Numerical simulations on the dynamics of a particle pair in a viscoelastic fluid in a microchannel: effect of rheology, particle shape, and confinement

  • Gaetano D’AvinoEmail author
  • Pier Luca Maffettone
Research Paper
Part of the following topical collections:
  1. Particle motion in non-Newtonian microfluidics


The dynamics of two particles suspended in a viscoelastic fluid and aligned on the centerline of a microfluidic channel is investigated by direct numerical simulations. The shear-thinning elastic fluid is modeled by the Giesekus constitutive equation. The relative particle velocity is studied by varying the interparticle distance, the Deborah number, fluid shear thinning, confinement ratio, and particle shape. Concerning the latter aspect, spherical and spheroidal particles with different aspect ratios are considered. The regimes of particle attraction and repulsion as well as the equilibrium configurations are identified and correlated with the fluid rheological properties and particle shape. The observed dynamics is related to the distribution of the viscoelastic normal stresses in the fluid between the particles. The results reported here provide useful insights into design efficient microfluidics devices to achieve particle ordering, i.e., the formation of equally spaced particle structures.


Particle pair Viscoelasticity Focusing Ordering Numerical simulations Microfluidics 



  1. Bogaerds ACB, Grillet AM, Peters GWM, Baaijens FPT (2002) Stability analysis of polymer shear flows using the extended pom-pom constitutive equations. J Non Newton Fluid Mech 108(1):187CrossRefGoogle Scholar
  2. Bogaerds ACB, Hulsen MA, Peters GWM, Baaijens FPT (2004) Stability analysis of injection molding flows. J Rheol 48:765CrossRefGoogle Scholar
  3. Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32(1):199MathSciNetCrossRefGoogle Scholar
  4. D’Avino G, Maffettone PL (2015) Particle dynamics in viscoelastic liquids. J Non Newton Fluid Mech 215:80MathSciNetCrossRefGoogle Scholar
  5. 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 12:1638CrossRefGoogle Scholar
  6. D’Avino G, Hulsen MA, Maffettone PL (2013) Dynamics of pairs and triplets of particles in a viscoelastic fluid flowing in a cylindrical channel. Comput Fluids 86:45MathSciNetCrossRefGoogle Scholar
  7. 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 49:341MathSciNetCrossRefGoogle Scholar
  8. D’Avino G, Hulsen MA, Greco F, Maffettone PL (2019) Numerical simulations on the dynamics of a spheroid in a viscoelastic liquid in a wide-slit microchannel. J Non Newton Fluid Mech 263:33MathSciNetCrossRefGoogle Scholar
  9. 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(21):4263CrossRefGoogle Scholar
  10. Del Giudice F, D’Avino G, Greco F, De Santo I, Netti PA, Maffettone PL (2015) Rheometry-on-a-chip: measuring the relaxation time of a viscoelastic liquid through particle migration in microchannel flows. Lab Chip 15:783CrossRefGoogle Scholar
  11. Del Giudice F, D’Avino G, Greco F, Maffettone PL, Shen AQ (2018) Fluid viscoelasticity drives self-assembly of particle trains in a straight microfluidic channel. Phys Rev Appl 10:064058CrossRefGoogle Scholar
  12. Fattal R, Kupferman R (2004) Constitutive laws for the matrix-logarithm of the conformation tensor. J Non Newton Fluid Mech 123:281CrossRefGoogle Scholar
  13. Gauthier F, Goldsmith HL, Mason SG (1971) Particle motions in non-Newtonian media. II. Poiseuille flow. Trans Soc Rheol 15:297CrossRefGoogle Scholar
  14. Geuzaine C, Remacle JF (2009) Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79:1309CrossRefGoogle Scholar
  15. Guénette R, Fortin M (1995) A new mixed finite element method for computing viscoelastic flows. J Non Newton Fluid Mech 60(1):27CrossRefGoogle Scholar
  16. Hu HH, Patankar NA, Zhu MY (2001) Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J Comput Phys 169:427MathSciNetCrossRefGoogle Scholar
  17. Hulsen MA, Fattal R, Kupferman R (2005) Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms. J Non Newton Fluid Mech 127(1):27CrossRefGoogle Scholar
  18. Kang K, Lee SS, Hyun K, Lee SJ, Kim JM (2013) DNA-based highly tunable particle focuser. Nat Commun 4:2567CrossRefGoogle Scholar
  19. Karnis A, Mason SG (1966) Particle motions in sheared suspensions. XIX. Viscoelastic media. Trans Soc Rheol 10:571CrossRefGoogle Scholar
  20. Larson RG (1988) Constitutive equations for polymer melts and solutions: Butterworths series in chemical engineering. Butterworth-Heinemann, OxfordGoogle Scholar
  21. Lee DJ, Brenner H, Youn JR, Song YS (2013) Multiplex particle focusing via hydrodynamic force in viscoelastic fluids. Sci Rep 3:3258CrossRefGoogle Scholar
  22. Leshansky AM, Bransky A, Korin N, Dinnar U (2007) Tunable nonlinear viscoelastic focusing in a microfluidic device. Phys Rev Lett 98(23):234501CrossRefGoogle Scholar
  23. Li D, Xuan X (2018) Fluid rheological effects on particle migration in a straight rectangular microchannel. Microfluid Nanofluid 22:49CrossRefGoogle Scholar
  24. Lim H, Nam J, Shin S (2014) Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow. Microfluid Nanofluid 17:683CrossRefGoogle Scholar
  25. Lu X, Xuan X (2015) Elasto-inertial pinched flow fractionation for continuous shape-based particle separation. Anal Chem 87:11523CrossRefGoogle Scholar
  26. Lu X, Zhu L, Hua R, Xuan X (2015) Continuous sheath-free separation of particles by shape in viscoelastic fluids. Appl Phys Lett 197:264102CrossRefGoogle Scholar
  27. Lu X, Liu C, Hu G, Xuan X (2017) Particle manipulations in non-Newtonian microfluidics: a review. J Colloid Interface Sci 500:182CrossRefGoogle Scholar
  28. Seo KW, Byeon HJ, Huh HK, Lee SJ (2014) Particle migration and single-line particle focusing in microscale pipe flow of viscoelastic fluids. RSC Adv 4:3512CrossRefGoogle Scholar
  29. Villone MM, D’Avino G, Hulsen MA, Greco F, Maffettone PL (2011) Simulations of viscoelasticity-induced focusing of particles in pressure-driven micro-slit flow. J Non Newton Fluid Mech 166:1396CrossRefGoogle Scholar
  30. Xiang N, Dai Q, Han Y, Ni Z (2019) Circular-channel particle focuser utilizing viscoelastic focusing. Microfluid Nanofluid 23:16CrossRefGoogle Scholar
  31. Xuan X, Zhu J, Church C (2010) Particle focusing in microfluidic devices. Microfluid Nanofluid 9:1CrossRefGoogle Scholar
  32. 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):266CrossRefGoogle Scholar
  33. Yang SH, Lee DJ, Youn JR, Song YS (2017) Multiple-line particle focusing under viscoelastic flow in a microfluidic device. Anal Chem 89:3639CrossRefGoogle Scholar
  34. 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(4):551CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione IndustrialeUniversità di Napoli Federico IINaplesItaly

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