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The motion of rigid particles in the Poiseuille flow of pseudoplastic fluids through straight rectangular microchannels

  • Di Li
  • Xiangchun XuanEmail author
Research Paper
Part of the following topical collections:
  1. Particle motion in non-Newtonian microfluidics

Abstract

There has been in the past decade a significantly growing interest in the use of flow-induced lift forces for a passive control of particle motion in microchannels. This nonlinear microfluidic technique can be implemented in both Newtonian and non-Newtonian fluids. The motions of rigid particles in confined flows of viscoelastic fluids with and without shear-thinning effects have each been well studied in the literature. However, a comprehensive understanding of particle motion in inelastic shear-thinning fluids is still lacking. We present herein a systematic experimental study of the motion of rigid particles in the Poiseuille flow of pseudoplastic xanthan gum (XG) solutions through straight rectangular microchannels. We find that the number and location of particle equilibrium positions are both a strong function of channel dimension, particle size and XG concentration. We attempt to explain the experimental observations using the competition of inertial and elastic lift forces acting on particles. Our experimental results imply a potentially high throughput separation of rigid particles by size in XG solutions.

Keywords

Shear thinning Particle motion Elastic lift Inertial lift Non-Newtonian Microfluidics 

Notes

Acknowledgements

This work was supported in part by NSF under Grant No. CBET-1704379.

References

  1. Amini H, Lee W, Di Carlo D (2014) Inertial microfluidic physics. Lab Chip 14:2739–2761Google Scholar
  2. Asghari M, Serhatlioglu M, Ortaç B, Solmaz ME, Elbuken C (2017) Sheathless microflow cytometry using viscoelastic fluids. Sci Rep 7:12342.  https://doi.org/10.1038/s41598-017-12558-2 CrossRefGoogle 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 381:63–87zbMATHGoogle Scholar
  4. Aytouna M, Paredes J, Shahidzadeh-Bonn N, Moulinet S, Wagner C, Amarouchene Y, Eggers J, Bonn D (2013) Drop formation in non-Newtonian fluids. Phys Rev Lett 110:034501Google Scholar
  5. Barnes HA, Hutton JF, Walters K (1989) An introduction to rheology. Elsevier, AmsterdamzbMATHGoogle Scholar
  6. Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, Vol. 1. Wiley, New YorkGoogle Scholar
  7. Chen Q, Li D, Lin J, Wang MH, Xuan X (2017) Simultaneous washing and separation of nonmagnetic particles in an inertial ferrofluid/water co-flow. Anal Chem 89:6915–6920Google Scholar
  8. Connacher W, Zhang N, Huang A, Mei J, Zhang S, Gopesh T, Friend J (2018) Micro/nano acoustofluidics: materials, phenomena, design, devices, and applications. Lab Chip 18:1952–1996Google Scholar
  9. D’Avino G, Romeo G, Villone MM, Greco F, Netti PA, Maffettone PL (2012) Single line particle focusing induced by viscoelasticity of the suspending liquid: theory, experiments and simulations to design a micropipe flow-focuser. Lab Chip 12:1638–1645Google Scholar
  10. D’Avino G, Maffettone PL (2015) Particle dynamics in viscoelastic liquids. J Non-Newton Fluid Mech 215:80–104MathSciNetGoogle Scholar
  11. D’Avino G, Greco F, Maffettone PL (2017) Particle migration due to viscoelasticity of the suspending liquid and its relevance in microfluidic devices. Annu Rev Fluid Mech 49:341–360MathSciNetzbMATHGoogle Scholar
  12. De Santo I, D’Avino G, Romeo G, Greco F, Maffettone PL (2014) Microfluidic Lagrangian trap for Brownian particles: three-dimensional focusing down to the nanoscale. Phys Rev Appl 2:064001Google Scholar
  13. Del Giudice F, Romeo G, D’Avino G, Greco F, Netti PA, Maffettone PL (2013) Particle alignment in a viscoelastic liquid flowing in a square-shaped microchannel. Lab Chip 13:4263–4271Google Scholar
  14. Del Giudice F, D’Avino G, Greco F, Netti PA, Maffettone PL (2015a) Effect of fluid rheology on particle migration in a square-shaped microchannel. Microfluid Nanofluid 19:95–104Google Scholar
  15. Del Giudice F, Madadi H, Villone MM, D’Avino G, Cusano AM, Vecchione R, Ventre M, Maffettone PL, Netti PA (2015b) Magnetophoresis ‘meets’ viscoelasticity: deterministic separation of magnetic particles in a modular microfluidic device. Lab Chip 15:1912–1922Google Scholar
  16. Del Giudice F, Sathish S, D’Avino G, Shen AQ (2017) “From the edge to the center”: viscoelastic migration of particles and cells in a strongly shear-thinning liquid flowing in a microchannel. Anal Chem 89:13146–13159Google Scholar
  17. Dhahir SA, Walters K (1989) On non-newtonian flow past a cylinder in a confined flow. J Rheo 33:781–804Google Scholar
  18. Di Carlo D (2009) Inertial microfluidics. Lab Chip 9:3038–3046Google Scholar
  19. Di Carlo D, Irimia D, Tompkins RG, Toner M (2007) Continuous inertial focusing, ordering, and separation of particles in microchannels. Proc Natl Acad Sci 104:18892–18897Google Scholar
  20. Di Carlo D, Edd JF, Humphry KJ, Stone HA, Toner M (2009) Particle segregation and dynamics in confined flows. Phy Rev Lett 102:094503Google Scholar
  21. Duffy DC, McDonald JC, Schueller OJA, Whitesides GM (1998) Rapid prototyping of microfluidic systems in Poly(dimethylsiloxane). Anal Chem 70:4974–4984Google Scholar
  22. Escudier MP, Smith S (1999) Turbulent flow of Newtonian and shear-thinning liquids through a sudden axisymmetric expansion. Exp Fluid 27:427–434Google Scholar
  23. Gauthier F, Goldsmith HL, Mason SG (1971a) Particle motions in non-Newtonian media. Rheo Acta 10:344–364Google Scholar
  24. Gauthier F, Goldsmith HL, Mason SG (1971b) Particle motions in non-newtonian media. II. Poiseuille flow. Trans Soc Rheol 15:297–330Google Scholar
  25. Geislinger TM, Franke T (2014) Hydrodynamic lift of vesicles and red blood cells in flow from Fåhræus & Lindqvist to microfluidic cell sorting. Adv Colloid Interface Sci 208:161–176Google Scholar
  26. Gou Y, Jia Y, Wang P, Sun C (2018) Progress of inertial microfluidics in principle and application. Sensors 18:1762Google Scholar
  27. Haase AS, Wood JA, Sprakel LM, Lammertink RG (2017) Inelastic non-Newtonian flow over heterogeneously slippery surfaces. Phys Rev E 95:023105Google Scholar
  28. Ho BP, Leal LG (1974) Inertial migration of rigid spheres in two-dimensional unidirectional flows. J Fluid Mech 65:365–400zbMATHGoogle Scholar
  29. Ho BP, Leal LG (1976) Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J Fluid Mech 76:783–799zbMATHGoogle Scholar
  30. Huang PY, Joseph DD (2000) Effects of shear thinning on migration of neutrally buoyant particles in pressure driven flow of Newtonian and viscoelastic fluids. J Non-Newton Fluid Mech 90:159–185zbMATHGoogle Scholar
  31. Huang L, Bian S, Cheng Y, Shi G, Liu P, Ye X, Wang W (2017) Microfluidics cell sample preparation for analysis: advances in efficient cell enrichment and precise single cell capture. Biomicrofluid 11:011501Google Scholar
  32. Hur SC, Tse HTK, Di Carlo D (2010) Sheathless inertial cell ordering for extreme throughput flow cytometry. Lab Chip 10:274–280Google Scholar
  33. Japper-Jaafar A, Escudier MP, Poole RJ (2010) Laminar, transitional and turbulent annular flow of drag-reducing polymer solutions. J Non-Newton Fluid Mech 165:1357–1372Google Scholar
  34. Kang K, Lee SS, Hyun K, Lee SJ, Kim JM (2013) DNA-based highly tunable particle focuser. Nat Commun 4:2567Google Scholar
  35. Karimi A, Yazdi S, Ardekani AM (2013) Hydrodynamic mechanisms of cell and particle trapping in microfluidics. Biomicrofluid 7:021501Google Scholar
  36. Karnis A, Mason SG (1966) Particle motions in sheared suspensions. XIX. Viscoelastic media. Tran Soc Rheol 10:571–592Google Scholar
  37. Karnis A, Goldsmith HL, Mason SG (1963) Axial migration of particles in Poiseuille flow. Nature 200:159–160Google Scholar
  38. Kim B, Kim JM (2016) Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel. Biomicrofluid 10:024111Google Scholar
  39. Kim MJ, Lee DJ, Youn JR, Song YS (2016) Two step label free particle separation in a microfluidic system using elasto-inertial focusing and magnetophoresis. RSC Adv 6:32090–32097Google Scholar
  40. Kung YC, Huang KW, Chong W, Chiou PY (2016) Tunnel dielectrophoresis for tunable, single-stream cell focusing in physiological buffers in high-speed microfluidic flows. Small 12:4343–4348Google Scholar
  41. Lapizco-Encinas BH (2018) On the recent developments of insulator-based dielectrophoresis: a review. Electrophoresis.  https://doi.org/10.1002/elps.201800285 CrossRefGoogle Scholar
  42. Leal LG (1979) The motion of small particles in non-Newtonian fluids. J Non-Newton Fluid Mech 5:33–78zbMATHGoogle Scholar
  43. Leal LG (1980) Particle motions in a viscous fluid. Annu Rev Fluid Mech 12:435–476MathSciNetzbMATHGoogle Scholar
  44. Lee DJ, Brenner H, Youn JR, Song YS (2013) Multiplex particle focusing via hydrodynamic force in viscoelastic fluids. Sci Rep 3:3258Google Scholar
  45. Leshansky AM, Bransky A, Korin N, Dinnar U (2007) Tunable nonlinear viscoelastic “focusing” in a microfluidic device. Phys Rev Lett 98:234501Google Scholar
  46. Li D, Xuan X (2018) Fluid rheological effects on particle migration in a straight rectangular microchannel. Microfluid Nanofluid 22:49Google Scholar
  47. Li G, McKinley GH, Ardekani AM (2015) Dynamics of particle migration in channel flow of viscoelastic fluids. J Fluid Mech 785:486–505MathSciNetzbMATHGoogle Scholar
  48. Li D, Lu X, Xuan X (2016) Viscoelastic separation of particles by size in straight rectangular microchannels: a parametric study for a refined understanding. Anal Chem 88:12303–12309Google Scholar
  49. Li D, Zielinski J, Kozubowski L, Xuan X (2018) Continuous sheath-free separation of drug-treated human fungal pathogen Cryptococcus Neoformans by morphology in biocompatible polymer solutions. Electrophoresis 39:2362–2369Google Scholar
  50. Liang L, Zhu J, Xuan X (2011) Three-dimensional diamagnetic particle deflection in ferrofluid microchannel flows. Biomicrofluid 5:034110Google Scholar
  51. Lim EJ, Ober TJ, Edd JF, Desai SP, Neal D, Bong KW, Doyle PS, McKinley GH, Toner M (2014a) Inertio-elastic focusing of bioparticles in microchannels at high throughput. Nat Comm 5:4120Google Scholar
  52. Lim H, Nam J, Shin S (2014b) Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow. Microfluid Nanofluid 17:683–692Google Scholar
  53. Lindner A, Bonn D, Meunier J (2000) Viscous fingering in a shear-thinning fluid. Phys Fluid 12:256–261MathSciNetzbMATHGoogle Scholar
  54. Liu C, Hu G (2017) High-throughput particle manipulation based on hydrodynamic effects in microchannels. Micromachines 8:73Google Scholar
  55. Liu C, Xue C, Chen X, Shan L, Tian Y, Hu G (2015) Size-based separation of particles and cells utilizing viscoelastic effects in straight microchannels. Anal Chem 87:6041–6048Google Scholar
  56. Liu C, Ding B, Xue C, Tian Y, Hu G, Sun J (2016) Sheathless focusing and separation of diverse nanoparticles in viscoelastic solutions with minimized shear thinning. Anal Chem 88:12547–12553Google Scholar
  57. Liu C, Guo J, Tian F, Yang N, Yan F, Ding Y, Wei J, Hu G, Nie G, Sun J (2017) Field-free isolation of exosomes from extracellular vesicles by microfluidic viscoelastic flows. ACS Nano 11:6968–6976Google Scholar
  58. Lu X, Xuan X (2015) Continuous microfluidic particle separation via elasto-inertial pinched flow fractionation. Anal Chem 87:6389–6396Google Scholar
  59. Lu X, Zhu L, Hua RM, Xuan X (2015) Continuous sheath-free separation of particles by shape in viscoelastic fluids. Appl Phys Lett 107:264102Google Scholar
  60. Lu X, Liu C, Hu G, Xuan X (2017) Particle manipulations in non-Newtonian microfluidics: a review. J Colloid Interface Sci 500:182–201Google Scholar
  61. Martel JM, Toner M (2014) Inertial focusing in microfluidics. Annu Rev Biomed Eng 16:371–396Google Scholar
  62. Mortazavi S, Tryggvason G (2000) A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop. J Fluid Mech 411:325–350zbMATHGoogle Scholar
  63. Munaz A, Shiddiky MJA, Nguyen NT (2018) Recent advances and current challenges in magnetophoresis based micro magnetofluidics. Biomicrofluid 12:031501Google Scholar
  64. Nam J, Tan JK, Khoo BL, Namgung B, Leo HL, Lim CT, Kim S (2015) Hybrid capillary-inserted microfluidic device for sheathless particle focusing and separation in viscoelastic flow. Biomicrofluid 9:064117Google Scholar
  65. Nilsson J, Evander M, Hammarstrom B, Laurell T (2009) Review of cell and particle trapping in microfluidic systems. Anal Chimica Acta 649:141–157Google Scholar
  66. Novo P, Dell’Aica M, Janasek D, Zahedi RP (2016) High spatial and temporal resolution cell manipulation techniques in microchannels. Analyst 141:1888–1905Google Scholar
  67. Poole RJ, Escudier MP (2004) Turbulent flow of viscoelastic liquids through an axisymmetric sudden expansion. J Non-Newton Fluid Mech 117:25–46Google Scholar
  68. Rodd LE, Scott TP, Boger DV, Cooper-White JJ, McKinley GH (2005) The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries. J Non-Newton Fluid Mech 129:1–22Google Scholar
  69. Romeo G, D’Avino G, Greco F, Netti PA, Maffettone PL (2013) Viscoelastic flow-focusing in microchannels: scaling properties of the particle radial distributions. Lab Chip 13:2802–2807Google Scholar
  70. Sajeesh P, Sen AK (2014) Particle separation and sorting in microfluidic devices: a review. Microfluid Nanofluidics 17:1–52Google Scholar
  71. Segre G, Silberberg A (1961) Radial particle displacements in Poiseuille flow of suspensions. Nature 189:209–210Google Scholar
  72. Seo KW, Byeon HJ, Huh HK, Lee SJ (2014a) Particle migration and single-line particle focusing in microscale pipe flow of viscoelastic fluids. RSC Adv 4:3512–3520Google Scholar
  73. Seo KW, Kang YJ, Lee SJ (2014b) Lateral migration and focusing of microspheres in a microchannel flow of viscoelastic fluids. Phys Fluids 26:063301Google Scholar
  74. Sibbitts J, Sellens KA, Jia S, Klasner SA, Culbertson CT (2018) Cellular analysis using microfluidics. Anal Chem 90:65–85Google Scholar
  75. Song HY, Lee SH, Salehiyan R, Hyun K (2016) Relationship between particle focusing and dimensionless numbers in elasto-inertial focusing. Rheol Acta 55:889–900Google Scholar
  76. Stoecklein D, Di Carlo D (2018) Nonlinear microfluidics. Anal Chem.  https://doi.org/10.1021/acs.analchem.8b05042 CrossRefGoogle Scholar
  77. Takemura F, Magnaudet J, Dimitrakopoulos P (2009) Migration and deformation of bubbles rising in a wall-bounded shear flow at finite Reynolds number. J Fluid Mech 634:463–486zbMATHGoogle Scholar
  78. Tian F, Cai L, Chang J, Li S, Liu C, Li T, Sun J (2018) Label-free isolation of rare tumor cells from untreated whole blood by interfacial viscoelastic microfluidics. Lab Chip 18:3436–3445Google Scholar
  79. Villone MM, D’Avino G, Hulsen MA, Greco F, Maffettone PL (2013) Particle motion in square channel flow of a viscoelastic liquid: migration vs. secondary flows. J NonNewton Fluid Mech 195:1–8Google Scholar
  80. Won D, Kim C (2004) Alignment and aggregation of spherical particles in viscoelastic fluid under shear flow. J Non-Newton Fluid Mech 117:141–146Google Scholar
  81. Xiang N, Dai Q, Ni Z (2016a) Multi-train elasto-inertial particle focusing in straight microfluidic channels. Appl Phys Lett 109:134101Google Scholar
  82. Xiang N, Zhang X, Dai Q, Cheng J, Chen K, Ni Z (2016b) Fundamentals of elasto-inertial particle focusing in curved microfluidic channels. Lab Chip 16:2626–2635Google Scholar
  83. Xiang N, Ni Z, Yi H (2018) Concentration-controlled particle focusing in spiral elasto-inertial microfluidic devices. Electrophoresis 39:417–424Google Scholar
  84. Xuan X, Zhu J, Church C (2010) Particle focusing in microfluidic devices. Microfluid Nanofluid 9:1–16Google Scholar
  85. Yan S, Zhang J, Yuan D, Li W (2017) Hybrid microfluidics combined with active and passive approaches for continuous cell separation. Electrophoresis 38:238–249Google Scholar
  86. Yang H, Gijs MAM (2018) Micro-optics for microfluidic analytical applications. Chem Soc Rev 47:1391–1458Google Scholar
  87. Yang S, Kim JY, Lee SJ, Lee SS, Kim JM (2011) Sheathless elasto-inertial particle focusing and continuous separation in a straight rectangular microchannel. Lab Chip 11:266–273Google Scholar
  88. Yang S, Lee SS, Ahn SW, Kang K, Shim W, Lee G, Hyun K, Kim JM (2012) Deformability-selective particle entrainment and separation in a rectangular microchannel using medium viscoelasticity. Soft Matt 8:5011–5019Google Scholar
  89. Yasuda K, Armstrong RC, Cohen RE (1981) Shear flow properties of concentrated solutions of linear and star branched polystyrenes. Rheo Acta 20:163–178Google Scholar
  90. Yuan D, Zhang J, Yan S, Pan C, Alici G, Nguyen NT, Li W (2015) Dean-flow-coupled elasto-inertial three-dimensional particle focusing under viscoelastic flow in a straight channel with asymmetrical expansion–contraction cavity arrays. Biomicrofluid 9:044108Google Scholar
  91. Yuan D, Zhang J, Yan S, Peng G, Zhao Q, Alici G, Du H, Li W (2016) Investigation of particle lateral migration in sample-sheath flow of viscoelastic fluid and Newtonian fluid. Electrophoresis 37:2147–2155Google Scholar
  92. Yuan D, Zhao Q, Yan S, Tang SY, Alici G, Zhang J, Li W (2018) Recent progress of particle migration in viscoelastic fluids. Lab Chip 18:551–567Google Scholar
  93. Zhang J, Yan S, Yuan D, Alici G, Nguyen NT, Warkiani ME, Li W (2016a) Fundamentals and applications of inertial microfluidics: a review. Lab Chip 16:10–34Google Scholar
  94. Zhang J, Yan S, Yuan D, Zhao Q, Tan SH, Nguyen NT, Li W (2016b) A novel viscoelastic-based ferrofluid for continuous sheathless microfluidic separation of nonmagnetic microparticles. Lab Chip 16:3947–3956Google Scholar
  95. Zhou Y, Song L, Yu L, Xuan X (2017) Inertially focused diamagnetic particle separation in ferrofluids. Microfluid Nanofluid 21:14Google Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringClemson UniversityClemsonUSA

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