Advertisement

Numerical simulations of the motion of ellipsoids in planar Couette flow of Giesekus viscoelastic fluids

  • Yelong Wang
  • Zhaosheng YuEmail author
  • Jianzhong LinEmail author
Research Paper
Part of the following topical collections:
  1. Particle motion in non-Newtonian microfluidics

Abstract

The motion of neutrally buoyant ellipsoids in a planar Couette flow of Giesekus viscoelastic fluids between two narrowly set plates is numerically simulated with a fictitious domain method. The aspect ratio of the ellipsoid is 4 (i.e., prolate spheroids) and the Deborah number (De) ranges from 0 to 4.0. For a single ellipsoid initially placed in the mid-plane between the two plates, the ellipsoid major axis rotates around the vorticity axis in a kayaking mode at relatively low Deborah numbers, and is tilted in the flow-vorticity plane when the Deborah number exceeds a critical value, with the orientation being closer to the flow direction for a larger De. For a single ellipsoid initially not placed in the mid-plane, the ellipsoid undergoes lateral migration toward the nearby wall, and it is interesting that the ellipsoid turns its orientation to the vorticity axis at relatively small De and a direction close to the vorticity axis at large De (above 3.0), in contrast to the ellipsoid placed in the mid-plane without lateral migration, whose terminal orientation exhibits a kayaking motion at relatively small De and is close to the flow direction for De > 3. As a result, for the multiple-ellipsoid case, there exists a transient stage where the average orientation of the ellipsoids turns toward the vorticity axis for all nonzero Deborah numbers studied, and the orientation close to the vorticity axis can be often observed for the isolated ellipsoids. Both the particle interactions and the wall effect promote the ellipsoids to align with the flow direction. Particle aggregation and the dynamic aligning structures are observed at large Deborah numbers.

Keywords

Lateral migration Planar Couette flow Giesekus viscoelastic fluid Ellipsoid 

Notes

Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant Nos. 11632016, 91752117).

References

  1. Bartram E, Goldsmith HL, Mason SG (1975) Particle motions in non-Newtonian media, III. Further observations in viscoelastic fluids. Rheol Acta 14:776–782CrossRefGoogle Scholar
  2. Borzacchiello D et al (2016) Orientation kinematics of short fibres in a second-order viscoelastic fluid. Rheol Acta 55:397–409CrossRefGoogle Scholar
  3. Brunn P (1980) The motion of rigid particles in viscoelastic fluids. J Non-Newton Fluid Mech 7:271–288CrossRefGoogle Scholar
  4. Caserta S, D’Avino G, Greco F, Guido S, Maffettone PL (2010) Migration of a sphere in a viscoelastic fluid under planar shear flow: experiments and numerical predictions. Soft Matter 7:1100–1106CrossRefGoogle Scholar
  5. Cohen C, Chung B, Stasiak W (1987) Orientation and rheology of rod-like particles with weak Brownian diffusion in a 2nd-order fluid under simple shear-flow. Rheol Acta 26:217–232CrossRefGoogle Scholar
  6. Crowe CT et al (2011) Multiphase flows with droplets and particles. CRC Press, Boca Raton, FLCrossRefGoogle Scholar
  7. D’Avino G, Maffettone PL (2015) Particle dynamics in viscoelastic liquids. J Non-Newton Fluid Mech 215:80–104MathSciNetCrossRefGoogle Scholar
  8. D’Avino G, Tuccillo T, Hulsen MA, Greco F, Maffettone PL (2010a) Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow. Comput Fluids 39:709–721MathSciNetCrossRefGoogle Scholar
  9. D’Avino G, Maffettone PL, Greco F, Hulsen MA (2010b) Viscoelasticity-induced migration of a rigid sphere in confined shear flow. J Non-Newton Fluid Mech 165:466–474CrossRefGoogle Scholar
  10. D’Avino G, Hulsen MA, Greco F, Maffettone PL (2014) Bistability and metabistability scenario in the dynamics of an ellipsoidal particle in a sheared viscoelastic fluid. Phys Rev E 89:043006CrossRefGoogle Scholar
  11. D’Avino G, Greco F, Maffettone PL (2015) Rheology of a dilute viscoelastic suspension of spheroids in unconfined shear flow. Rheol Acta 54:915–928CrossRefGoogle Scholar
  12. 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 49:341–360MathSciNetCrossRefGoogle Scholar
  13. 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 263:33–41MathSciNetCrossRefGoogle Scholar
  14. de Oliveira IS, den Otter WK, Briels WJ (2013) Alignment and segregation of bidisperse colloids in a shear-thinning viscoelastic fluid under shear flow. Europhys Lett 101:28002CrossRefGoogle Scholar
  15. Férec J, Bertevas E, Khoo BC, Ausias G, Thien NP (2017) Steady-shear rheological properties for suspensions of axisymmetric particles in second-order fluids. J Non-Newton Fluid Mech 239:62–72MathSciNetCrossRefGoogle Scholar
  16. Gauthier F, Goldsmith HL, Mason SG (1971) Particle motions in non-Newtonian media. I. Couette flow. Rheol Acta 10:344–364CrossRefGoogle Scholar
  17. Glowinski R, Pan TW, Hesla TI, Joseph DD (1999) A distributed lagrange multiplier/fictitious domain method for particulate flows. Int J Multiph Flow 25:755–794MathSciNetCrossRefGoogle Scholar
  18. Gunes DZ, Scirocco R, Mewis J, Vermant J (2008) Flow-induced orientation of nonspherical particles: effect of aspect ratio and medium rheology. J Non-Newton Fluid Mech 155:39–50CrossRefGoogle Scholar
  19. Harlen OG, Koch DL (1993) Simple shear-flow of a suspension of fibers in a dilute polymer-solution at high Deborah number. J Fluid Mech 252:187–207CrossRefGoogle Scholar
  20. Hobbie EK et al (2003) Orientation of carbon nanotubes in a sheared polymer melt. Phys Fluids 15:1196–1202CrossRefGoogle Scholar
  21. Huang H, Lu X (2017) An ellipsoidal particle in tube Poiseuille flow. J Fluid Mech 822:664–688MathSciNetCrossRefGoogle Scholar
  22. Huang PY, Feng J, Hu HH, Joseph DD (1997) Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids. J Fluid Mech 343:73–94MathSciNetCrossRefGoogle Scholar
  23. Huang H, Yang X, Krafczyk M, Lu X (2012) Rotation of spheroidal particles in Couette flows. J Fluid Mech 692:369–394MathSciNetCrossRefGoogle Scholar
  24. Iso Y, Koch DL, Cohen C (1996a) Orientation in simple shear flow of semi-dilute fiber suspensions 1. Weakly elastic fluids. J Non-Newton Fluid Mech 62:115–134CrossRefGoogle Scholar
  25. Iso Y, Koch DL, Cohen C (1996b) Orientation in simple shear flow of semi-dilute fiber suspensions 2. Highly elastic fluids. J Non-Newton Fluid Mech 62:135–153CrossRefGoogle Scholar
  26. Jaensson NO, Hulsen MA, Anderson PD (2016) Direct numerical simulation of particle alignment in viscoelastic fluids. J Non-Newton Fluid Mech 235:125–142MathSciNetCrossRefGoogle Scholar
  27. Jeffery GB (1922) The motion of ellipsoidal particles immersed in a viscous fluid. Proc R Soc Ser A 102:161–179CrossRefGoogle Scholar
  28. Johnson SJ, Salem AJ, Fuller GG (1990) Dynamics of colloidal particles in sheared non-newtonian fluids. J Non-Newton Fluid Mech 34:89–121CrossRefGoogle Scholar
  29. Karnis A, Gldsmith HL, Masion SG (1966) The flow of suspensions through tubes. Part V: inertial effects. Can J Chem Eng 44:181–193CrossRefGoogle Scholar
  30. Leal LG (1975) Slow motion of slender rod-like particles in 2nd order fluid. J Fluid Mech 69:305–337CrossRefGoogle Scholar
  31. Leer BV (1979) Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J Comput Phys 32:101–136CrossRefGoogle Scholar
  32. Lin A, Han SP (2002) On the distance between two ellipsoids. SIAM J Optim 13:298–308MathSciNetCrossRefGoogle Scholar
  33. Lin J, Wang Y, Zhang P, Ku X (2018) Mixing and orientation behaviors of cylindrical particles in a mixing layer of an Oldroyd-B fluid. Chem Eng Sci 176:270–284CrossRefGoogle Scholar
  34. Lu X, Liu C, Hu G, Xuan X (2017) Particle manipulations in non-newtonian microfluidics: a review. J Colloid Interface Sci 500:182–201CrossRefGoogle Scholar
  35. Lyon MK, Mead DW, Elliott RE, Leal LG (2001) Structure formation in moderately concentrated viscoelastic suspensions in simple shear flow. J Rheol 45:881–890CrossRefGoogle Scholar
  36. Madani A et al (2010) Fractionation of non-Brownian rod-like particle suspensions in a viscoplastic fluid. Chem Eng Sci 65:1762–1772CrossRefGoogle Scholar
  37. Michele J, Patzold R, Donis R (1977) Alignment and aggregation effects in suspensions of spheres in non-Newtonian media. Rheol Acta 16:317–321CrossRefGoogle Scholar
  38. Pan TW, Chang CC, Glowinski R (2008) On the motion of a neutrally buoyant ellipsoid in a three-dimensional Poiseuille flow. Comput Methods Appl Mech Eng 197:2198–2209MathSciNetCrossRefGoogle Scholar
  39. Pasquino R, Snijkers F, Grizzuti N, Vermant J (2010) The effect of particle size and migration on the formation of flow-induced structures in viscoelastic suspensions. Rheol Acta 49:993–1001CrossRefGoogle Scholar
  40. Pasquino R, Panariello D, Grizzuti N (2013) Migration and alignment of spherical particles in sheared viscoelastic suspensions: a quantitative determination of the flow-induced self-assembly kinetics. J Colloid Interface Sci 394:49–54CrossRefGoogle Scholar
  41. Pasquino R, D’Avino G, Maffettone PL, Greco F, Grizzuti N (2014) Migration and chaining of noncolloidal spheres suspended in a sheared viscoelastic medium: experiments and numerical simulations. J Non-Newton Fluid Mech 203:1–8CrossRefGoogle Scholar
  42. Qi DW, Luo LS (2003) Rotational and orientational behaviour of three-dimensional spheroidal particles in Couette flows. J Fluid Mech 477:201–213CrossRefGoogle Scholar
  43. Rosén T, Do-Quang M, Aidun CK, Lundell F (2015) The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia. J Fluid Mech 771:115–158CrossRefGoogle Scholar
  44. Saffman PG (1956) On the motion of small spheroidal particles in a viscous liquid. J Fluid Mech 1:540–553MathSciNetCrossRefGoogle Scholar
  45. Scirocco R, Vermant J, Mewis J (2004) Effect of the viscoelasticity of the suspending fluid on structure formation in suspensions. J Non-Newton Fluid Mech 117:183–192CrossRefGoogle Scholar
  46. Trofa M, D’Avino G, Hulsen MA, Greco F, Maffettone PL (2016a) Numerical simulations of the dynamics of a slippery particle in Newtonian and viscoelastic fluids subjected to shear and poiseuille flows. J Non-Newton Fluid Mech 228:46–54MathSciNetCrossRefGoogle Scholar
  47. Trofa M, D’Avino G, Hulsen MA, Maffettone PL (2016b) The effect of wall slip on the dynamics of a spherical particle in Newtonian and viscoelastic fluids subjected to shear and poiseuille flows. J Non-Newton Fluid Mech 236:123–131MathSciNetCrossRefGoogle Scholar
  48. Wang P, Yu Z, Lin J (2018) Numerical simulations of particle migration in rectangular channel flow of Giesekus viscoelastic fluids. J Non-Newton Fluid Mech 262:142–168MathSciNetCrossRefGoogle Scholar
  49. Won D, Kim C (2004) Alignment and aggregation of spherical particles in viscoelastic fluid under shear flow. J Non-Newton Fluid Mech 117:141–146CrossRefGoogle Scholar
  50. Yu Z, Shao X (2007) A direct-forcing fictitious domain method for particulate flows. J Comput Phys 227:292–314CrossRefGoogle Scholar
  51. Yu Z, Wachs A (2007) A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids. J Non-Newton Fluid Mech 145:78–91CrossRefGoogle Scholar
  52. Yu Z, Phan-Thien N, Fan Y, Tanner R (2002) Viscoelastic mobility problem of a system of particles. J Non-Newton Fluid Mech 104:87–124CrossRefGoogle Scholar
  53. Yu Z, Wachs A, Peysson Y (2006) Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method. J Non-Newton Fluid Mech 136:126–139CrossRefGoogle Scholar
  54. Yu Z, Phan TN, Roger IT (2007) Rotation of a spheroid in a Couette flow at moderate Reynolds numbers. Phys Rev E 76:026310CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Fluid Power and Mechatronic System, Department of MechanicsZhejiang UniversityHangzhouChina

Personalised recommendations