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

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Transport of flexible fibers in confined microchannels

Jean Cappello1,*, Mathias Bechert2,*, Camille Duprat3, Olivia du Roure1, François Gallaire2, and Anke Lindner1,†

  • 1Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR 7636, CNRS, ESPCI Paris, PSL Research University, Université Paris Diderot, Sorbonne Université, Paris 75005, France
  • 2Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
  • 3Laboratoire d'Hydrodynamique (LadHyX), École polytechnique, Department of Mechanics, Palaiseau, France

  • *These authors contributed equally.
  • †Corresponding author: anke.lindner@espci.fr
PDF

Phys. Rev. Fluids 4, 034202 – Published 5 March, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.034202

Abstract

When transported in confined geometries rigid fibers show interesting transport dynamics induced by friction with the top and bottom walls. Fiber flexibility causes an additional coupling between fiber deformation and transport and is expected to lead to more complex dynamics. A first crucial step for their understanding is the characterization of the deformed fiber shape. Here we characterize this shape for a fiber transported in a confined plug flow perpendicular to the flow direction using a combination of microfluidic experiments and numerical simulations. In the experiments, size, initial orientation, and mechanical properties of the fibers are controlled using microfabrication techniques and in situ characterization methods. The numerical simulations use modified Brinkman equations as well as full three-dimensional simulations. We show that the bending of a perpendicular fiber results from the force distribution acting on the elongated object and is proportional to the elasto-viscous number, which compares viscous to elastic forces. We quantitatively characterize the influence of the confinement on the fiber deformation. The precise understanding of the deformation of a flexible fiber in a confined geometry can also be used in future to understand the deformation and transport of more complex deformable particles in confined flows, such as vesicles or red blood cells.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (41)

  1. J. M. Stockie and S. I. Green, Simulating the motion of flexible pulp fibres using the immersed boundary method, J. Comput. Phys. 147, 147 (1998).
  2. F. Lundell, L. D. Söderberg, and P. H. Alfredsson, Fluid mechanics of papermaking, Annu. Rev. Fluid Mech. 43, 195 (2011).
  3. 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).
  4. E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
  5. 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, Trans. Porous Med. 84, 389 (2009).
  6. G. K. Batchelor, Slender-body theory for particles of arbitrary cross-section in Stokes flow, J. Fluid Mech. 44, 419 (1970).
  7. G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. London A 102, 161 (1922).
  8. 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).
  9. H. Berthet, M. Fermigier, and A. Lindner, Single fiber transport in a confined channel: Microfluidic experiments and numerical study, Phys. Fluids 25, 103601 (2013).
  10. W. E. Uspal and P. S. Doyle, Scattering and nonlinear bound states of hydrodynamically coupled particles in a narrow channel, Phys. Rev. E 85, 016325 (2012).
  11. B. Shen, M. Leman, M. Reyssat, and P. Tabeling, Dynamics of a small number of droplets in microfluidic Hele-Shaw cells, Exp. Fluids 55, 1728 (2014).
  12. B. Bet, R. Georgiev, W. Uspal, H. B. Eral, R. van Roij, and S. Samin, Calculating the motion of highly confined, arbitrary-shaped particles in Hele-Shaw channels, Microfluid. Nanofluid. 22, 77 (2018).
  13. B. Bet, S. Samin, R. Georgiev, H. B. Eral, and René van Roij, Steering particles by breaking symmetries, J. Phys.: Condens. Matter 30, 224002 (2018).
  14. L. E. Becker and M. J. Shelley, Instability of Elastic Filaments in Shear Flow Yields First-Normal-Stress Differences, Phys. Rev. Lett. 87, 198301 (2001).
  15. Y. Liu, B. Chakrabarti, D. Saintillan, A. Lindner, and O. du Roure, Tumbling, buckling, snaking: Morphological transitions of semiflexible filaments in shear flow, Proc. Natl. Acad. Sci. USA 115, 9438 (2018)
  16. N. Quennouz, M. J. Shelley, O. du Roure, and A. Lindner, Transport and buckling dynamics of an elastic fiber in a viscous cellular flow, J. Fluid Mech. 769, 387 (2015).
  17. B. Engineering, The motion of long slender bodies in a viscous fluid, J. Fluid Mech. 44, 791 (1970).
  18. X. Xu and A. Nadim, Deformation and orientation of an elastic slender body sedimenting in a viscous liquid, Phys. Fluids 6, 2889 (1994).
  19. L. Li, H. Manikantan, D. Saintillan, and S. E. Spagnolie, The sedimentation of flexible filaments, J. Fluid Mech. 735, 705 (2013).
  20. B. Marchetti, V. Raspa, A. Lindner, O. du Roure, L. Bergougnoux, É. Guazzelli, and C. Duprat, Deformation of a flexible fiber settling in a quiescent viscous fluid, Phys. Rev. Fluids 3, 104102 (2018).
  21. M. V. D'Angelo, J. P. Hulin, and H. Auradou, Oscillations and translation of a free cylinder in a viscous confined flow, Phys. Fluids 25, 014102 (2013).
  22. M. Nagel and F. Gallaire, Boundary elements method for microfluidic two-phase flows in shallow channels, Comput. Fluids 107, 272 (2015).
  23. D. Dendukuri, P. Panda, R. Haghgooie, J. M. Kim, T. A. Hatton, and P. S. Doyle, Modeling of oxygen-inhibited free radical photopolymerization in a PDMS microfluidic device, Macromolecules 41, 8547 (2008).
  24. D. Dendukuri and P. S. Doyle, The synthesis and assembly of polymeric microparticles using microfluidics, Adv. Mater. 21, 4071 (2009).
  25. D. Dendukuri, S. S. Gu, D. C. Pregibon, T. A. Hatton, and P. S. Doyle, Stop-flow lithography in a microfluidic device, Lab Chip 7, 818 (2007).
  26. M. E. Helgeson, S. C. Chapin, and P. S. Doyle, Hydrogel microparticles from lithographic processes: Novel materials for fundamental and applied colloid science, Curr. Opin. Colloid Interface Sci. 16, 106 (2011).
  27. A. Lindner, Flow of complex suspensions, Phys. Fluids 26, 101307 (2014).
  28. J. S. Wexler, P. H. Trinh, H. Berthet, N. Quennouz, O. du Roure, H. E. Huppert, A. Lindner, and H. A. Stone, Bending of elastic fibres in viscous flows: the influence of confinement, J. Fluid Mech. 720, 517 (2013).
  29. C. Duprat, H. Berthet, J. S. Wexler, O. du Roure, and A. Lindner, Microfluidic in situ mechanical testing of photopolymerized gels, Lab Chip 15, 244 (2014).
  30. O. du Roure, A. Lindner, E. Nazockdast, and M. Shelley, Dynamics of flexible fibers in viscous flows and fluids, Annu. Rev. Fluid Mech. 51, 539 (2019).
  31. S. Champmartin, A. Ambari, and A. B. Richou, Kinematics of a free particle moving between two parallel walls, ASME 2010 8th International Conference on Nanochannels, Microchannels, and Minichannels Collocated with 3rd Joint US-European Fluids Engineering Summer Meeting (American Society of Mechanical Engineers, 2010), pp. 1677–1685.
  32. E. Wandersman, N. Quennouz, M. Fermigier, A. Lindner, and O. du Roure, Buckled in translation, Soft Matter 6, 5715 (2010).
  33. H. Berthet, O. du Roure, and A. Lindner, Microfluidic fabrication solutions for tailor-designed fiber suspensions, Appl. Sci. 6, 385 (2016).
  34. L. Chen, K. X. Wang, and P. S. Doyle, Effect of internal architecture on microgel deformation in microfluidic constrictions, Soft Matter 13, 1920 (2017).
  35. B. Audoly and Y. Pomeau, Elasticity and geometry, in Peyresq Lectures in Nonlinear Phenomena, edited by R. Kaiser and J. Montaldi (World Scientific, Singapore, 2000), pp. 1–35.
  36. N. Quennouz, Ph.D. thesis, UPMC, Paris 2013.
  37. G. Xu, K. S. Wilson, R. J. Okamoto, Jin-yu Shao, S. K. Dutcher, and P. V. Bayly, Flexural rigidity and shear stiffness of flagella estimated from induced bends and counterbends, Biophys. J. 110, 2759 (2016).
  38. D. Coombs, G. Huber, J. O. Kessler, and R. E. Goldstein, Periodic Chirality Transformations Propagating on Bacterial Flagella, Phys. Rev. Lett. 89, 118102 (2002).
  39. J. Gittes, F. Mickey, B. Nettleton, and J. Howard, Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape, J. Cell Biol. 120, 923 (1993).
  40. B. N. J. Persson, C. Ganser, F. Schmied, C. Teichert, R. Schennach, E. Gilli, and U. Hirn, Adhesion of cellulose fibers in paper, J. Phys.: Condens. Matter 25, 045002 (2012).
  41. C. A. Schneider, W. S. Rasband, and K. W. Eliceiri, HISTORICAL commentary NIH Image to ImageJ: 25 years of image analysis, Nature Methods 9, 671 (2012).

Outline

Information

Phys. Rev. Fluids 4, 034202– Published 5 March, 2019
  • Received 13 July 2018
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation