Suspension of deformable particles in Newtonian and viscoelastic fluids in a microchannel

  • Amir Hossein Raffiee
  • Sadegh Dabiri
  • Arezoo M. ArdekaniEmail author
Research Paper
Part of the following topical collections:
  1. Particle motion in non-Newtonian microfluidics


In this paper, we study a suspension of cells at a moderate volume fraction flowing in a microchannel filled with Newtonian or viscoelastic fluids and investigate the role of cell size, cell volume fraction, inertia, deformability, and fluid elasticity on the cell distribution. Our results suggest that the use of constant-viscosity viscoelastic fluid pushes the cells toward the channel centerline which can be used in microfluidic devices used for cell focusing such as cytometers. The cell-free layer increases which provides larger gap for separating rare cells in microfluidic devices. Furthermore, we show that the volumetric flow rate can be significantly enhanced with the addition of polymers in the suspending fluid. This effect enhances the processing speed which is of interest in designing microfluidic devices. This fundamental study can provide insight on the role of rheological properties of the fluid that can be tuned to control the motion of the cells for efficient design of microfluidic devices.


Cell migration in polymeric fluids Cell focusing Elasto-inertial cell migration 



This research was partially supported by a Grant from National Science Foundation [CBET-1705371].

Compliance with ethical standards

Conflict of interest

There are no conflicts of interest to declare.


  1. 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
  2. Chang K-S, Olbricht WL (1993) Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow. J Fluid Mech 250:609–633Google Scholar
  3. Charrier J, Shrivastava S, Wu R (1989) Free and constrained inflation of elastic membranes in relation to thermoforming non-axisymmetric problems. J Strain Anal Eng Des 24(2):55–74Google Scholar
  4. Choi Y-S, Seo K-W, Lee S-J (2011) Lateral and cross-lateral focusing of spherical particles in a square microchannel. Lab Chip 11(3):460–465Google Scholar
  5. Chorin AJ (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22(104):745–762MathSciNetzbMATHGoogle Scholar
  6. Chung TD, Kim HC (2007) Recent advances in miniaturized microfluidic flow cytometry for clinical use. Electrophoresis 28(24):4511–4520Google Scholar
  7. Cooley M, Sarode A, Hoore M, Fedosov DA, Mitragotri S, Gupta AS (2018) Influence of particle size and shape on their margination and wall-adhesion: implications in drug delivery vehicle design across nano-to-micro scale. Nanoscale 10(32):15350–15364Google Scholar
  8. 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(9):1638–1645Google Scholar
  9. 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
  10. Del Giudice F, DAvino G, Greco F, Netti PA, Maffettone PL (2015) Effect of fluid rheology on particle migration in a square-shaped microchannel. Microfluid Nanofluid 19(1):95–104Google Scholar
  11. Del Giudice F, Sathish S, DAvino 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 ChemiGoogle Scholar
  12. Di Carlo D (2009) Inertial microfluidics. Lab Chip 9(21):3038–3046Google Scholar
  13. 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(48):18892–18897Google Scholar
  14. Di Carlo D, Edd JF, Humphry KJ, Stone HA, Toner M (2009) Particle segregation and dynamics in confined flows. Phys Rev Lett 102(9):094503Google Scholar
  15. Doddi SK, Bagchi P (2009) Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. Phys Rev E 79(4):046318Google Scholar
  16. Faridi MA, Ramachandraiah H, Banerjee I, Ardabili S, Zelenin S, Russom A (2017) Elasto-inertial microfluidics for bacteria separation from whole blood for sepsis diagnostics. J Nanobiotechnol 15(1):3Google Scholar
  17. Fedosov DA, Caswell B, Popel AS, Karniadakis GE (2010) Blood flow and cell-free layer in microvessels. Microcirculation 17(8):615–628Google Scholar
  18. Feng J, Hu HH, Joseph DD (1994) Direct simulation of initial value problems for the motion of solid bodies in a newtonian fluid part 1. Sedimentation. J Fluid Mech 261:95–134zbMATHGoogle Scholar
  19. Friend J, Yeo LY (2011) Microscale acoustofluidics: microfluidics driven via acoustics and ultrasonics. Rev Mod Phys 83(2):647Google Scholar
  20. Godin J, Chen C-H, Cho SH, Qiao W, Tsai F, Lo Y-H (2008) Microfluidics and photonics for bio-system-on-a-chip: a review of advancements in technology towards a microfluidic flow cytometry chip. J Biophoton 1(5):355–376Google Scholar
  21. Gossett DR, Weaver WM, Mach AJ, Hur SC, Tse HTK, Lee W, Amini H, Di Carlo D (2010) Label-free cell separation and sorting in microfluidic systems. Anal Bioanal Chem 397(8):3249–3267Google Scholar
  22. Ho B, Leal L (1974) Inertial migration of rigid spheres in two-dimensional unidirectional flows. J Fluid Mech 65(2):365–400zbMATHGoogle Scholar
  23. Howell PB Jr, Golden JP, Hilliard LR, Erickson JS, Mott DR, Ligler FS (2008) Two simple and rugged designs for creating microfluidic sheath flow. Lab Chip 8(7):1097–1103Google Scholar
  24. Hur SC, Tse HTK, Di Carlo D (2010) Sheathless inertial cell ordering for extreme throughput flow cytometry. Lab Chip 10(3):274–280Google Scholar
  25. Karimi A, Yazdi S, Ardekani AM (2013) Hydrodynamic mechanisms of cell and particle trapping in microfluidics. Biomicrofluidics 7(2):021501Google Scholar
  26. Karnis A, Goldsmith H, Mason S (1966) The flow of suspensions through tubes: V. inertial effects. Can J Chem Eng 44(4):181–193Google Scholar
  27. Kilimnik A, Mao W, Alexeev A (2011) Inertial migration of deformable capsules in channel flow. Phys Fluids 23(12):123302Google Scholar
  28. Krüger T, Kaoui B, Harting J (2014) Interplay of inertia and deformability on rheological properties of a suspension of capsules. J Fluid Mech 751:725–745Google Scholar
  29. Kunze A, Che J, Karimi A, Di Carlo D (2015) Research highlights: cell separation at the bench and beyond. Lab Chip 15(3):605–609Google Scholar
  30. Lancaster C, Kokoris M, Nabavi M, Clemmens J, Maloney P, Capadanno J, Gerdes J, Battrell C (2005) Rare cancer cell analyzer for whole blood applications: microcytometer cell counting and sorting subcircuits. Methods 37(1):120–127Google Scholar
  31. Lee DJ, Brenner H, Youn JR, Song YS (2013) Multiplex particle focusing via hydrodynamic force in viscoelastic fluids. Sci Repo:3Google Scholar
  32. Leonard BP (1979) A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput Methods Appl Mech Eng 19(1):59–98zbMATHGoogle Scholar
  33. Leshansky A, Bransky A, Korin N, Dinnar U (2007) Tunable nonlinear viscoelastic focusing in a microfluidic device. Phys Rev Lett 98(23):234501Google Scholar
  34. Li X, Pozrikidis C (2000) Wall-bounded shear flow and channel flow of suspensions of liquid drops. Int J Multiphase Flow 26(8):1247–1279zbMATHGoogle Scholar
  35. Li G, McKinley GH, Ardekani AM (2015) Dynamics of particle migration in channel flow of viscoelastic fluids. J Fluid Mech 785:486–505MathSciNetzbMATHGoogle Scholar
  36. Lim EJ, Ober TJ, Edd JF, Desai SP, Neal D, Bong KW, Doyle PS, McKinley GH, Toner M (2014) Inertio-elastic focusing of bioparticles in microchannels at high throughput. Nat Commun 2014:5Google Scholar
  37. 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(12):6041–6048Google Scholar
  38. Lu X, Liu C, Hu G, Xuan X (2017) Particle manipulations in non-Newtonian microfluidics: a review. J Colloid Interface Sci 500:182Google Scholar
  39. Nam J, Tan JKS, 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. Biomicrofluidics 9(6):064117Google Scholar
  40. Paiè P, Bragheri F, Di Carlo D, Osellame R (2017) Particle focusing by 3D inertial microfluidics. Microsyst Nanoeng 3:17027Google Scholar
  41. Pamme N (2006) Magnetism and microfluidics. Lab Chip 6(1):24–38Google Scholar
  42. Pethig R (2010) Dielectrophoresis: status of the theory, technology, and applications. Biomicrofluidics 4(2):022811Google Scholar
  43. Popel AS, Johnson PC (2005) Microcirculation and hemorheology. Annu Rev Fluid Mech 37:43–69MathSciNetzbMATHGoogle Scholar
  44. Pozrikidis C (2003) Modeling and simulation of capsules and biological cells. CRC Press, Boca RatonzbMATHGoogle Scholar
  45. Pranay P, Henríquez-Rivera RG, Graham MD (2012) Depletion layer formation in suspensions of elastic capsules in newtonian and viscoelastic fluids. Phys Fluids 24(6):061902Google Scholar
  46. Raffiee AH, Dabiri S, Ardekani AM (2017a) Deformation and buckling of microcapsules in a viscoelastic matrix. Phys Rev E 96(3):032603Google Scholar
  47. Raffiee AH, Dabiri S, Ardekani AM (2017b) Elasto-inertial migration of deformable capsules in a microchannel. Biomicrofluidics 11(6):064113Google Scholar
  48. Ramanujan S, Pozrikidis C (1998) Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities. J Fluid Mech 361:117–143MathSciNetzbMATHGoogle Scholar
  49. 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(14):2802–2807Google Scholar
  50. Saadat A, Guido CJ, Iaccarino G, Shaqfeh ESG (2018) Immersed-finite-element method for deformable particle suspensions in viscous and viscoelastic media. Phys Rev E 98(6):063316Google Scholar
  51. Schaaf C, Stark H (2017) Inertial migration and axial control of deformable capsules. Soft MatterGoogle Scholar
  52. Schonberg JA, Hinch E (1989) Inertial migration of a sphere in Poiseuille flow. J Fluid Mech 203:517–524MathSciNetzbMATHGoogle Scholar
  53. Segre G (1961) Radial particle displacements in poiseuille flow of suspensions. Nature 189:209–210Google Scholar
  54. Seo KW, Kang YJ, Lee SJ (2014) Lateral migration and focusing of microspheres in a microchannel flow of viscoelastic fluids. Phys Fluids 26(6):063301Google Scholar
  55. Sethu P, Sin A, Toner M (2006) Microfluidic diffusive filter for apheresis (leukapheresis). Lab Chip 6(1):83–89Google Scholar
  56. Skalak R, Tozeren A, Zarda R, Chien S (1973) Strain energy function of red blood cell membranes. Biophys J 13(3):245–264Google Scholar
  57. Sundararajan N, Pio MS, Lee LP, Berlin AA (2004) Three-dimensional hydrodynamic focusing in polydimethylsiloxane (PDMS) microchannels. J Microelectromech Syst 13(4):559–567Google Scholar
  58. Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys 100(1):25–37zbMATHGoogle Scholar
  59. van de Stolpe A, Pantel K, Sleijfer S, Terstappen LW, Den Toonder JM (2011) Circulating tumor cell isolation and diagnostics: toward routine clinical useGoogle Scholar
  60. Villone M, DAvino G, Hulsen M, Greco F, Maffettone P (2013) Particle motion in square channel flow of a viscoelastic liquid: migration vs. secondary flows. J Non-Newtonian Fluid Mech 195:1–8Google Scholar
  61. 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(2):266–273Google Scholar
  62. Zeng L, Balachandar S, Fischer P (2005) Wall-induced forces on a rigid sphere at finite Reynolds number. J Fluid Mech 536:1–25zbMATHGoogle Scholar
  63. Zhao H, Shaqfeh ES, Narsimhan V (2012) Shear-induced particle migration and margination in a cellular suspension. Phys Fluids 24(1):011902Google Scholar

Copyright information

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

Authors and Affiliations

  • Amir Hossein Raffiee
    • 1
  • Sadegh Dabiri
    • 1
    • 2
  • Arezoo M. Ardekani
    • 1
    Email author
  1. 1.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Department of Agricultural and Biological EngineeringPurdue UniversityWest LafayetteUSA

Personalised recommendations