Sorting and Extraction of Self-Propelled Chiral Particles by Polarized Wall Currents

The dynamics of self-propelled particles with curved trajectories is investigated. Two modes are observed, a bulk mode with a quasicircular motion and a surface mode with the particles following the walls. The surface mode is the only mode of ballistic transport and the particle current is polar and depends on the particles’ chirality. We show that a robust sorting and extraction occurs when the particles explore a domain with two exit gates collecting selectively the particles circling left and right. With a counterslope, the extraction rate is found to increase while the sorting error is reduced.

Figure 1

(a) Trajectory of an isolated right-turning particle (2.6 s). (b) Trajectory of the same particle in surface mode. (c) Root mean square displacement (RMSD) for seven particles in a circular box as a function of the time increment. The solid line is the RMSD averaged over the particles that are not in contact with the walls. The dashed line is the RMSD for the particles close to the wall. A ballistic regime with a slope 1 and a diffusive regime with a slope $1/2$ are also represented (logarithmic axes).

Figure 2

(a) Average instantaneous velocity field obtained from a set of $N=7$ right-turning particles in a circular box. The color of the arrows indicates the orientation of the velocity with respect to the center of the box. Two pairs of schematic trajectories are represented on top of the vector field to illustrate the clockwise circulations. The dashed line is a nonexisting trajectory because of the wall presence. Two green boxes are represented to illustrate the trajectory sampling. (b) $D_{\tau }/\tau (\mathrm{m}{\mathrm{s}}^{-1})$ with $D_{\tau }$ the distance increment during a time $\tau$. Here, the value selected for $\tau$ is 1.5 s, close to the first minimum in the MSD of a particle in bulk mode [see Fig. 1]. For a particle moving straight, $D_{\tau }/\tau$ is the instantaneous velocity of the particle. For a particle describing perfect circles with a period $T$, $D_{\tau }/\tau =0$ for $\tau =T$.

Figure 3

(a) Top view of the sorting experiment with $N_r=4$ right-turning particles and $N_l=4$ left-turning particles. Most of the particles are in the bulk mode except for one right-handed particle that is about to reach the gate $R$ and one left-handed particle following the wall toward the gate $L$. This snapshot is for the horizontal experiment ($\alpha =0°$). The whole experiment can be tilted to induce a horizontal external field $g\sin \alpha$. (b) Particle extraction rate as a function of the total number of particles in the channel for the horizontal ($\alpha =0°$) and the tilted experiment ($\alpha =1.8°$). Once a particle is counted in a compartment, it is replaced in the channel. The circle charts indicate the error ratio. (c) Particle locations in the channel (right-handed red dots, left-handed blue dots) without tilt. (d) Particle locations in the channel (right-handed red dots, left-handed blue dots) with a tilt $\alpha =1.8°$.