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Effects of viscoelasticity on droplet dynamics and break-up in microfluidic T-Junctions: a lattice Boltzmann study

  • Anupam GuptaEmail author
  • Mauro Sbragaglia
Regular Article
Part of the following topical collections:
  1. Multi-scale phenomena in complex flows and flowing matter

Abstract.

The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number (Ca), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to Ca \( \approx\) 3×10-2. A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). We present the results of three-dimensional simulations in a range of Ca which is broad enough to characterize all the three characteristic mechanisms of break-up in the confined T-junction, i.e. squeezing, dripping and jetting regimes. The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time \( \tau_{P}\) and the finite extensibility parameter L2, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. We will analyze cases with Droplet Viscoelasticity (DV), where viscoelastic properties are confined in the dispersed (d) phase, as well as cases with Matrix Viscoelasticity (MV), where viscoelastic properties are confined in the continuous (c) phase. Moderate flow-rate ratios Q \( \approx\) O(1) of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, as the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by the polymer stresses.

Graphical abstract

Keywords

Topical Issue: Multi-scale phenomena in complex flows and flowing matter 

References

  1. 1.
    G.F. Christopher, S.L. Anna, J. Phys. D Appl. Phys. 40, R319 (2007)CrossRefADSGoogle Scholar
  2. 2.
    R. Seemann, M. Brinkmann, T. Pfohl, S. Herminghaus, Rep. Prog. Phys. 75, 016601 (2012)CrossRefADSGoogle Scholar
  3. 3.
    G.F. Christopher, N.N. Noharuddin, J.A. Taylor, S.L. Anna, Phys. Rev. E 78, 036317 (2008)CrossRefADSGoogle Scholar
  4. 4.
    S. Teh, R. Lin, L. Hung, A. Lee, Lab Chip 8, 198 (2008)CrossRefGoogle Scholar
  5. 5.
    C.N. Baroud, F. Gallaire, R. Dangla, Lab Chip 10, 2032 (2010)CrossRefGoogle Scholar
  6. 6.
    T. Glawdel, C. Elbuken, L. Ren, Phys. Rev. E 85, 016322 (2012)CrossRefADSGoogle Scholar
  7. 7.
    T. Glawdel, C. Elbuken, L. Ren, Phys. Rev. E 85, 016323 (2012)CrossRefADSGoogle Scholar
  8. 8.
    T. Glawdel, L. Ren, Phys. Rev. E 85, 026308 (2012)CrossRefADSGoogle Scholar
  9. 9.
    M.D. Menech, P. Garstecki, F. Jousse, H.A. Stone, J. Fluid. Mech. 595, 141 (2008)CrossRefADSzbMATHGoogle Scholar
  10. 10.
    M.D. Menech, Phys. Rev. E 73, 031505 (2006)CrossRefADSGoogle Scholar
  11. 11.
    H. Liu, Y. Zhang, J. Appl. Phys. 106, 034906 (2009)CrossRefADSGoogle Scholar
  12. 12.
    H. Liu, Y. Zhang, Phys. Fluids 23, 082101 (2011)CrossRefADSGoogle Scholar
  13. 13.
    L. Derzsi, M. Kasprzyk, J.P. Plog, P. Garstecki, Phys. Fluids 25, 092001 (2013)CrossRefADSGoogle Scholar
  14. 14.
    P. Garstecki, M.J. Fuerstman, H.A. Stone, G.M. Whiteside, Lab Chip 6, 437 (2006)CrossRefGoogle Scholar
  15. 15.
    P.E. Arratia, J.P. Gollub, D.J. Durian, Phys. Rev. E 77, 036309 (2008)CrossRefADSGoogle Scholar
  16. 16.
    B. Steinhaus, A.Q. Shen, R. Sureshkumar, Phys. Fluids 19, 073103 (2007)CrossRefADSGoogle Scholar
  17. 17.
    J. Husny, J. Cooper-White, J. Non-Newton. Fluid Mech. 137, 121 (2006)CrossRefGoogle Scholar
  18. 18.
    P.E. Arratia, L.A. Cramer, J.P. Gollub, D.J. Durian, New J. Phys. 11, 115006 (2009)CrossRefADSGoogle Scholar
  19. 19.
    W. Wang, Z. Liu, Y. Jin, Y. Cheng, Chem. Eng. J. 173, 828 (2011)CrossRefGoogle Scholar
  20. 20.
    S. Van der Graaf, T. Nisisako, R. Schron, C.G.P.H. Van der Sman, R. Boom, Langmuir 22, 4144 (2006)CrossRefGoogle Scholar
  21. 21.
    S. Arias, D. Legendre, R. González-Cinca, Comput. Fluids 56, 49 (2012)CrossRefGoogle Scholar
  22. 22.
    A. Gupta, S.M.S. Murshed, R. Kumar, Appl. Phys. lett. 94, 164107 (2009)CrossRefADSGoogle Scholar
  23. 23.
    A. Gupta, R. Kumar, Phys. Fluids 22, 122001 (2010)CrossRefADSGoogle Scholar
  24. 24.
    C. Wagner, Y. Amarouchene, D. Bonn, J. Eggers, Phys. Rev. Lett. 95, 164504 (2005)CrossRefADSGoogle Scholar
  25. 25.
    A. Lindner, J. Vermant, D. Bonn, Physica A 319, 125 (2003)CrossRefADSGoogle Scholar
  26. 26.
    R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids (J. Wiley & Sons, 1987)Google Scholar
  27. 27.
    M. Herrchen, H. Oettinger, J. Non-Newton. Fluid Mech. 68, 17 (1997)CrossRefGoogle Scholar
  28. 28.
    J. Zhang, Microfluid Nanofluid 10, 1 (2011)CrossRefzbMATHGoogle Scholar
  29. 29.
    C.K. Aidun, J.R. Clausen, Annu. Rev. Fluid Mech. 42, 439 (2010)CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    H. Xi, C. Duncan, Phys. Rev. E 59, 3022 (1999)CrossRefADSGoogle Scholar
  31. 31.
    R.G.M.V. der Sman, S.V. der Graaf, Comput. Phys. Commun. 178, 492 (2008)CrossRefADSzbMATHGoogle Scholar
  32. 32.
    A.E. Komrakovaa, O. Shardt, D. Eskinb, J.J. Derksen, Int. J. Multiphase Flow 59, 23 (2014)CrossRefGoogle Scholar
  33. 33.
    H. Liu, A.J. Valocchi, Q. Kang, Phys. Rev. E 85, 046309 (2012)CrossRefADSGoogle Scholar
  34. 34.
    N. Moradi, F. Varnik, I. Steinbach, EPL 95, 44003 (2011)CrossRefADSGoogle Scholar
  35. 35.
    S. Thampi, R. Adhikari, R. Govindarajan, Langmuir 29, 3339 (2013)CrossRefGoogle Scholar
  36. 36.
    P. Yue, J.J. Feng, C. Liu, J. Shen, J. Fluid Mech. 515, 293 (2004)CrossRefADSMathSciNetzbMATHGoogle Scholar
  37. 37.
    P. Yue, J.J. Feng, C. Liu, J. Shen, J. Non-Newton. Fluid Mech. 129, 163 (2005)CrossRefzbMATHGoogle Scholar
  38. 38.
    P. Yue, C. Zhou, J.J. Feng, C.F. Ollivier-Gooch, H.H. Hu, J. Comput. Phys. 219, 47 (2006)CrossRefADSMathSciNetzbMATHGoogle Scholar
  39. 39.
    P. Yue, C. Zhou, J.J. Feng, Phys. Fluids 18, 102102 (2006)CrossRefADSGoogle Scholar
  40. 40.
    D. Zhou, P. Yue, J.J. Feng, J. Rheol. 52, 469 (2008)CrossRefADSGoogle Scholar
  41. 41.
    P. Yue, J.J. Feng, J. Non-Newton. Fluid Mech. 189, 8 (2012)CrossRefGoogle Scholar
  42. 42.
    A. Gupta, M. Sbragaglia, A. Scagliarini, J. Comput. Phys. 291, 177 (2015)CrossRefADSMathSciNetGoogle Scholar
  43. 43.
    A. Gupta, M. Sbragaglia, Phys. Rev. E 90, 023305 (2014)CrossRefADSGoogle Scholar
  44. 44.
    X. Shan, H. Chen, Phys. Rev. E 47, 1815 (1993)CrossRefADSGoogle Scholar
  45. 45.
    X. Shan, H. Chen, Phys. Rev. E 49, 2941 (1994)CrossRefADSGoogle Scholar
  46. 46.
    M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, F. Toschi, Phys. Rev. Lett. 97, 204503 (2006)CrossRefADSGoogle Scholar
  47. 47.
    M. Sbragaglia, K. Sugiyama, L. Biferale, J. Fluid. Mech. 614, 471 (2008)CrossRefADSMathSciNetzbMATHGoogle Scholar
  48. 48.
    F. Greco, J. Non-Newton. Fluid Mech. 107, 111 (2002)CrossRefzbMATHGoogle Scholar
  49. 49.
    F. Greco, Phys. Fluids 14, 946 (2002)CrossRefADSMathSciNetzbMATHGoogle Scholar
  50. 50.
    M. Minale, S. Caserta, S. Guido, Langmuir 26, 126 (2010)CrossRefGoogle Scholar
  51. 51.
    M. Minale, J. Non-Newton. Fluid Mech. 123, 151 (2004)CrossRefzbMATHGoogle Scholar
  52. 52.
    M. Minale, Rheol. Acta 49, 789 (2010)CrossRefGoogle Scholar
  53. 53.
    D. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction (Springer Verlag, 2001)Google Scholar
  54. 54.
    L. Amaya-Bower, T. Lee, Philos. Trans. Roy. Soc. A 369, 2405 (2011)CrossRefADSMathSciNetzbMATHGoogle Scholar
  55. 55.
    O. Shonibare, K. Feigl, F.X. Tanner, (2015) pp. 1--12, DOI:10.13140/RG.2.1.1198.4806
  56. 56.
    S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, 2001)Google Scholar
  57. 57.
    B. Dü, Phys. Rev. E 76, 036704 (2007)CrossRefADSMathSciNetGoogle Scholar
  58. 58.
    D. d’Humiè, Philos. Trans. Roy. Soc. London 360, 437 (2002)CrossRefGoogle Scholar
  59. 59.
    K. Premnath, J. Abraham, J. Comput. Phys. 224, 539 (2007)CrossRefADSMathSciNetzbMATHGoogle Scholar
  60. 60.
    M. Sega, M.S.S.S. Kantorovich, A.O. Ivanovd, Soft Matter 9, 10092 (2013)CrossRefADSGoogle Scholar
  61. 61.
    Z. Guo, C. Zheng, B. Shi, Phys. Rev. E 65, 046308 (2002)CrossRefADSGoogle Scholar
  62. 62.
    R. Benzi, M. Sbragaglia, S. Succi, M. Bernaschi, S. Chibbaro, J. Chem. Phys. 131, 104903 (2009)CrossRefADSGoogle Scholar
  63. 63.
    M. Sbragaglia, R. Benzi, M. Bernaschi, S. Succi, Soft Matter 8, 10773 (2012)CrossRefADSGoogle Scholar
  64. 64.
    M. Sbragaglia, D. Belardinelli, Phys. Rev. E 88, 013306 (2013)CrossRefADSGoogle Scholar
  65. 65.
    P. Perlekar, D. Mitra, R. Pandit, Phys. Rev. Lett. 97, 264501 (2006)CrossRefADSGoogle Scholar
  66. 66.
    T. Vaithianathan, L.R. Collins, J. Comput. Phys. 187, 1 (2003)CrossRefADSzbMATHGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Physics and INFNUniversity of “Tor Vergata”RomeItaly

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