Fig. 2: Collective dynamics of hydrodynamically interacting rotors.
From: Simultaneous emergence of active turbulence and odd viscosity in a colloidal chiral active system
a–c Fluorescent optical images of rotors at ϕ = 0.008, 0.031 and 0.144 with an overlay of a few typical trajectories. Here, only a quarter of the full probe chamber is shown (see Supplementary Movies 2–4) and \({{{{{{{\rm{Re}}}}}}}}\simeq 1{0}^{-5}\). d–f Simulated rotors configurations at ϕ = 0.007, 0.04 and 0.14 with all trajectories in grey and few highlighted ones for comparison with experimental images. Trajectories are all drawn for a time Ωt = 6. Only a part of the full simulation domain is shown and \({{{{{{{\rm{Re}}}}}}}}\simeq 0.09\). g–i Full simulation domains with trajectories, showing the formation of multiscale vortices. Dashed inset frames indicate the domains in (d–f). j Mean-square displacements for experiments (orange triangles) and simulations (purple bullets) at different packing fractions in a square simulation box of length L = 100σ with periodic boundary conditions. The lines correspond to the respective least-square fits to the active Brownian particle mean-square displacement. Simulation data was obtained with tav = 7 × 105 and nav = 1, and experiments with tav = 150. k, l Active velocity va, normalized by the rotor surface velocity vs = πσΩ, and rotational diffusion time τr with values and errors corresponding to the fits in (j). Dotted (black) lines correspond to the analytical prediction \({v}_{{{{{{{{\rm{a}}}}}}}}}\simeq \pi {{\Omega }}\sigma {(1-\phi /{\phi }_{{{{{{{{\rm{cp}}}}}}}}})}^{2{\phi }_{{{{{{{{\rm{cp}}}}}}}}}}\sqrt{\phi /\pi }\); dash-dotted lines take into account an additional multiplicative fit factor of 3.3.
