Self-propelled particle transport in regular arrays of rigid asymmetric obstacles

We report numerical results which show the achievement of net transport of self-propelled particles (SPPs) in the presence of a two-dimensional regular array of convex, either symmetric or asymmetric, rigid obstacles. The repulsive interparticle (soft disks) and particle-obstacle interactions present no alignment rule. We find that SPPs present a vortex-type motion around convex symmetric obstacles even in the absence of hydrodynamic effects. Such a motion is not observed for a single SPP, but is a consequence of the collective motion of SPPs around the obstacles. A steady particle current is spontaneously established in an array of nonsymmetric convex obstacles (which presents no cavity in which particles may be trapped), and in the absence of an external field. Our results are mainly a consequence of the tendency of the self-propelled particles to attach to solid surfaces.

Figure 1

The configuration [(a) circle, (c) half circle] and the average velocity field [(b) circle, (d) half circle] of SPP in the presence of a single obstacle. Other system parameters are $D=50$, $\varphi =0.596$, $\eta =0.005$.

Figure 2

Normalized particle displacement probabilities along the $x$ direction, $P\left(\Delta x\right)$, for (a) circular and (b) half-circular obstacles. In both cases the obstacle diameter is $D=5$ and $\varphi =0.244$, $\eta =0.005$. The cumulative distributions for positive $F(\Delta x>0)$ (solid lines) and negative $F(\Delta x<0)$ (dot-dashed lines) displacements in the lattice of half-circle obstacles are shown as inset in (b) for $a=10$ (black) and $a=50$ (red, gray).

Figure 3

(a) The average $x$ component of the drift velocity $\langle v_x\rangle$ of the SPPs (in a lattice of half-circle obstacles) as a function of noise $\eta$ (log scale) for $a=10$, two obstacle sizes $D=5$ (solid symbols) and $7.5$ (open symbols), and three different area fractions $\varphi$. (b) Same quantity, but now as a function of $a$, for two obstacle sizes $D=5$ (solid symbols) and $7.5$ (open symbols). (c) $x$ and $y$ components of the drift velocity as a function of the orientation angle $\delta$ of the half-circle obstacles with respect to the $x$ direction (inset).