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Preferred interparticle spacings in trains of particles in inertial microchannel flows

Published online by Cambridge University Press:  25 November 2015

Soroush Kahkeshani ,
Hamed Haddadi  and
Dino Di Carlo
Soroush Kahkeshani
Affiliation:
Department of Bioengineering, California NanoSystems Institute, University of California, Los Angeles, CA 90095, USA
Hamed Haddadi
Affiliation:
Department of Bioengineering, California NanoSystems Institute, University of California, Los Angeles, CA 90095, USA
Dino Di Carlo*
Affiliation:
Department of Bioengineering, California NanoSystems Institute, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: [email protected]
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Abstract

Suspended particles migrate towards inertial focusing positions close to walls and align into trains in finite inertia conduit flow. The relative contribution of inertial and viscous forces at the particle length scale, defined by the particle Reynolds number ($\mathit{Re}_{p}$), is a key parameter, where $\mathit{Re}_{p}=\langle \dot{\unicode[STIX]{x1D6FE}}\rangle D^{2}/\unicode[STIX]{x1D708}$ depends on the mean shear rate $\langle \dot{\unicode[STIX]{x1D6FE}}\rangle$, particle diameter $D$ and fluid kinematic viscosity $\unicode[STIX]{x1D708}$. Controlling the location of inertial focusing positions and the interparticle distance is critical in applications such as flow cytometry, imaging and cell entrapment in droplets. By using experimental observations in rectangular microchannels and lattice Boltzmann numerical simulations of dilute suspension flow, the spacing between particles aligned in trains is measured. From the modes of the probability density function of interparticle spacing, preferred spacings at $5D$ and $2.5D$ are observed. At lower $\mathit{Re}_{p}$, the preferred spacing forms around $5D$, and with increasing $\mathit{Re}_{p}$ the spacing at $2.5D$ becomes more pronounced. With increasing concentration of the suspension the spacing is influenced by particle crowding effects until stable trains are no longer observed.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Complex Fluids: Suspensions
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , R3
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Copyright
© 2015 Cambridge University Press 

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References

Aidun, C. K. & Clausen, J. R. 2010 Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439–472.CrossRefGoogle Scholar
Aidun, C. K., Lu, Y. & Ding, E. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287–311.CrossRefGoogle Scholar
Amini, H., Lee, W. & Di Carlo, D. 2014 Inertial microfluidic physics. Lab on a Chip 14, 2739–2761.CrossRefGoogle ScholarPubMed
Asmolov, E. S. 1999 The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J. Fluid Mech. 381, 63–87.CrossRefGoogle Scholar
Chun, B. & Ladd, A. J. C. 2006 Inertial migration of neutrally buoyant particles in a square duct: an investigation of multiple equilibrium positions. Phys. Fluids 18, 031704.CrossRefGoogle Scholar
Clausen, J. R. & Aidun, C. K. 2009 Galilean invariance in the lattice-Boltzmann method and its effect on the calculation of rheological properties in suspensions. Intl J. Multiphase Flow 35, 307–311.CrossRefGoogle Scholar
Dendukuri, D., Gu, S. S., Pregibon, D. C., Hatton, T. A. & Doyle, P. S. 2007 Stop-flow lithography in a microfluidic device. Lab on a Chip 7, 818–828.CrossRefGoogle Scholar
Di Carlo, D. 2009 Inertial microfluidics. Lab on a Chip 9, 3038–3046.CrossRefGoogle ScholarPubMed
Di Carlo, D., Edd, J. F., Humphry, K. J., Stone, H. A. & Toner, M. 2009 Particle segregation and dynamics in confined flows. Phys. Rev. Lett. 102, 094503.CrossRefGoogle ScholarPubMed
Di Carlo, D., Irimia, D., Tompkins, R. G. & Toner, M. 2007 Continuous inertial focusing, ordering, and separation of particles in microchannels. Proc. Natl Acad. Sci. USA 104, 18892–18897.CrossRefGoogle ScholarPubMed
Duffy, D. C., Mcdonald, C. J., Schueller, O. J. A. & Whitesides, G. M. 1998 Rapid prototyping of microfluidic systems in poly(dimethylsiloxane). Anal. Chem. 70, 4974–4984.CrossRefGoogle ScholarPubMed
Edd, J. F., Di Carlo, D., Humphry, K. J., Koster, S., Irimia, D., Weitz, D. A. & Toner, M. 2008 Controlled encapsulation of single-cells into monodisperse picolitre drops. Lab on a Chip 8, 1262–1264.CrossRefGoogle ScholarPubMed
Haddadi, H. & Morris, J. F. 2014 Microstructure and rheology of finite inertia neutrally buoyant suspensions. J. Fluid Mech. 749, 431–459.CrossRefGoogle Scholar
Haddadi, H. & Morris, J. F. 2015 Topology of pair-sphere trajectories in finite inertia suspension shear flow and its effects on microstructure and rheology. Phys. Fluids 27, 043302.CrossRefGoogle Scholar
Ho, B. P. & Leal, L. G. 1976 Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J. Fluid Mech. 76, 783–799.CrossRefGoogle Scholar
Hood, K., Lee, S. & Roper, M. 2015 Inertial migration of a rigid sphere in three-dimensional Poiseuille flow. J. Fluid Mech. 765, 452–479.CrossRefGoogle Scholar
Humphry, K. J., Kulkarni, P. M., Weitz, D. A., Morris, J. F. & Stone, H. A. 2010 Axial and lateral particle ordering in finite Reynolds number channel flows. Phys. Fluids 22, 081703.CrossRefGoogle Scholar
Hur, S. C., Tse, H. T. K. & Di Carlo, D. 2010 Sheathless inertial cell ordering for extreme throughput flow cytometry. Lab on a Chip 10, 274–280.CrossRefGoogle ScholarPubMed
Ladd, A. J. C. 1994a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309.CrossRefGoogle Scholar
Ladd, A. J. C. 1994b Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311–339.CrossRefGoogle Scholar
Lee, W., Amini, H., Stone, H. A. & Di Carlo, D. 2010 Dynamic self-assembly and control of microfluidic particle crystals. Proc. Natl Acad. Sci. USA 107, 22413–22418.CrossRefGoogle ScholarPubMed
Martel, J. & Toner, M. 2014 Inertial focusing in microfluidics. Annu. Rev. Biomed. Engng 16, 371–396.CrossRefGoogle ScholarPubMed
Matas, J. P., Glezer, V., Guazzelli, E. & Morris, J. F. 2004 Trains of particles in finite-Reynolds-number pipe flow. Phys. Fluids 16, 4192–4195.CrossRefGoogle Scholar
Nguyen, N. Q. & Ladd, A. J. C. 2002 Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys. Rev. E 66, 046708.Google ScholarPubMed
Segre, G. & Silberberg, A. 1961 Radial particle displacements in Poiseuille flow of suspensions. Nature 189, 209–210.CrossRefGoogle Scholar
Uspal, W. E. & Doyle, P. S. 2012 Collective dynamics of small clusters of particles flowing in a quasi-two-dimensional microchannel. Soft Matt. 8, 10676–10686.CrossRefGoogle Scholar