Active Brownian particles moving in a random Lorentz gas

TL;DR

This study numerically investigates how active Brownian particles behave in a two-dimensional random Lorentz gas, revealing their subdiffusive, superdiffusive, and trapping behaviors influenced by obstacle density and propulsion speed.

Contribution

It provides new insights into the dynamics of active particles in complex environments, highlighting the impact of propulsion speed and obstacle density on long-term diffusion and trapping.

Findings

Active Brownian particles perform subdiffusive and superdiffusive motions near the percolation transition.

Long-time diffusion decreases with increasing propulsion speed in dense obstacle environments.

Trapping occurs above a critical obstacle density, affecting long-term particle mobility.

Abstract

Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study non-interacting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density $\eta_c$ the ABPs are trapped, their long-time diffusion below $\eta_c$ is strongly influenced by the propulsion speed $v_0$. With increasing $v_0$, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.