Topologically Protected Transport of Cargo in a Chiral Active Fluid Aided by Odd-Viscosity-Enhanced Depletion Interactions

The discovery of topological edge states that unidirectionally propagate along the boundary of system without backscattering has enabled the development of new design principles for material or information transport. Here, we show that the topological edge flow supported by the chiral active fluid composed of spinners can even robustly transport an immersed intruder with the aid of the spinner-mediated depletion interaction between the intruder and boundary. Importantly, the effective interaction significantly depends on the dissipationless odd viscosity of the chiral active fluid, which originates from the spinning-induced breaking of time-reversal and parity symmetries, rendering the transport controllable. Our findings propose a novel avenue for robust cargo transport and could open a range of new possibilities throughout biological and microfluidic systems.

Figure 1

(a) Top view (top) and side view (bottom) of the gearlike spinner in experiments. The arrow denotes the clockwise rotation of the spinner. (b) Sketch of the counterclockwise rotating spinner in simulations, which is intendedly represented as a Janus particle to highlight its orientation. (c) Experimental and (d) simulation snapshots of a large passive disk transported in the chiral active fluid confined by a circular boundary with a rodlike obstacle, where ${\sigma }_p=4{\sigma }_s$ and $\rho =0.6$. In (c) and (d), the red numbers denote the experimental and the scaled simulation times, respectively, and the arrows represent the direction of the edge transport (edge flow). In the simulation $T_d=20$ is used.

Figure 2

Dwell probability (circle, left longitudinal axis) and transport velocity (triangle, right longitudinal axis) of the intruder as a function of the spinner packing fraction (a),(c) and the intruder size (b),(d). For comparison, the spinner edge flow velocity (square) is plotted. Here, the velocities are reduced by an isolated-spinner quantity ${\omega }_s{\sigma }_s$ [40]. The star in (a) denotes Pr in the passive gear fluid. The data in (a),(b) and (c),(d) correspond to the experiment and simulation, respectively. In (a),(c), ${\sigma }_p=4{\sigma }_s$; and in (b),(d), $\rho =0.55$ for experiments and $\rho =0.6$ for simulations. In simulations $T_d=10$ is used.

Figure 3

(a) Edge flow velocity of the spinner (square) and transport velocity (triangle) and dwell probability (circle) of the intruder as a function of $T_d$. Dashed and dotted lines are separately the velocities of the spinner and the intruder, obtained from Eq. (4). (b) Effective attraction on the intruder versus $T_d$, obtained from simulation (circle) and theory (square). The inset plots the odd viscosity of the spinner fluid versus $T_d$. Here, we fix $\rho =0.6$ and ${\sigma }_p=4{\sigma }_s$.

Figure 4

Sketch of the frictional collisions between spinners separated by an imaginary plane (dashed line), illustrating the origin of the odd viscosity. The yellow arrow at one spinner surface denotes the friction exerted by the other. (a) In the absence of shear flow, the interparticle collision direction (from center to center) is uniformly distributed, so the interparticle friction averagely produces a tangential stress parallel to the plane, corresponding to the rotational viscosity term in Eq. (2), and does not contribute to normal stress. (b),(c) In the presence of a shear flow ${\partial }_x{v}_y>0$ (red arrow), the spinners on the right have larger upward velocity, so they are inclined to collide with their left neighbors from below, resulting in a biased collision direction. Such biased collisions contribute to a nonzero normal stress ${\sigma }^o$ across the imaginary plane, which is (b) negative for a plane parallel to the flow and (c) positive for a plane perpendicular to the flow.