- Open Access
Rolling at right angles: Magnetic anisotropy enables dual-anisotropic active matter
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 () leads to circular trajectories interspersed with short spontaneous runs. Intermediate fields () linearize the motion along the axis perpendicular to . At high magnetic fields, we observe the surprising emergence of a second, distinct linearization along the axis parallel to . With numerical simulations, we show that this behavior can be explained by anisotropic magnetic susceptibility.
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References (52)
- 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).
- M. J. Bowick, N. Fakhri, M. C. Marchetti, and S. Ramaswamy, Symmetry, thermodynamics, and topology in active matter, Phys. Rev. X 12, 010501 (2022).
- 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).
- R. Voituriez, J. F. Joanny, and J. Prost, Spontaneous flow transition in active polar gels, Europhys. Lett. 70, 404 (2005).
- S. R. McCandlish, A. Baskaran, and M. F. Hagan, Spontaneous segregation of self-propelled particles with different motilities, Soft Matter 8, 2527 (2012).
- 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).
- B. Liebchen and D. Levis, Collective behavior of chiral active matter: Pattern formation and enhanced flocking, Phys. Rev. Lett. 119, 058002 (2017).
- A. Chardac, L. A. Hoffmann, Y. Poupart, L. Giomi, and D. Bartolo, Topology-Driven ordering of flocking matter, Phys. Rev. X 11, 031069 (2021).
- 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).
- 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).
- H. C. Berg and R. A. Anderson, Bacteria swim by rotating their flagellar filaments, Nature (London) 245, 380 (1973).
- F. Ndlec, T. Surrey, A. C. Maggs, and S. Leibler, Self-organization of microtubules and motors, Nature (London) 389, 305 (1997).
- 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).
- 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).
- 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).
- G. E. Pradillo, H. Karani, and P. M. Vlahovska, Quincke rotor dynamics in confinement: Rolling and hovering, Soft Matter 15, 6564 (2019).
- B. Liebchen and H. Lowen, Synthetic chemotaxis and collective behavior in active matter, Acc. Chem. Res. 51, 2982 (2018).
- H. Stark, Artificial chemotaxis of self-phoretic active colloids: Collective behavior, Acc. Chem. Res. 51, 2681 (2018).
- K. Villa and M. Pumera, Fuel-free light-driven micro/nanomachines: Artificial active matter mimicking nature, Chem. Soc. Rev. 48, 4966 (2019).
- 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).
- 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).
- J. Yan, M. Han, J. Zhang, C. Xu, E. Luijten, and S. Granick, Reconfiguring active particles by electrostatic imbalance, Nat. Mater. 15, 1095 (2016).
- A. Kaiser, A. Snezhko, and I. S. Aranson, Flocking ferromagnetic colloids, Sci. Adv. 3, e1601469 (2017).
- A. Snezhko, M. Belkin, I. S. Aranson, and W.-K. Kwok, Self-assembled magnetic surface swimmers, Phys. Rev. Lett. 102, 118103 (2009).
- 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).
- G. Quincke, Ueber rotationen im constanten electrischen felde, Ann. Phys. 295, 417 (1896).
- T. B. Jones, Quincke rotation of spheres, IEEE Transactions on Industry Applications IA-20, 845 (1984).
- T. B. Jones, Electromechanics of Particles (Cambridge University Press, New York, 1995), pp. 227–230.
- 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).
- N. Pannacci, L. Lobry, and E. Lemaire, How insulating particles increase the conductivity of a suspension, Phys. Rev. Lett. 99, 094503 (2007).
- 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).
- 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).
- S. Maity and A. Morin, Spontaneous demixing of binary colloidal flocks, Phys. Rev. Lett. 131, 178304 (2023).
- 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).
- 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).
- D. Saville, Electrohydrodynamics: The Taylor-Melcher leaky dielectric model, Annu. Rev. Fluid Mech. 29, 27 (1997).
- J. Melcher and G. Taylor, Electrohydrodynamics: A review of the role of interfacial shear stresses, Annu. Rev. Fluid Mech. 1, 111 (1969).
- 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.
- J. C. Crocker and D. G. Grier, Methods of digital video microscopy for colloidal studies, J. Colloid Interface Sci. 179, 298 (1996).
- B. Zhang, H. Karani, P. M. Vlahovska, and A. Snezhko, Persistence length regulates emergent dynamics in active roller ensembles, Soft Matter 17, 4818 (2021).
- 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).
- Y. Chen, L. Wang, and T. Hui Zhang, Tunable collective dynamics of ellipsoidal quincke particles, Soft Matter 19, 512 (2023).
- E. M. Purcell, Life at low reynolds number, Am. J. Phys. 45, 3 (1977).
- I. Turcu, Electric field induced rotation of spheres, J. Phys. A: Math. Gen. 20, 3301 (1987).
- D. Das and D. Saintillan, Electrohydrodynamic interaction of spherical particles under quincke rotation, Phys. Rev. E 87, 043014 (2013).
- 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].
- 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).
- 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.
- A. Gray, Viviani's curve, in Modern Differential Geometry of Curves and Surfaces with Mathematica (CRC Press, Boca Raton, FL, 1997), pp. 201–202.
- E. W. Weisstein, Viviani's curve, wolfram research, inc. (accessed: 2025-06-17), https://mathworld.wolfram.com/VivianisCurve.html.
- C. P. Bean and J. D. Livingston, Superparamagnetism, J. Appl. Phys. 30, S120 (1959).
- 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).