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Sounds and hydrodynamics of polar active fluids

Nature Materials volume 17, pages 789–793 (2018)Cite this article

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Abstract

Spontaneously flowing liquids have been successfully engineered from a variety of biological and synthetic self-propelled units1,2,3,4,5,6,7,8,9,10,11. Together with their orientational order, wave propagation in such active fluids has remained a subject of intense theoretical studies12,13,14,15,16,17. However, the experimental observation of this phenomenon has remained elusive. Here, we establish and exploit the propagation of sound waves in colloidal active materials with broken rotational symmetry. We demonstrate that two mixed modes, coupling density and velocity fluctuations, propagate along all directions in colloidal-roller fluids. We then show how the six material constants defining the linear hydrodynamics of these active liquids can be measured from their spontaneous fluctuation spectrum, while being out of reach of conventional rheological methods. This active-sound spectroscopy is not specific to synthetic active materials and could provide a quantitative hydrodynamic description of herds, flocks and swarms from inspection of their large-scale fluctuations18,19,20,21.

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Fig. 1: Colloidal rollers self-assemble into a spontaneously-flowing liquid.
Fig. 2: Sound modes in polar active fluids.
Fig. 3: Active-fluid spectroscopy.

References

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

    Article  Google Scholar 

  2. Sanchez, T., Chen, D. T. N., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).

    Article  Google Scholar 

  3. Wioland, H., Woodhouse, F. G., Dunkel, J., Kessler, J. O. & Goldstein, R. E. Confinement stabilizes a bacterial suspension into a spiral vortex. Phys. Rev. Lett. 110, 268102 (2013).

    Article  Google Scholar 

  4. DeCamp, S. J., Redner, G. S., Baskaran, A., Hagan, M. F. & Dogic, Z. Orientational order of motile defects in active nematics. Nat. Mater. 14, 1110–1115 (2015).

    Article  Google Scholar 

  5. Nishiguchi, D., Nagai, K. H., Chaté, H. & Sano, M. Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria. Phys. Rev. E 95, 020601 (2017).

    Article  Google Scholar 

  6. Ellis, P. W. et al. Curvature-induced defect unbinding and dynamics in active nematic toroids. Nat. Phys. 14, 85–90 (2017).

    Article  Google Scholar 

  7. Deseigne, J., Dauchot, O. & Chaté, H. Collective motion of vibrated polar disks. Phys. Rev. Lett. 105, 098001 (2010).

    Article  Google Scholar 

  8. 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  Google Scholar 

  9. Chen, Q., Bae, S. C. & Granick, S. Directed self-assembly of a colloidal kagome lattice. Nature 469, 381–384 (2011).

    Article  Google Scholar 

  10. Kumar, N., Soni, H., Ramaswamy, S. & Sood, A. K. Flocking at a distance in active granular matter. Nat. Commun. 5, 4688 (2014).

    Article  Google Scholar 

  11. Nishiguchi, D. & Sano, M. Mesoscopic turbulence and local order in janus particles self-propelling under an ac electric field. Phys. Rev. E 92, 052309 (2015).

    Article  Google Scholar 

  12. Toner, J. & Tu, Y. Long-range order in a two-dimensional dynamical XY model: How birds fly together. Phys. Rev. Lett. 75, 4326–4329 (1995).

    Article  Google Scholar 

  13. Toner, J. & Tu, Y. Flocks, herds, and schools: A quantitative theory of flocking. Phys. Rev. E 58, 4828–4858 (1998).

    Article  Google Scholar 

  14. Tu, Y., Toner, J. & Ulm, M. Sound waves and the absence of galilean invariance in flocks. Phys. Rev. Lett. 80, 4819–4822 (1998).

    Article  Google Scholar 

  15. Simha, R. A. & Ramaswamy, S. Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys. Rev. Lett. 89, 058101 (2002).

    Article  Google Scholar 

  16. Shankar, S., Bowick, M. J. & Marchetti, M. C. Topological sound and flocking on curved surfaces. Phys. Rev. X 7, 031039 (2017).

    Google Scholar 

  17. Souslov, A., Van Zuiden, B. C., Bartolo, D., & Vitelli, V. Topological sound in active-liquid metamaterials. Nat. Phys. 13, 1091–1094 (2017).

    Article  Google Scholar 

  18. Cavagna, A. & Giardina, I. Bird flocks as condensed matter. Annu. Rev. Condens. Matter Phys. 5, 183–207 (2014).

    Article  Google Scholar 

  19. Ginelli, F. et al. Intermittent collective dynamics emerge from conflicting imperatives in sheep herds. Proc. Natl Acad. Sci. USA 112, 12729–12734 (2015).

    Article  Google Scholar 

  20. Buhl, J., Sword, G. A. & Simpson, S. J. Using field data to test locust migratory band collective movement models. Interface Focus 2, 757–763 (2012).

    Article  Google Scholar 

  21. Cavagna, A. et al. Dynamic scaling in natural swarms. Nat. Phys. 13, 914–918 (2017).

    Article  Google Scholar 

  22. Quincke, G. Über rotationen im constanten electrischen Felde. Ann. Physik 59, 417–486 (1896).

    Article  Google Scholar 

  23. Melcher, J. R. & Taylor, G. I. Electrohydrodynamics: A review of the role of interfacial shear stresses. Annu. Rev. Fluid. Mech. 1, 111–146 (1969).

    Article  Google Scholar 

  24. Lavrentovich, O. D. Active colloids in liquid crystals. Curr. Opin. Colloid Interface Sci. 21, 97–109 (2016).

    Article  Google Scholar 

  25. Toner, J., Tu, Y., & Ramaswamy, S. Hydrodynamics and phases of flocks. Ann. Phys. 318, 170–244 (2005).

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. Daniels, L. J. & Durian, D. J. Propagating waves in a monolayer of gas-fluidized rods. Phys. Rev. E 83, 061304 (2011).

    Article  Google Scholar 

  28. Kyriakopoulos, N., Ginelli, F. & Toner, J. Leading birds by their beaks: the response of flocks to external perturbations. New J. Phys. 18, 073039 (2016).

    Article  Google Scholar 

  29. Mishra, S., Baskaran, A. & Marchetti, M. C. Fluctuations and pattern formation in self-propelled particles. Phys. Rev. E 81, 061916 (2010).

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Morin, A., Desreumaux, N., Caussin, J.-B. & Bartolo, D. Distortion and destruction of colloidal flocks in disordered environments. Nat. Phys. 13, 63–67 (2017).

    Article  Google Scholar 

  32. Cavagna, A. et al. Silent flocks: Constraints on signal propagation across biological groups. Phys. Rev. Lett. 114, 218101 (2015).

    Article  Google Scholar 

  33. Yang, X. & Marchetti, M. C. Hydrodynamics of turning flocks. Phys. Rev. Lett. 115, 258101 (2015).

    Article  Google Scholar 

  34. Hansen, J.-P. & McDonald, I. R. Theory of Simple Liquids 4th edn (Academic, Oxford, 2013).

  35. Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298–310 (1996).

    Article  Google Scholar 

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Acknowledgements

We acknowledge support from ANR program MiTra and Institut Universitaire de France. We thank O. Dauchot, A. Souslov and, especially, H. Chaté, B. Mahault, S. Ramaswamy, Y. Tu and J. Toner for invaluable comments and discussions.

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Authors and Affiliations

  1. Univerversité Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, Lyon, France

    Delphine Geyer, Alexandre Morin & Denis Bartolo

Authors
  1. Delphine Geyer
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  2. Alexandre Morin
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  3. Denis Bartolo
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Contributions

D.B. conceived the project. D.G. and D.B. designed the experiments. D.G. and A.M. performed the experiments. D.G. and D.B. analysed and discussed the results. D.G. and D.B. wrote the paper.

Corresponding author

Correspondence to Denis Bartolo.

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Supplementary information

Supplementary Information

Supplementary Video Legends 1–3, Supplementary Notes 1–3, Supplementary Figures 1–5, Supplementary References 1–11

Supplementary Video 1

An active polar liquid composed of colloidal rollers flows in a microfluidic racetrack. We show the trajectories of five particles, and the instantaneous orientation of their velocity (black arrows). They fluctuate around the average direction of the emergent flow. The polar liquid does not move like a rigid body, the particles rearrange. The area fraction of the colloids is ρ0 = 0.11. Colloid diameter: 4.8 μm. Field amplitude: E0 = 2 V μm−1. Video recorded at 500 fps, played at 30 fps.

Supplementary Video 2

An active polar liquid composed of ~ 3 × 106 colloidal rollers flows in a microfluidic racetrack. The colour indicates the magnitude of the velocity-component transverse to the mean flow. Blue particles are moving up, red particles are moving down. Transverse velocity fluctuations propagate through the polar liquid. The area fraction of the colloids is ρ0 = 0.11. Colloid diameter: 4.8 μm. Field amplitude: E0 = 2 V μm−1. Video recorded at 500 fps, played at 20 fps.

Supplementary Video 3

Density field of a polar liquid flowing in a microfluidic racetrack. The density field is defined in the Voronoi cells centred on the particles. The colour of the cells indicates the inverse of the cell area, and therefore corresponds to the local colloid density. The density fluctuations propagate in different directions when the polar liquid flows. The area fraction of the colloids is ρ0 = 0.11. Colloid diameter: 4.8 μm. Field amplitude: E0 = 2 V μm−1. Video recorded at 500 fps, played at 20 fps.

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Geyer, D., Morin, A. & Bartolo, D. Sounds and hydrodynamics of polar active fluids. Nature Mater 17, 789–793 (2018). https://doi.org/10.1038/s41563-018-0123-4

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