Self-ordered particle trains in inertial microchannel flows

Abstract

Controlling the transport of particles in flowing suspensions at microscale is of interest in numerous contexts such as the development of miniaturized and point-of-care analytical devices (in bioengineering, for foodborne illnesses detection, etc.) and polymer engineering. In square microchannels, neutrally buoyant spherical particles are known to migrate across the flow streamlines and concentrate at specific equilibrium positions located at the channel centerline at low flow inertia and near the four walls along their symmetry planes at moderate Reynolds numbers. Under specific flow and geometrical conditions, the spherical particles are also found to line up in the flow direction and form evenly spaced trains. In order to statistically explore the dynamics of train formation and their dependence on the physical parameters of the suspension flow (particle-to-channel size ratio, Reynolds number and solid volume fraction), experiments have been conducted based on in situ visualizations of the flowing particles by optical microscopy. The trains form only once particles have reached their equilibrium positions (following lateral migration). The percentage of particles in trains and the interparticle distance in a train have been extracted and analyzed. The percentage of particles organized in trains increases with the particle Reynolds number up to a threshold value which depends on the concentration and then decreases for higher values. The average distance between the surfaces of consecutive particles in a train decreases as the particle Reynolds number increases and is independent of the particles size and concentration, if the concentration remains below a threshold value related to the degree of confinement of the suspension flow.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

References

  1. Abbas M, Magaud P, Gao Y, Geoffroy S (2014) Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers. Phys Fluids 26:123301

    Article  Google Scholar 

  2. Amini H, Lee W, Di Carlo D (2014) Inertial microfluidic physics. Lab Chip 14:2739–2761

    Article  Google Scholar 

  3. Asmolov ES (1999) The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J Fluid Mech 381:63–87

    Article  MATH  Google Scholar 

  4. Bhagat AAS, Kuntaegowdanahalli SS, Papautsky I (2008) Inertial microfluidics for continuous particle filtration and extraction. Microfluid Nanofluid 7:217–226

    Article  MATH  Google Scholar 

  5. Choi YS, Seo KW, Lee SJ (2011) Lateral and cross-lateral focusing of spherical particles in a square microchannel. Lab Chip 11:460–465

    Article  Google Scholar 

  6. Chun B, Ladd A (2006) Inertial migration of neutrally buoyant particles in a square duct: an investigation of multiple equilibrium positions. Phys Fluids 18:031704

    Article  Google Scholar 

  7. Di Carlo D (2009) Inertial microfluidics. Lab Chip 9:3038–3046

    Article  Google Scholar 

  8. Di Carlo D, Irimia D, Tompkins RG, Toner M (2007) Continuous inertial focusing, ordering, and separation of particles in microchannels. Proc Natl Acad Sci 104:18892–18897

    Article  Google Scholar 

  9. Di Carlo D, Edd JF, Humphry KJ, Stone HA, Toner M (2009) Particle segregation and dynamics in confined flows. Phys Rev Lett 102:094503

    Article  Google Scholar 

  10. Edd JF, Di Carlo D, Humphry KJ, Koster S, Irimia D, Weitz DA, Toner M (2008) Controlled encapsulation of single-cells into monodisperse picolitre drops. Lab Chip 8:1262–1264

    Article  Google Scholar 

  11. Haddadi H, Morris JF (2015) Topology of pair-sphere trajectories in finite inertia suspension shear flow and its effects on microstructure and rheology. Phys Fluids 27:043302

    Article  Google Scholar 

  12. Ho B, Leal L (1974) Inertial migration of rigid spheres in two-dimensional unidirectional flows. J Fluid Mech 65:365–400

    Article  MATH  Google Scholar 

  13. Hood K, Lee S, Roper M (2015) Inertial migration of a rigid sphere in three-dimensional Poiseuille flow. J Fluid Mech 765:452–479

    Article  MATH  MathSciNet  Google Scholar 

  14. Humphry KJ, Kulkarni PM, Weitz DA, Morris JF, Stone HA (2010) Axial and lateral particle ordering in finite Reynolds number channel flows. Phys Fluids 22:081703

    Article  Google Scholar 

  15. Hur SC, Tse HT, Di Carlo D (2010) Sheathless inertial cell ordering for extreme throughput flow cytometry. Lab Chip 10:274–280

    Article  Google Scholar 

  16. Kahkeshani S, Haddadi H, Di Carlo D (2016) Preferred interparticle spacings in trains of particles in inertial microchannel flows. J Fluid Mech 786:R3

    Article  Google Scholar 

  17. Kulkarni PM, Morris JF (2008) Pair-sphere trajectories in finite-Reynolds-number shear flow. J Fluid Mech 596:413–435

    Article  MATH  MathSciNet  Google Scholar 

  18. Lee W, Amini H, Stone HA, Di Carlo D (2010) Dynamic self-assembly and control of microfluidic particle crystals. Proc Natl Acad Sci USA 107:22413–22418

    Article  Google Scholar 

  19. Martel JM, Toner M (2013) Particle Focusing in Curved Microfluidic Channels. Scientific Reports 3

  20. Matas J-P, Glezer V, Guazzelli É, Morris JF (2004) Trains of particles in finite-Reynolds-number pipe flow. Phys Fluids 16:4192–4195

    Article  MATH  Google Scholar 

  21. Mikulencak DR, Morris JF (2004) Stationary shear flow around fixed and free bodies at finite Reynolds number. J Fluid Mech 520:215–242

    Article  MATH  MathSciNet  Google Scholar 

  22. Nakagawa N, Yabu T, Otomo R, Kase A, Makino M, Itano T, Sugihara-Seki M (2015) Inertial migration of a spherical particle in laminar square channel flows from low to high Reynolds numbers. J Fluid Mech 779:776–793

    Article  MATH  MathSciNet  Google Scholar 

  23. Oakey J, Applegate RW Jr, Arellano E, Di Carlo D, Graves SW, Toner M (2010) Particle focusing in staged inertial microfluidic devices for flow cytometry. Anal Chem 82:3862–3867

    Article  Google Scholar 

  24. Pamme N (2007) Continuous flow separations in microfluidic devices. Lab Chip 7:1644–1659

    Article  Google Scholar 

  25. Poiseuille J (1836) Observations of blood flow. Ann Sci Nat Srie 5:1836

    Google Scholar 

  26. Saffman P (1965) The lift on a small sphere in a slow shear flow. J Fluid Mech 22:385–400

    Article  MATH  Google Scholar 

  27. Schonberg JA, Hinch E (1989) Inertial migration of a sphere in Poiseuille flow. J Fluid Mech 203:517–524

    Article  MATH  MathSciNet  Google Scholar 

  28. Segre G, Silberberg A (1962) Behaviour of macroscopic rigid spheres in Poiseuille flow Part 2. Experimental results and interpretation. J Fluid Mech 14:136–157

    Article  MATH  Google Scholar 

  29. Shao X, Yu Z, Sun B (2008) Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers. Phys Fluids 20:103307

    Article  MATH  Google Scholar 

  30. Vasseur P, Cox R (1976) The lateral migration of a spherical particle in two-dimensional shear flows. J Fluid Mech 78:385–413

    Article  MATH  Google Scholar 

  31. Zurita-Gotor M, BŁAwzdziewicz J, Wajnryb E (2007) Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres. J Fluid Mech 592:447–469

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was partly supported by the Fédération de Recherche FERMAT, FR 3089 and the China Scholarship Council.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Lucien Baldas.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gao, Y., Magaud, P., Baldas, L. et al. Self-ordered particle trains in inertial microchannel flows. Microfluid Nanofluid 21, 154 (2017). https://doi.org/10.1007/s10404-017-1993-5

Download citation

Keywords

  • Microfluidics
  • Inertial focusing
  • Train of particles
  • Hydrodynamic self-assembly