Run-and-tumble in a crowded environment: persistent exclusion process for swimmers

TL;DR

This study models how crowding affects run-and-tumble swimmer dynamics, revealing cluster formation and scaling laws that could inform biofilm development understanding.

Contribution

Introduces a lattice model capturing crowding effects on run-and-tumble particles, highlighting cluster formation and scaling behaviors in 1D and 2D environments.

Findings

Clusters scale as alpha^{-0.5} in size

Stopping time scales as T^{0.85} in 1D and T^{0.8} in 2D

Potential implications for biofilm formation

Abstract

The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate $\alpha$. In stationary state, the system is found to break into dense clusters in which particles are trapped or stopped from moving. The characteristic size of these clusters predominantly scales as $\alpha^{-0.5}$ both in 1D and 2D. For a range of densities, due to cooperative effects, the stopping time scales as ${\cal T}_{1d}^{0.85}$ and as ${\cal T}_{2d}^{0.8}$, where ${\cal T}_d$ is the diffusive time associated with the motion of cluster boundaries. Our findings might be helpful in understanding the early stages of biofilm formation.