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.
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Diffusive regimes in a two-dimensional chiral fluid
Communications Physics Open Access 21 October 2022
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The raw data supporting the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.
All custom codes used for the data processing and numerical modeling are available from the corresponding author upon reasonable request.
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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.
The authors declare no competing interests.
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 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.
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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
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