Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Polar state reversal in active fluids

Nature Physics volume 18, pages 154–159 (2022)Cite this article

Subjects

Abstract

Spontaneous emergence of correlated states such as flocks and vortices is a prime example of collective dynamics and self-organization observed in active matter1,2,3,4,5,6. In geometrically confined systems, the formation of globally correlated polar states proceeds through the emergence of a macroscopic steadily rotating vortex, which spontaneously selects a clockwise or counterclockwise global chiral state7,8. Here, we reveal that a global vortex formed by colloidal rollers exhibits polar state reversal and that a subsequent formation of the collective states upon re-energizing the system is not random. We combine experiments and simulations to elucidate how a combination of hydrodynamic and electrostatic interactions leads to hidden asymmetries in the local particle positional order, reflecting the chiral state of the system. These asymmetries can be exploited to systematically command subsequent polar states of active liquids through temporal control of the activity.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Vortex chiral state reversal induced by a temporal modulation of activity.
Fig. 2: Roller dynamics during chirality reversal of the polar state.
Fig. 3: Positional order asymmetries in polar active fluids.
Fig. 4: Role of microscopic interactions in the chiral state reversal.

Similar content being viewed by others

Data availability

The raw data supporting the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.

Code availability

All custom codes used for the data processing and numerical modeling are available from the corresponding author upon reasonable request.

References

  1. Vicsek, T. & Zafeiris, A. Collective motion. Phys. Rep. 517, 71–140 (2012).

    Article  ADS  Google Scholar 

  2. Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).

    Article  ADS  Google Scholar 

  3. Aranson, I. S. Active colloids. Phys.-Usp. 56, 79–92 (2013).

    Article  ADS  Google Scholar 

  4. Snezhko, A. Complex collective dynamics of active torque-driven colloids at interfaces. Curr. Opin. Colloid Interface Sci. 21, 65–75 (2016).

    Article  Google Scholar 

  5. Zöttl, A. & Stark, H. Hydrodynamics determines collective motion and phase behavior of active colloids in quasi-two-dimensional confinement. Phys. Rev. Lett. 112, 118101 (2014).

    Article  ADS  Google Scholar 

  6. Wu, K.-T. et al. Transition from turbulent to coherent flows in confined three-dimensional active fluids. Science 355, eaal1979 (2017).

    Article  MathSciNet  Google Scholar 

  7. Bricard, A. et al. Emergent vortices in populations of colloidal rollers. Nat. Commun. 6, 7470 (2015).

    Article  ADS  Google Scholar 

  8. Kaiser, A., Snezhko, A. & Aranson, I. S. Flocking ferromagnetic colloids. Sci. Adv. 3, e1601469 (2017).

    Article  ADS  Google Scholar 

  9. Peruani, F. et al. Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria. Phys. Rev. Lett. 108, 098102 (2012).

    Article  ADS  Google Scholar 

  10. Schaller, V., Weber, C., Semmrich, C., Frey, E. & Bausch, A. R. Polar patterns of driven filaments. Nature 467, 73–77 (2010).

    Article  ADS  Google Scholar 

  11. Sumino, Y. et al. Large-scale vortex lattice emerging from collectively moving microtubules. Nature 483, 448–452 (2012).

    Article  ADS  Google Scholar 

  12. Sokolov, A. & Aranson, I. S. Physical properties of collective motion in suspensions of bacteria. Phys. Rev. Lett. 109, 248109 (2012).

    Article  ADS  Google Scholar 

  13. Bricard, A., Caussin, J.-B., Desreumaux, N., Dauchot, O. & Bartolo, D. Emergence of macroscopic directed motion in populations of motile colloids. Nature 503, 95–98 (2013).

    Article  ADS  Google Scholar 

  14. Yan, J. et al. Reconfiguring active particles by electrostatic imbalance. Nat. Mater. 15, 1095–1099 (2016).

    Article  ADS  Google Scholar 

  15. Kokot, G. et al. Active turbulence in a gas of self-assembled spinners. Proc. Natl Acad. Sci. USA 114, 12870–12875 (2017).

    Article  ADS  Google Scholar 

  16. Doostmohammadi, A., Ignés-Mullol, J., Yeomans, J. M. & Sagués, F. Active nematics. Nat. Commun. 9, 3246 (2018).

    Article  ADS  Google Scholar 

  17. Zhang, B., Sokolov, A. & Snezhko, A. Reconfigurable emergent patterns in active chiral fluids. Nat. Commun. 11, 4401 (2020).

    Article  ADS  Google Scholar 

  18. Martin, J. E. & Snezhko, A. Driving self-assembly and emergent dynamics in colloidal suspensions by time-dependent magnetic fields. Rep. Prog. Phys. 76, 126601 (2013).

    Article  ADS  Google Scholar 

  19. Driscoll, M. et al. Unstable fronts and motile structures formed by microrollers. Nat. Phys. 13, 375–379 (2017).

    Article  Google Scholar 

  20. Weber, C. A. et al. Long-range ordering of vibrated polar disks. Phys. Rev. Lett. 110, 208001 (2013).

    Article  ADS  Google Scholar 

  21. Kokot, G. & Snezhko, A. Manipulation of emergent vortices in swarms of magnetic rollers. Nat. Commun. 9, 2344 (2018).

    Article  ADS  Google Scholar 

  22. Massana-Cid, H., Codina, J., Pagonabarraga, I. & Tierno, P. Active apolar doping determines routes to colloidal clusters and gels. Proc. Natl Acad. Sci. USA 115, 10618–10623 (2018).

    Article  ADS  Google Scholar 

  23. Han, K. et al. Reconfigurable structure and tunable transport in synchronized active spinner materials. Sci. Adv. 6, eaaz8535 (2020).

    Article  ADS  Google Scholar 

  24. Palacci, J., Sacanna, S., Steinberg, A. P., Pine, D. J. & Chaikin, P. M. Living crystals of light-activated colloidal surfers. Science 339, 936–940 (2013).

    Article  ADS  Google Scholar 

  25. Quincke, G. Ueber Rotationen im constanten electrischen Felde. Ann. der Phys. 295, 417–486 (1896).

    Article  ADS  Google Scholar 

  26. Melcher, J. & Taylor, G. Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. fluid Mech. 1, 111–146 (1969).

    Article  ADS  Google Scholar 

  27. Das, D. & Saintillan, D. Electrohydrodynamic interaction of spherical particles under Quincke rotation. Phys. Rev. E 87, 043014 (2013).

    Article  ADS  Google Scholar 

  28. Pannacci, N., Lobry, L. & Lemaire, E. How insulating particles increase the conductivity of a suspension. Phys. Rev. Lett. 99, 094503 (2007).

    Article  ADS  Google Scholar 

  29. Durlofsky, L., Brady, J. F. & Bossis, G. Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21–49 (1987).

    Article  ADS  Google Scholar 

  30. Kim, S. & Karrila, S. J. Microhydrodynamics - Principles and Selected Applications (Dover Publications, 2005).

  31. Brady, J. F. & Bossis, G. Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157 (1988).

    Article  ADS  Google Scholar 

  32. Rotne, J. & Prager, S. Variational treatment of hydrodynamic interaction in polymers. J. Chem. Phys. 50, 4831–4837 (1969).

    Article  ADS  Google Scholar 

  33. Wajnryb, E., Mizerski, K. A., Zuk, P. J. & Szymczak, P. Generalization of the Rotne–Prager–Yamakawa mobility and shear disturbance tensors. J. Fluid Mech. 731, R3 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  34. Blake, J. R. A note on the image system for a stokeslet in a no-slip boundary. Math. Proc. Camb. Philos. Soc. 70, 303–310 (1971).

    Article  ADS  Google Scholar 

  35. Swan, J. W. & Brady, J. F. Simulation of hydrodynamically interacting particles near a no-slip boundary. Phys. Fluids 19, 113306 (2007).

    Article  ADS  Google Scholar 

  36. Balboa Usabiaga, F., Delmotte, B. & Donev, A. Brownian dynamics of confined suspensions of active microrollers. J. Chem. Phys. 146, 134104 (2017).

    Article  ADS  Google Scholar 

  37. Jones, T. B. Electromechanics of Particles (Cambridge Univ. Press, 2005).

  38. Sainis, S. K., Germain, V., Mejean, C. O. & Dufresne, E. R. Electrostatic interactions of colloidal particles in nonpolar solvents: role of surface chemistry and charge control agents. Langmuir 24, 1160–1164 (2008).

    Article  Google Scholar 

  39. Ermak, D. L. & McCammon, J. A. Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 69, 1352–1360 (1978).

    Article  ADS  Google Scholar 

  40. Kazoe, Y. & Yoda, M. Measurements of the near-wall hindered diffusion of colloidal particles in the presence of an electric field. Appl. Phys. Lett. 99, 124104 (2021).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The research of B.Z., A. Sokolov and A. Snezhko at Argonne National Laboratory was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. H.Y. and M.O.d.l.C. were supported by the Center for Bio-Inspired Energy Science, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under Award DE-SC0000989.

Author information

Authors and Affiliations

  1. Materials Science Division, Argonne National Laboratory, Argonne, IL, USA

    Bo Zhang, Andrey Sokolov & Alexey Snezhko

  2. Applied Physics Graduate Program, Northwestern University, Evanston, IL, USA

    Hang Yuan

  3. Department of Materials Science and Engineering, Northwestern University, Evanston, IL, USA

    Monica Olvera de la Cruz

  4. Department of Physics and Astronomy, Northwestern University, Evanston, IL, USA

    Monica Olvera de la Cruz

Authors
  1. Bo Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrey Sokolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Monica Olvera de la Cruz
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alexey Snezhko
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A. Snezhko and B.Z. conceived the research. B.Z. performed the experiments. H.Y. and A. Sokolov performed simulations. B.Z., H.Y., A. Sokolov, M.O.d.l.C. and A. Snezhko analysed the data and wrote the manuscript.

Corresponding author

Correspondence to Alexey Snezhko.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–8 and Notes 1–3.

Supplementary Video 1

Part 1. Reversal of a roller vortex chiral state in a well induced by a temporal modulation of activity. Left: experimental video of the system. Right: superimposed velocity (arrows) and vorticity (background colour) fields of the rollers during the chiral state reversal. The size of the well D = 1 mm. The area fraction ϕ = 0.12. The total duration is 5 s and the field-off time τoff = 0.5 s. The playback is 0.2× the real time. Part 2. Multiple successive reversals of a vortex chiral state in a well. The size of the well D = 2 mm. The area fraction ϕ = 0.08. The period of 1 cycle is 10 s and τoff = 0.5 s. The total duration is 40 s. The playback is 2× the real time.

Supplementary Video 2

Time evolution of tangential roller velocities in the course of one chirality reversal event. Rollers are shown as circles coloured according to the magnitude of the tangential velocity vt. The size of the well D = 1 mm. The area fraction ϕ = 0.12. The total duration is 4.9 s and the field-off time τoff = 0.5 s. The playback is 0.2× the real time.

Supplementary Video 3

Part 1. Reversal of a chiral state in a track on a temporal modulation of activity. The outer diameter of the track D = 2 mm and the width W = 0.25 mm. The area fraction ϕ = 0.12. The total duration is 5 s and the field-off time τoff = 0.5 s. The playback is 0.2× the real time. Part 2. Multiple successive reversals of a vortex chiral state in a track. The outer diameter of the track D = 2 mm and the width W = 0.25 mm. The period of 1 cycle is 10 s and τoff = 0.5 s. The total duration is 100 s. The playback is 2× the real time. Part 3. Multiple successive reversals of a vortex chiral state in an elongated track. The length of the track L = 10 mm. The outer diameter D = 2 mm. The width W = 0.5 mm. The period of 1 cycle is 10 s andτoff = 0.5 s. The total duration is 50 s. The playback is 2× the real time.

Supplementary Video 4

Multiple successive reversals of chiral states in wells by the particle-based simulations under three different scenarios. Scenario a-both electrostatic and hydrodynamic interactions between rollers are included in the model. Scenario b-only hydrodynamic interactions drive roller dynamics and Scenario c-only electrostatic interactions contribute to the dynamics. Red arrows indicate the directions of particle velocities and yellow arrows show the in-plane components of the dipoles. The size of the well D = 1 mm. The area fraction ϕ = 0.10. The period of one cycle is 5.25 s for Scenarios a and b and 15.25 s for Scenario c. The field-off time τoff = 0.25 s. The total duration is 15 s for Scenarios a and b and 45 s for Scenario c. The playback is 0.5× the real time for Scenarios a and b and 1.5× for Scenario c.

Supplementary Video 5

Time evolution of tangential roller velocities during a chirality reversal as obtained in simulations for a vortex in a well under Scenario a. Rollers are shown as circles coloured according to the magnitude of the tangential velocity vt. The size of the well D = 1 mm. The area fraction ϕ = 0.10. The total duration is 5.25 s and the field-off time τoff = 0.25 s. The playback is 0.2× the real time.

Supplementary Video 6

Part 1. Competition of multiple flocks in experiments. The playback is 0.25× the real time. Part 2. Competition of multiple flocks in simulations. The playback is 0.25× the real time.

Supplementary Video 7

Time evolution of tangential velocities of particles in the course of the chirality reversal for a vortex in a well as described by the phenomenological minimalistic model. Particles are shown as circles coloured according to the magnitude of the tangential velocity vt.

Supplementary Video 8

Part 1. Multiple successive reversals of a chiral vortex in a confined droplet. The size of the droplet D = 1.8 mm. The period of 1 cycle is 10 s and the field-off time τoff = 0.5 s. The total duration is 40 s. The playback is 2× the real time. Part 2. Multiple successive simultaneous reversals of two chiral vortices in two confined droplets. Two vortices have opposite chiralities. The total duration is 50 s. The playback is 2× the real time.

Supplementary Video 9

Multiple successive reversals of a chiral vortex under non-circular confinement. The period of 1 cycle is 10 s and the field-off time τoff = 1 s. The total duration is 30 s. The playback is 1× the real time.

Source data

Source Data Fig. 1

Source data for all subfigures in Fig. 1.

Source Data Fig. 2

Source data for all subfigures in Fig. 2.

Source Data Fig. 3

Source data for all subfigures in Fig. 3.

Source Data Fig. 4

Source data for all subfigures in Fig. 4.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, B., Yuan, H., Sokolov, A. et al. Polar state reversal in active fluids. Nat. Phys. 18, 154–159 (2022). https://doi.org/10.1038/s41567-021-01442-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-021-01442-6

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing