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Dynamics of spheroids in pressure-driven flows of shear thinning fluids

Vishal Anand and Vivek Narsimhan*

  • Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA

  • *To whom the correspondence should be addressed: vnarsim@purdue.edu
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Phys. Rev. Fluids 8, 113302 – Published 6 November, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.113302

Abstract

Particles in inertialess flows of shear thinning fluids are a model representation for several systems in biology, ecology, and microfluidics. In this paper, we analyze the motion of a spheroid in a pressure-driven flow of a shear thinning fluid. The shear thinning rheology is characterized by the Carreau model. We use a combination of perturbative techniques and the reciprocal theorem to delineate the kinematics of prolate and oblate spheroids. There are two perturbative strategies adopted, one near the zero shear Newtonian plateau and the other near the infinite shear Newtonian plateau. In both limits, we find that a reduction in effective viscosity decreases the spheroid's rotational time period in pressure-driven flows. The extent to which shear thinning alters the kinematics is a function of the particle shape. For a prolate particle, the effect of shear thinning is most prominent when the spheroid projector is aligned in the direction of the velocity gradient, while for an oblate particle the effect is most prominent when the projector is aligned along the flow direction. Last, we compare the tumbling behavior of spheroids in pressure-driven flow to those in simple shear flow. While the time period decreases monotonically with Carreau number for pressure-driven flows, the trend is nonmonotonic for shear flows where time period first increases at low Carreau number and then decreases at high Carreau numbers. Shear thinning does not resolve the degeneracy of Jefferey's orbits.

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References (49)

  1. E. M. Purcell, Life at low Reynolds number, Am. J. Phys. 45, 3 (1977).
  2. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: Mechanics of Fluids and Transport Processes, 2nd ed. (Springer Netherlands, Dordrecht, 1983).
  3. L. G. Leal, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, Vol. 7 (Cambridge University Press, Cambridge, UK, 2007).
  4. S. Kim and S. Karilla, Microhydrodynamics: Principles and Selected Application, 2nd ed. (Dover, Mineola, NY, 2005).
  5. L. G. Leal, Particle motions in a viscous fluid, Annu. Rev. Fluid Mech. 12, 435 (1980).
  6. G. Subramanian and D. L. Koch, Inertial effects on the orientation of nearly spherical particles in simple shear flow, J. Fluid Mech. 557, 257 (2006).
  7. V. Dabade, N. K. Marath, and G. Subramanian, The effect of inertia on the orientation dynamics of anisotropic particles in simple shear flow, J. Fluid Mech. 791, 631 (2016).
  8. N. K. Marath and G. Subramanian, The inertial orientation dynamics of anisotropic particles in planar linear flows, J. Fluid Mech. 844, 357 (2018).
  9. J. Einarsson, F. Candelier, F. Lundell, J. R. Angilella, and B. Mehlig, Effect of weak fluid inertia uponJeffery orbits, Phys. Rev. E 91, 041002 (2015).
  10. J. Einarsson, F. Candelier, F. Lundell, J. R. Angilella, and B. Mehlig, Rotation of a spheroid in a simple shear at small Reynolds number, Phys. Fluids 27, 063301 (2015).
  11. G. D'Avino and P. L. Maffettone, Particle dynamics in viscoelastic liquids, J. Non-Newtonian Fluid Mech. 215, 80 (2015).
  12. G. D'Avino, F. Greco, and P. L. Maffettone, Particle migration due to viscoelasticity of the suspending liquid and its relevance in microfluidic devices, Annu. Rev. Fluid Mech. 49, 341 (2017).
  13. J. Einarsson, M. Yang, and E. S. Shaqfeh, Einstein viscosity with fluid elasticity, Phys. Rev. Fluids 3, 013301 (2018).
  14. W. L. Murch and E. S. Shaqfeh, Collective effects in the sedimentation of particles in a viscoelastic fluid, Phys. Rev. Fluids 5, 073301 (2020).
  15. A. Zhang, W. L. Murch, J. Einarsson, and E. S. G. Shaqfeh, Lift and drag force on a spherical particle in a viscoelastic shear flow, J. Non-Newtonian Fluid Mech. 280, 104279 (2020).
  16. S. Wang, C. W. Tai, and V. Narsimhan, Dynamics of spheroids in an unbound quadratic flow of a general second-order fluid, Phys. Fluids 32, 113106 (2020).
  17. P. Brunn, The motion of rigid particles in viscoelastic fluids, J. Non-Newton. Fluid Mech. 7, 271 (1980).
  18. S. Kim, The motion of ellipsoids in a second order fluid, J. Non-Newton. Fluid Mech. 21, 255 (1986).
  19. P. Brunn, The slow motion of a rigid particle in a second-order fluid, J. Fluid Mech. 82, 529 (1977).
  20. C. W. Tai, S. Wang, and V. Narsimhan, Cross-stream migration of non-spherical particles in a second-order fluid-theories of particle dynamics in arbitrary quadratic flows, J. Fluid Mech. 895, A6 (2020).
  21. J. Gong, V. A. Shaik, and G. J. Elfring, Active particles crossing sharp viscosity gradients, Sci. Rep. 13, 596 (2023).
  22. V. A. Shaik and G. J. Elfring, On the hydrodynamics of active particles in viscosity gradients, Phys. Rev. Fluids 6, 103103 (2021).
  23. C. Datt and G. J. Elfring, Active particles in viscosity gradients, Phys. Rev. Lett. 123, 158006 (2019).
  24. C. Datt and G. J. Elfring, Dynamics and rheology of particles in shear-thinning fluids, J. Non-Newton. Fluid Mech. 262, 107 (2018).
  25. S. A. Abtahi and G. J. Elfring, Jeffery orbits in shear-thinning fluids, Phys. Fluids 31, 103106 (2019).
  26. K. Pietrzyk, H. Nganguia, C. Datt, L. Zhu, G. J. Elfring, and O. S. Pak, Flow around a squirmer in a shear-thinning fluid, J. Non-Newtonian Fluid Mech. 268, 101 (2019).
  27. G. J. Elfring, Force moments of an active particle in a complex fluid, J. Fluid Mech. 829, R3 (2017).
  28. B. Van Gogh, E. Demir, D. Palaniappan, and O. S. Pak, The effect of particle geometry on squirming through a shear-thinning fluid, J. Fluid Mech. 938, A3 (2022).
  29. G. J. Elfring and E. Lauga, Theory of locomotion through complex fluids, in Complex Fluids in Biological Systems, Biological and Medical Physics, Biomedical Engineering, edited by S. Spagnolie (Springer Science+Business Media, New York, 2015).
  30. C. Datt, L. Zhu, G. J. Elfring, and O. S. Pak, Squirming through shear-thinning fluids, J. Fluid Mech. 784, R1 (2015).
  31. H. Nganguia, K. Pietrzyk, and O. S. Pak, Swimming efficiency in a shear-thinning fluid, Phys. Rev. E 96, 062606 (2017).
  32. K. Qin and O. S. Pak, Purcell's swimmer in a shear-thinning fluid, Phys. Rev. Fluids 8, 033301 (2023).
  33. R. P. Chhabra and J. F. Richardson, Non-Newtonian fluid behaviour, in Non-Newtonian Flow and Applied Rheology, 2nd ed. (Butterworth-Heinemann, Oxford, 2008), pp. 1–55.
  34. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. 1, 2nd ed. (John Wiley, New York, 1987).
  35. E. Boyko and H. A. Stone, Flow rate-pressure drop relation for shear-thinning fluids in narrow channels: Approximate solutions and comparison with experiments, J. Fluid Mech. 923, R5 (2021).
  36. C. J. Pipe, T. S. Majmudar, and G. H. McKinley, High shear rate viscometry, Rheol. Acta 47, 6212008.
  37. C. P. Martin, S. Wang, and S. Kim, Surface tractions on an ellipsoid in Stokes flow: Quadratic ambient fields, Phys. Fluids 31, 021209 (2019).
  38. S. Wang, C. P. Martin, and S. Kim, Improper integrals as a puzzle for creeping flow around an ellipsoid, Phys. Fluids 31, 021101 (2019).
  39. M. D. Graham, Microhydrodynamics, Brownian Motion, and Complex Fluids, 1st ed. (Cambridge University Press, Cambridge, UK, 2018).
  40. P. Y. Huang, J. Feng, H. H. Hu, and D. D. Joseph, Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids, J. Fluid Mech. 343, 73 (1997).
  41. P. Y. Huang, H. H. Hu, and D. D. Joseph, Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids, J. Fluid Mech. 362, 297 (1998).
  42. D. Z. Gunes, R. Scirocco, J. Mewis, and J. Vermant, Flow-induced orientation of non-spherical particles: Effect of aspect ratio and medium rheology, J. Non-Newtonian Fluid Mech. 155, 39 (2008).
  43. R. Dandekar and A. M. Ardekani, Swimming sheet in a viscosity-stratified fluid, J. Fluid Mech. 895, R2 (2020).
  44. A. K. Varanasi, N. K. Marath, and G. Subramanian, The rotation of a sedimenting spheroidal particle in a linearly stratified fluid, J. Fluid Mech. 933, A17 (2022).
  45. A. K. Varanasi and G. Subramanian, Motion of a sphere in a viscous density stratified fluid, J. Fluid Mech. 949, A29 (2022).
  46. R. V. More and A. M. Ardekani, Motion in stratified fluids, Annu. Rev. Fluid Mech. 55, 157 (2023).
  47. R. Dandekar, V. A. Shaik, and A. M. Ardekani, Swimming sheet in a density-stratified fluid, J. Fluid Mech. 874, 210 (2019).
  48. F. Candelier and B. Mehlig, Settling of an asymmetric dumbbell in a quiescent fluid, J. Fluid Mech. 802, 174 (2016).
  49. P. Anand and G. Subramanian, Inertial migration in pressure-driven channel flow: Beyond the Segre-Silberberg pinch, arXiv:2301.00789 (2023).

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Phys. Rev. Fluids 8, 113302– Published 6 November, 2023
  • Received 8 March 2023
  • Accepted 2 October 2023
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