Skip to main content
SpringerLink
Log in

Nonlinear dynamics and manipulation of dripping in capillary flow focusing

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

In this study, we carried out experimental and numerical investigations on the dripping dynamics in axisymmetric capillary flow focusing. For the direct numerical simulations, we solved the Navier-Stokes equations coupled with a diffuse interface method. For the experiments, we observed both periodic and non-periodic dripping modes at different focused and focusing liquid flow rates. The non-periodic dripping that results in polydispersed droplets downstream the orifice can be attributed to the nonlinear dynamics of the flow; thus, we constructed numerical plots of the streamlines and temporal evolutions of the focused liquid cone in different modes. We identified a phase diagram of the dripping regimes in the plane of mainly dimensionless parameters, which led us to further investigate the effects of liquid physical properties, such as viscosity and interface tension, on the mode transition. For suppression of the nonlinear dynamics, we proposed a geometrical optimization that imports a guiding rod positioning along the axis of the capillary tube. Here, we conducted a numerical analysis on the manipulation of the dripping process, as well as scaling analysis on the appearance of the nonlinear dripping. We expect this study to provide an insight into the underlying physical mechanisms of dripping in flow focusing, which are advantageous in the generation of monodispersed microdroplets for various applications.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. L. Anna, Annu. Rev. Fluid Mech. 48, 285 (2016).

    ADS  MathSciNet  Google Scholar 

  2. P. Zhu, and L. Wang, Lab. Chip. 17, 34 (2017).

    Google Scholar 

  3. Y. S. Yu, X. L. Xia, X. Zheng, X. Huang, and J. Z. Zhou, Sci. China-Phys. Mech. Astron. 60, 094612 (2017).

    ADS  Google Scholar 

  4. B. Liao, G. F. Zhang, Y. J. Zhu, Z. F. Li, E. Q. Li, and J. M. Yang, Sci. China-Phys. Mech. Astron. 61, 104721 (2018).

    ADS  Google Scholar 

  5. S. L. Anna, N. Bontoux, and H. A. Stone, Appl. Phys. Lett. 82, 364 (2003).

    ADS  Google Scholar 

  6. G. M. Whitesides, Nature 442, 368 (2006).

    ADS  Google Scholar 

  7. A. S. Utada, E. Lorenceau, D. R. Link, P. D. Kaplan, H. A. Stone, and D. A. Weitz, Science 308, 537 (2005).

    ADS  Google Scholar 

  8. A. S. Utada, A. Fernandez-Nieves, H. A. Stone, and D. A. Weitz, Phys. Rev. Lett. 99, 094502 (2007).

    ADS  Google Scholar 

  9. C. D. Xue, X. D. Chen, C. Liu, and G. Q. Hu, Sci. China-Phys. Mech. Astron. 59, 674711 (2016).

    Google Scholar 

  10. A. M. Gañán-Calvo, Phys. Rev. Lett. 80, 285 (1998).

    ADS  Google Scholar 

  11. A. Barrero, and I. G. Loscertales, Annu. Rev. Fluid Mech. 39, 89 (2007).

    ADS  Google Scholar 

  12. A. M. Gañán-Calvo, J. M. Montanero, L. Martín-Banderas, and M. Flores-Mosquera, Adv. Drug Deliver. Rev. 65, 1447 (2013).

    Google Scholar 

  13. T. Si, G. B. Li, and X. Z. Yin, Adv. Mech. 47, 201701 (2017).

    Google Scholar 

  14. T. Si, F. Li, X. Y. Yin, and X. Z. Yin, J. Fluid Mech. 629, 1 (2009).

    ADS  Google Scholar 

  15. T. Si, F. Li, X. Y. Yin, and X. Z. Yin, Phys. Fluids 22, 112105 (2010).

    ADS  Google Scholar 

  16. A. M. Gañán-Calvo, and J. M. Gordillo, Phys. Rev. Lett. 87, 274501 (2001).

    Google Scholar 

  17. A. M. Gañán-Calvo, Phys. Rev. E 69, 027301 (2004).

    ADS  Google Scholar 

  18. A. M. Gañán-calvo, J. Fluid Mech. 553, 75 (2006).

    ADS  Google Scholar 

  19. K. Mu, H. Ding, and T. Si, Microfluid Nanofluid 22, 138 (2018).

    Google Scholar 

  20. T. Si, H. Feng, X. Luo, and R. X. Xu, Microfluid Nanofluid 18, 967 (2015).

    Google Scholar 

  21. Z. Zhu, T. Si, and R. X. Xu, Lab. Chip. 15, 646 (2015).

    Google Scholar 

  22. T. Si, G. Li, Q. Wu, Z. Zhu, X. Luo, and R. X. Xu, Appl. Phys. Lett. 108, 111109 (2016).

    ADS  Google Scholar 

  23. Q. Wu, C. Yang, G. Liu, W. Xu, Z. Zhu, T. Si, and R. X. Xu, Lab. Chip. 17, 3168 (2017).

    Google Scholar 

  24. M. A. Herrada, A. M. Gañán-Calvo, A. Ojeda-Monge, B. Bluth, and P. Riesco-Chueca, Phys. Rev. E 78, 036323 (2008), arXiv: 0804.3138.

    ADS  Google Scholar 

  25. F. Cruz-Mazo, J. M. Montanero, and A. M. Gañán-Calvo, Phys. Rev. E 94, 053122 (2016).

    ADS  Google Scholar 

  26. E. J. Vega, A. J. Acero, J. M. Montanero, M. A. Herrada, and A. M. Gañán-Calvo, Phys. Rev. E 89, 063012 (2014).

    ADS  Google Scholar 

  27. C. Clanet, and J. C. Lasheras, J. Fluid Mech. 383, 307 (1999).

    ADS  MathSciNet  Google Scholar 

  28. B. Ambravaneswaran, S. D. Phillips, and O. A. Basaran, Phys. Rev. Lett. 85, 5332 (2000).

    ADS  Google Scholar 

  29. B. Ambravaneswaran, H. J. Subramani, S. D. Phillips, and O. A. Basaran, Phys. Rev. Lett. 93, 034501 (2004).

    ADS  Google Scholar 

  30. H. J. Subramani, H. K. Yeoh, R. Suryo, Q. Xu, B. Ambravaneswaran, and O. A. Basaran, Phys. Fluids 18, 032106 (2006).

    ADS  MathSciNet  Google Scholar 

  31. C. Cramer, P. Fischer, and E. J. Windhab, Chem. Eng. Sci. 59, 3045 (2004).

    Google Scholar 

  32. C. Cramer, S. Studer, E. J. Windhab, and P. Fischer, Phys. Fluids 24, 093101 (2012).

    ADS  Google Scholar 

  33. P. Garstecki, I. Gitlin, W. DiLuzio, G. M. Whitesides, E. Kumacheva, and H. A. Stone, Appl. Phys. Lett. 85, 2649 (2004).

    ADS  Google Scholar 

  34. P. Garstecki, M. J. Fuerstman, and G. M. Whitesides, Phys. Rev. Lett. 94, 234502 (2005).

    ADS  Google Scholar 

  35. D. Jacqmin, J. Comput. Phys. 155, 96 (1999).

    ADS  MathSciNet  Google Scholar 

  36. P. Zuo, and Y. P. Zhao, Phys. Chem. Chem. Phys. 17, 287 (2015).

    Google Scholar 

  37. Y. P. Zhao, Physical Mechanics of Surfaces and Interfaces (Science Press, Beijing, 2012)

    Google Scholar 

  38. F. Magaletti, F. Picano, M. Chinappi, L. Marino, and C. M. Casciola, J. Fluid Mech. 714, 95 (2013).

    ADS  MathSciNet  Google Scholar 

  39. H. Ding, P. D. M. Spelt, and C. Shu, J. Comput. Phys. 226, 2078 (2007).

    ADS  Google Scholar 

  40. K. Mu, T. Si, E. Li, R. X. Xu, and H. Ding, Phys. Fluids 30, 012111 (2018).

    ADS  Google Scholar 

  41. H. Ding, and P. D. M. Spelt, Phys. Rev. E 75, 46708 (2007).

    ADS  Google Scholar 

  42. Y. Sui, H. Ding, and P. D. M. Spelt, Annu. Rev. Fluid Mech. 46, 97 (2014).

    ADS  Google Scholar 

  43. H. Liu, K. Mu, and H. Ding, Appl. Math. Mech.-Engl. Ed. 37, 1405 (2016).

    Google Scholar 

  44. H. Ding, B. Q. Chen, H. R. Liu, C. Y. Zhang, P. Gao, and X. Y. Lu, J. Fluid Mech. 783, 504 (2015).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230026, China

    Kai Mu, Ting Si & Hang Ding

Authors
  1. Kai Mu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ting Si
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hang Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ting Si.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mu, K., Si, T. & Ding, H. Nonlinear dynamics and manipulation of dripping in capillary flow focusing. Sci. China Phys. Mech. Astron. 62, 124713 (2019). https://doi.org/10.1007/s11433-019-9444-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-019-9444-8

Keywords

Search

Navigation