Article  Google Scholar 

  57. 57

    Q. Zou, X. He, Phys. Fluids 9, 1070 (1997)

    Article  Google Scholar 

  58. 58

    N. Ioannou, H. Liu, Y.H. Zhang, J. Comput. Sci. 17, 463 (2016)

    MathSciNet  Article  Google Scholar 

  59. 59

    L.D. Landau, E.M. Lifschitz, Fluid Mechanics, 2nd edition (Pergamon Press, 1987)

  60. 60

    W. Yu, M. Bousmina, M. Grmela, C. Zhou, J. Rheol. 46, 1401 (2002)

    ADS  Article  Google Scholar 

  61. 61

    R.G. Cox, J. Fluid Mech. 37, 601 (1969)

    ADS  Article  Google Scholar 

  62. 62

    R. Cavallo, S. Guido, M. Simeone, Rheol. Acta 42, 1 (2002)

    Article  Google Scholar 

  63. 63

    A. Farutin, C. Misbah, J. Fluid Mech. 700, 362 (2012)

    ADS  MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to F. Milan.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Milan, F., Sbragaglia, M., Biferale, L. et al. Lattice Boltzmann simulations of droplet dynamics in time-dependent flows. Eur. Phys. J. E 41, 6 (2018). https://doi.org/10.1140/epje/i2018-11613-0

Download citation

Keywords

  • Topical issue: Fluids and Structures: Multi-scale coupling and modeling