Confinement-induced collective motion in suspensions of run-and-tumble particles

TL;DR

The paper investigates how confinement can induce collective motion in active matter without explicit alignment by studying a 2D suspension of run-and-tumble particles confined by funnel-like obstacles. Using percolation-based band identification, center-of-mass tracking, and a flux-balance framework, it reveals a confinement-induced traveling band that propagates with a mean speed $\langle V_{CM} \rangle \approx \frac{1}{3} v_0$ and organizes into four orientation domains. Motion relies on a forward thrust (domain II) and a lower-part counter-flow mediated by vacancy diffusion and sliding along obstacles, a mechanism that stabilizes the band only within a narrow range of obstacle tilt $\theta_{obs}$. The findings show a geometric route to directed transport in active systems and point to experimental realizations in ring-shaped microfluidic devices and potential applications in fast one-dimensional particle transport.

Abstract

Collective motion is ubiquitous in active systems at all length and time scales. The mechanisms behind such collective motion usually are alignment interactions between active particles, effective alignment after collisions between agents or symmetry-breaking fluctuations induced by passive species in active suspensions. In this article, we introduce a new type of collective motion in the shape of a traveling band induced purely by confinement, where no explicit or effective alignment are prescribed among active agents. We study a suspension of run-and-tumble particles confined in microchannels comprising asymmetric boundaries: one flat wall and one array of funnel-like obstacles. We study the phase behavior of the confined active suspension upon changes in the packing fraction and the persistence length to define the stability region of the traveling band. We characterize the traveling band structurally and dynamically and study its stability with respect to the tilt angle of the obstacles. Lastly, we describe the mechanism of motion of the band, which resembles the tracked locomotion of some heavy vehicles like tractors, finding that a counter-flux of active particles in the lower part of the band, explained in terms of source-sink and vacancy diffusion mechanisms, is the facilitator of the traveling band and sustains its motion. We name this new collective phenomenon confinement-induced tracked locomotion

Figures (6)

• Figure 1: Scheme of the geometry of the system. The top boundary of the microchannel is a flat wall, and the bottom boundary of an array of funnel-like obstacles with period $l_{obs} = 2\left( L_{obs}\cos\theta_{obs} + d + \sigma_{22}\right)$, where $d = 1.25\sigma_{22}$ is the gap size, $L_{obs} = 3.0\sigma_{22}$ is the length of the obstacles and $\theta_{obs}$ the angle formed between the obstacles and the $x$-axis. The walls of the microchannel are composed of frozen particles (in yellow) of diameter $\sigma_{22}$, with a lattice constant, $l_w = 0.12\sigma_{22}$. The axis $y = 0$ is placed at the center of the obstacles. The active particles (i pink) follow the run-and-tumble phenotype observed in different motile microorganisms.
• Figure 2: Phase behavior of the confined active suspension.(a) Dynamic phase diagram in the plane $\phi-l_p$ for the active suspension confined in a microchannel with funnel-like obstacles configured at $\theta_{obs}=30^\circ$. The different phases are represented by symbols and colors: (b) non-percolated system (blue circles); (c) clogging ( green triangles); and (d) traveling band (red diamonds). The color code of the active particles in b-d represent the orientation angle, $\theta$, with respect to the $x$-axis, according to the color bar on the right. All the graphics of trajectories of simulations presented in this article were generated in part using the visualization software OVITO stukowski2009visualization.
• Figure 3: Center of mass velocity of the system (a) Probability distributions of the Center-of-mass velocity of the system for $\phi=0.3$ and $\theta_{obs} = 30^{\circ}$, at different values of $l_p$, for clogging and traveling states. (b) Average Center-of-mass velocity of the system as a function of the persistent length, $l_p$.
• Figure 4: Probability distributions of the orientation angle , $\theta$, of active particles for four selected cases. (a) Clogging states. Filled markers correspond to $\phi = 0.40$, and empty to $\phi = 0.35$. (b) Traveling states. Filled markers correspond to $\phi = 0.275$ and empty to $\phi = 0.25$. (c) Orientation domains within the band. I: Particles pointing mainly upwards. II: Particles pointing towards the direction of motion of the traveling band, constituting the thrust. III: Particles forming a thin layer in the lower part of the band pointing opposite to the band's motion. This domain is the facilitator of the collective motion. IV: Particles trapped in the funnels mainly pointing downwards. The distributions are computed using only the orientations of the largest cluster in the system. The band moves to the right and $\theta_{obs} = 30^{\circ}$.
• Figure 5: (a) Representative particle trajectories depending on their initial positions along the $y$-axis inside the traveling band, for $l_p = 10^5$, $\phi = 0.3$ and $\theta_{obs} = 30^\circ$. The wall particles are not shown for the sake of clarity. (b) Corresponding local density profiles $\rho(y)$, total flux $j_x(y)$, and counter-current $\Delta(y)$ along the $y$-axis. The channel walls are depicted in yellow for reference.