Sounds and hydrodynamics of polar active fluids

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.

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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

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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