How do flocks, herds and swarms proceed through disordered environments? This question is not only crucial to animal groups in the wild, but also to virtually all applications of collective robotics, and active materials composed of synthetic motile units [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In stark contrast, appart from very rare exceptions [15][16][17], our physical understanding of flocking has been hitherto limited to homogeneous media [18][19][20]. Here we explain how collective motion survives to geometrical disorder. To do so, we combine experiments on motile colloids cruising through random microfabricated obstacles, and analytical theory. We explain how disorder and bending elasticity compete to channel the flow of polar flocks along sparse river networks akin those found beyond plastic depinning in driven condensed matter [21]. Further increasing disorder, we demonstrate that collective motion is suppressed in the form of a first-order phase transition generic to all polar active materials.We use the experimental system introduced in [10,22], which consists in colloidal rollers powered by the so-called Quincke electro-rotation mechanism [23], see Methods and Supplementary Methods. The motile colloids experience both hydrodynamic and electrostatic interactions which promote alignement of their translational velocity [10,22]. When the roller packing fraction, ρ, exceeds 3 × 10 −3 , these polar interactions overcome rotational diffusion and macroscopic collective motion emerges [10,22]. In the homogeneous slab geometry shown in Fig. 1a, a seven-millimeter-long flock spontaneously forms and cruises through a dilute ensemble of rollers moving isotropically, see Supplementary Video 1. The flock has a sharp front, a long tail, and endlessly cruises at a constant speed along the x-axis, bouncing back and forth on the confining walls. The flock speed c F is found to be equal to the speed of an isolated roller v 0 = 1.4 ± 0.1 mm s −1 .Can flocks propagate in disorder media? How does this broken-symmetry phase survive to geometrical disorder? In order to answer these questions, we include randomly distributed circular obstacles of radius a = 5 µm in the microfluidic channel. When the obstacle packing fraction φ o is small, collective motion still emerges according to the same nucleation and propagation scenario, see Fig. 1b and Supplementary Video 2. However as φ o exceeds a critical value, φ o , the obstacle collisions suppress any form of global orientational order and macroscopic transport. Correlated motion persists only at short scales, as illustrated in Supplementary Video 3. As expected, dense flocks are more robust to disorder and φ o monotonically increases with the roller fraction ρ, Fig. 1c.In all that follows, the sole control parameter of our experiments is the obstacle fraction φ o . The roller fraction is set to a constant value above the flocking threshold in a obstacle-free channel, ρ = (1.02 ± 0.06) × 10 −2 . A natural order parameter for the flocking transition is the magnitude J x...
Spontaneously flowing liquids have been successfully engineered from a variety of biological and synthetic self-propelled units. Together with their orientational order, wave propagation in such active fluids has remained a subject of intense theoretical studies. 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 fluctuations.
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