Perspective on "Active Brownian Particles Moving in a Random Lorentz Gas"

Abstract

Self-propelled active matter can exhibit vastly different behavior than systems with purely Brownian motion. In Eur. Phys. J. E 40, 23 (2017), Zeitz, Wolf, and Stark compared an active matter particle with a Brownian particle moving in a random obstacle array. They showed that near the obstacle percolation density, both Brownian and active particles exhibit the same subdiffusive behavior, but the active particle reaches a steady state more rapidly. They also found that for high activity, the active particle has a lower effective diffusion than the Brownian particle due to the increased self-trapping effect generated by the activity. This result opens new directions for the study of active matter in disordered media, including bacteria in porous media, active colloids on quenched disorder,and active particles in crowded environments.

Figures (6)

• Figure 1: (a) Illustration of a two-dimensional (2D) active Brownian particle moving with speed $v$ at an orientation of $\phi$. (b-e) Four representative 10 second particle trajectories for a particle with radius $R=1 \mu$m and viscosity $\eta=0.001$ Pa s in water at different velocities of (b) $v=0 \mu$m/s (Brownian limit), (c) $v=1 \mu$m/s, (d) $v=2 \mu$m/s, and (e) $v=3 \mu$m/s. From Fig. 2 of Bechinger16.
• Figure 2: Particle trajectories with time $t/\tau_d$ encoded by color for (a) a Brownian particle and (b) an active Brownian particle in a system with a background obstacle density of $\eta=0.3$. From Fig. 1 of Zeitz17.
• Figure 3: (a, b) Mean squared displacement $\langle \Delta r^2(t)\rangle/(2R)^2$, (c, d) local exponent $\alpha(t)$, and (e, f) local diffusion coefficient $D(t)/D_0$ versus scaled time $t/\tau_d$ for (a, c, e) a Brownian particle with $Pe=0.0$ and (b, d, f) an active Brownian particle with $Pe=100$ at obstacle densities ranging from $\eta=0.0$ to $\eta=0.6$. The percolation transition occurs near $\eta_c=0.28$. The active particles have an extended region at short times where the motion is superdiffusive, but for $\eta > \eta_c$ the motion of the active particles is reduced compared to the Brownian particles due to self trapping effects. From Fig. 2 of Zeitz17.
• Figure 4: Diffusive and ballistic motions at different Péclet values. (a) The diffusion coefficient $D_\infty/D_0$ vs $\eta$, where $D_0$ is the $\eta=0$ diffusion coefficient. From Fig. 5 of Ref. Zeitz17. (b) The effective propulsion velocity $v_{\rm eff}/v_0$ vs $\eta$, where $v_0$ is the propulsion speed. From Fig. 7(a) of Ref. Zeitz17.
• Figure 5: (a, b) Motion of individual particles through a periodic array of posts (red) with lattice constant $a_s$. (a) Trajectory of a Brownian particle. (b) Trajectory of a run-and-tumble active particle with run correlation length $l_a=20 a_s$. The motion is channeled along substrate symmetry directions. (c, d) The corresponding distribution of instantaneous $x$ direction velocities $P(v_x)$ for (c) the Brownian particle from panel (a), where the distribution is Gaussian, and (d) the active particle from panel (b), where the peaks indicate the locking of the motion to the substrate symmetry directions. From Fig. \ref{['fig:2']} of Reichhardt22a.