Hyperuniform Active Chiral Fluids with Tunable Internal Structure

Large density fluctuations observed in active systems and hyperuniformity are two seemingly incompatible phenomena. However, the formation of hyperuniform states has been recently predicted in nonequilibrium fluids formed by chiral particles performing circular motion with the same handedness. Here we report evidence of hyperuniformity realized in a chiral active fluid comprised of pear-shaped Quincke rollers of arbitrary handedness. We show that hyperuniformity and large density fluctuations, triggered by dynamic clustering, coexist in this system at different length scales. The system loses its hyperuniformity as the curvature of particles’ motion increases, transforming them into localized spinners. Our results experimentally demonstrate a novel hyperuniform active fluid and provide new insights into an interplay between chirality, activity, and hyperuniformity.

Figure 1

(a) A sketch of the experimental setup. The red arrow depicts the rotational motion and the black arrows show the direction of the translational motion of the pear-shaped particles energised by an external dc electric field $\mathbf{E}$. The white arrow indicates the particle orientation $\mathbf{n}$. The gray circle illustrates a trajectory of a roller that can be either in the CW or CCW state. (b) The curvature $k$ of the particles’ trajectories in a dilute sample obtained at different field strengths. Particles do not perform steady rotations when $E<E_c=1.6\mathrm{V}\mu {\mathrm{m}}^{-1}$ (shown as gray background). Inset: Average particle velocity $\mathbf{v}$ of the rollers in a dilute sample as a function of the electric field strength. The area fraction $\varphi =0.011$. (c) Velocity temporal correlation function $C_t$ in a dilute suspension. $\varphi =0.011$. (d) Mean square displacements of circle rollers at different field strengths. The dotted and dashed lines indicate ${\tau }^1$ and ${\tau }^2$ dependencies, respectively. $\varphi =0.116$.

Figure 2

Snapshots of collective emergent patterns (left) and corresponding trajectories (right) formed by circle rollers. (a) Spontaneous localized vortices. $E=2.0\mathrm{V}\mu {\mathrm{m}}^{-1}$. (b) Rotating flocks. $E=2.4\mathrm{V}\mu {\mathrm{m}}^{-1}$. (c) Gas of spinners. $E=3.2\mathrm{V}\mu {\mathrm{m}}^{-1}$. Only a part of the whole experimental image and 10% of the corresponding trajectories are shown for clarity. The scale bar is 0.5 mm. $\varphi =0.116$.

Figure 3

Dynamic hyperuniform states with local density fluctuations. (a) Density fluctuations $⟨\delta \rho (L{)}^2⟩$ of pear-shaped rollers as a function of the window size $L$. The solid, dotted, and dashed lines show $L^{-2}$, $L^{-2.5}$, and $L^{-3}$ scalings, respectively. Inset: Curvatures of particle trajectories at different electric field strengths. (b) Structure factors $S(q)$ of circle rollers at different dynamic states. Solid, dashed, and dotted lines show $q^1$, $q^{0.5}$, and $q^{0.25}$ scalings, respectively. The shapes and color of the symbols correspond to different dynamic phases: vortices (blue circles), rotating flocks (green squares), and spinners (red triangles). The area fraction $\varphi =0.116$.

Figure 4

Flocks of spherical rollers powered by a pulsed electric field. (a) A snapshot of a flocking state of spherical rollers. (b) Trajectories of rollers in flocks shown in (a). Only part of the whole experimental image and 10% of the trajectories are shown for clarity. The scale bar is 0.5 mm. The electric field strength is $2.5\mathrm{V}\mu {\mathrm{m}}^{-1}$; the area fraction $\varphi =0.124$. The frequency and duty cycle of the pulsed electric field are 100 Hz and 85%, respectively. See also video S5 in Ref. [44]. (c)–(d) Local density fluctuations $⟨\delta \rho (L{)}^2⟩$ as a function of the window size $L$ and structure factor $S(q)$ of the rollers. The size of spherical particles $d_{\mathrm{sp}}=4.8\mu \mathrm{m}$.