Preventing clustering of active particles in microchannels

TL;DR

This paper develops a kinetic theory incorporating effective displacements caused by swimmer interactions and tumble events to predict the critical density for clustering of microswimmers in narrow channels, validated with bacterial tracking data.

Contribution

It introduces a novel kinetic modeling approach that accounts for effective displacements without relying on density-dependent speed, enabling prediction of clustering thresholds.

Findings

Critical density for clustering is approximately 0.10 bact/μm.

The model accurately predicts cluster formation prior to observation.

Effective displacements are directly measured from swimmer trajectories.

Abstract

The trajectories of microswimmers moving in narrow channels of widths comparable to their sizes are significantly altered when they encounter another microswimmer moving in the opposite direction. The consequence of these encounters is a delay in the progress of both swimmers, which can be conceptualized as an instantaneous effective backward displacement. Similarly, the modeling of tumble events in bacteria, which occur over a finite time, can be represented as an instantaneous effective displacement in addition to a change in direction. Such effective displacements can be incorporated directly into a kinetic theory for the partial densities of swimmers moving in the channel. The linear analysis of the resulting equation yields the critical density at which clusters emerge. The methodology is then applied to the case of soil bacteria moving in long channels of cross-section 1.8~${\mu}$m $\times$ 1.8~${\mu}$m. The tracking of the swimmers permits the straightforward acquisition of the effective displacements, which in turn allows the critical density (${\rho}_{\text{crit}}\simeq$ 0.10 bact/${\mu}$m) to be predicted prior to cluster formation. The advantage of this proposed approach is that it does not necessitate the determination of an effective density-dependent speed, which is a requisite of the standard motility-induced phase separation theory.