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Rolling at right angles: Magnetic anisotropy enables dual-anisotropic active matter

Eavan Fitzgerald1, Cécile Clavaud1,2, Debasish Das3, Isaac C. D. Lenton1, and Scott R. Waitukaitis1,*

  • *Contact author: scott.waitukaitis@ist.ac.at

Phys. Rev. E 112, 065418 – Published 12 December, 2025

DOI: https://doi.org/10.1103/1ss8-31rb

Abstract

We report on an experimental active matter system with motion restricted to four cardinal directions. Our particles are magnetite-doped colloidal spheres driven by the Quincke electrorotational instability. The absence of a magnetic field (|B|=0) leads to circular trajectories interspersed with short spontaneous runs. Intermediate fields (|B|≲20mT) linearize the motion along the axis perpendicular to B. At high magnetic fields, we observe the surprising emergence of a second, distinct linearization along the axis parallel to B. With numerical simulations, we show that this behavior can be explained by anisotropic magnetic susceptibility.

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References (52)

  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. M. J. Bowick, N. Fakhri, M. C. Marchetti, and S. Ramaswamy, Symmetry, thermodynamics, and topology in active matter, Phys. Rev. X 12, 010501 (2022).
  3. 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).
  4. R. Voituriez, J. F. Joanny, and J. Prost, Spontaneous flow transition in active polar gels, Europhys. Lett. 70, 404 (2005).
  5. S. R. McCandlish, A. Baskaran, and M. F. Hagan, Spontaneous segregation of self-propelled particles with different motilities, Soft Matter 8, 2527 (2012).
  6. 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).
  7. B. Liebchen and D. Levis, Collective behavior of chiral active matter: Pattern formation and enhanced flocking, Phys. Rev. Lett. 119, 058002 (2017).
  8. A. Chardac, L. A. Hoffmann, Y. Poupart, L. Giomi, and D. Bartolo, Topology-Driven ordering of flocking matter, Phys. Rev. X 11, 031069 (2021).
  9. A. Bricard, J.-B. Caussin, N. Desreumaux, O. Dauchot, and D. Bartolo, Emergence of macroscopic directed motion in populations of motile colloids, Nature (London) 503, 95 (2013).
  10. A. Bricard, J.-B. Caussin, D. Das, C. Savoie, V. Chikkadi, K. Shitara, O. Chepizhko, F. Peruani, D. Saintillan, and D. Bartolo, Emergent vortices in populations of colloidal rollers, Nat. Commun. 6, 7470 (2015).
  11. H. C. Berg and R. A. Anderson, Bacteria swim by rotating their flagellar filaments, Nature (London) 245, 380 (1973).
  12. F. Ndlec, T. Surrey, A. C. Maggs, and S. Leibler, Self-organization of microtubules and motors, Nature (London) 389, 305 (1997).
  13. T. Sanchez, D. T. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, Spontaneous motion in hierarchically assembled active matter, Nature (London) 491, 431 (2012).
  14. Y. Sumino, K. H. Nagai, Y. Shitaka, D. Tanaka, K. Yoshikawa, H. Chaté, and K. Oiwa, Large-scale vortex lattice emerging from collectively moving microtubules, Nature (London) 483, 448 (2012).
  15. J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living crystals of light-activated colloidal surfers, Science 339, 936 (2013).
  16. G. E. Pradillo, H. Karani, and P. M. Vlahovska, Quincke rotor dynamics in confinement: Rolling and hovering, Soft Matter 15, 6564 (2019).
  17. B. Liebchen and H. Lowen, Synthetic chemotaxis and collective behavior in active matter, Acc. Chem. Res. 51, 2982 (2018).
  18. H. Stark, Artificial chemotaxis of self-phoretic active colloids: Collective behavior, Acc. Chem. Res. 51, 2681 (2018).
  19. K. Villa and M. Pumera, Fuel-free light-driven micro/nanomachines: Artificial active matter mimicking nature, Chem. Soc. Rev. 48, 4966 (2019).
  20. B. Vincenti, G. Ramos, M. L. Cordero, C. Douarche, R. Soto, and E. Clement, Magnetotactic bacteria in a droplet self-assemble into a rotary motor, Nat. Commun. 10, 5082 (2019).
  21. 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).
  22. J. Yan, M. Han, J. Zhang, C. Xu, E. Luijten, and S. Granick, Reconfiguring active particles by electrostatic imbalance, Nat. Mater. 15, 1095 (2016).
  23. A. Kaiser, A. Snezhko, and I. S. Aranson, Flocking ferromagnetic colloids, Sci. Adv. 3, e1601469 (2017).
  24. A. Snezhko, M. Belkin, I. S. Aranson, and W.-K. Kwok, Self-assembled magnetic surface swimmers, Phys. Rev. Lett. 102, 118103 (2009).
  25. R. Reyes Garza, N. Kyriakopoulos, Z. M. Cenev, C. Rigoni, and J. V. I. Timonen, Magnetic quincke rollers with tunable single-particle dynamics and collective states, Sci. Adv. 9, eadh2522 (2023).
  26. G. Quincke, Ueber rotationen im constanten electrischen felde, Ann. Phys. 295, 417 (1896).
  27. T. B. Jones, Quincke rotation of spheres, IEEE Transactions on Industry Applications IA-20, 845 (1984).
  28. T. B. Jones, Electromechanics of Particles (Cambridge University Press, New York, 1995), pp. 227–230.
  29. H. Karani, Gerardo E. Pradillo, and Petia M. Vlahovska, Tuning the random walk of active colloids: From individual run-and-tumble to dynamic clustering, Phys. Rev. Lett. 123, 208002 (2019).
  30. N. Pannacci, L. Lobry, and E. Lemaire, How insulating particles increase the conductivity of a suspension, Phys. Rev. Lett. 99, 094503 (2007).
  31. G. Kokot, H. A. Faizi, G. E. Pradillo, A. Snezhko, and P. M. Vlahovska, Spontaneous self-propulsion and nonequilibrium shape fluctuations of a droplet enclosing active particles, Commun. Phys. 5, 91 (2022).
  32. B. Zhang, A. Glatz, I. S. Aranson, and A. Snezhko, Spontaneous shock waves in pulse-stimulated flocks of quincke rollers, Nat. Commun. 14, 7050 (2023).
  33. S. Maity and A. Morin, Spontaneous demixing of binary colloidal flocks, Phys. Rev. Lett. 131, 178304 (2023).
  34. A. Mauleon-Amieva, M. P. Allen, T. B. Liverpool, and C. P. Royall, Dynamics and interactions of quincke roller clusters: From orbits and flips to excited states, Sci. Adv. 9, eadf5144 (2023).
  35. Z. Zhang, H. Yuan, Y. Dou, M. O. de la Cruz, and K. J. M. Bishop, Quincke oscillations of colloids at planar electrodes, Phys. Rev. Lett. 126, 258001 (2021).
  36. D. Saville, Electrohydrodynamics: The Taylor-Melcher leaky dielectric model, Annu. Rev. Fluid Mech. 29, 27 (1997).
  37. J. Melcher and G. Taylor, Electrohydrodynamics: A review of the role of interfacial shear stresses, Annu. Rev. Fluid Mech. 1, 111 (1969).
  38. D. B. Allan, T. Caswell, N. C. Keim, C. M. van der Wel, and R. W. Verweij, Soft-matter/trackpy: V0.6.2 (2024), https://doi.org/10.5281/zenodo.10674547.
  39. J. C. Crocker and D. G. Grier, Methods of digital video microscopy for colloidal studies, J. Colloid Interface Sci. 179, 298 (1996).
  40. B. Zhang, H. Karani, P. M. Vlahovska, and A. Snezhko, Persistence length regulates emergent dynamics in active roller ensembles, Soft Matter 17, 4818 (2021).
  41. F. Kümmel, B. ten Hagen, R. Wittkowski, I. Buttinoni, R. Eichhorn, G. Volpe, H. Löwen, and C. Bechinger, Circular motion of asymmetric self-propelling particles, Phys. Rev. Lett. 110, 198302 (2013).
  42. Y. Chen, L. Wang, and T. Hui Zhang, Tunable collective dynamics of ellipsoidal quincke particles, Soft Matter 19, 512 (2023).
  43. E. M. Purcell, Life at low reynolds number, Am. J. Phys. 45, 3 (1977).
  44. I. Turcu, Electric field induced rotation of spheres, J. Phys. A: Math. Gen. 20, 3301 (1987).
  45. D. Das and D. Saintillan, Electrohydrodynamic interaction of spherical particles under quincke rotation, Phys. Rev. E 87, 043014 (2013).
  46. See Supplemental Material at http://link.aps.org/supplemental/10.1103/1ss8-31rb for movies and more details on experimental and numerical methods, which includes Refs. [47, 48, 49, 50].
  47. A. J. Goldman, R. G. Cox, and H. Brenner, Slow viscous motion of a sphere parallel to a plane wall—I motion through a quiescent fluid, Chem. Eng. Sci. 22, 637 (1967).
  48. M. F. Beatty, Finite rigid body displacements, in Principles of Engineering Mechanics: Kinematics—The Geometry of Motion (Springer US, Boston, MA, 1986), pp. 151–227.
  49. A. Gray, Viviani's curve, in Modern Differential Geometry of Curves and Surfaces with Mathematica (CRC Press, Boca Raton, FL, 1997), pp. 201–202.
  50. E. W. Weisstein, Viviani's curve, wolfram research, inc. (accessed: 2025-06-17), https://mathworld.wolfram.com/VivianisCurve.html.
  51. C. P. Bean and J. D. Livingston, Superparamagnetism, J. Appl. Phys. 30, S120 (1959).
  52. M. M. van Oene, L. E. Dickinson, F. Pedaci, M. Köber, D. Dulin, J. Lipfert, and N. H. Dekker, Biological magnetometry: Torque on superparamagnetic beads in magnetic fields, Phys. Rev. Lett. 114, 218301 (2015).

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