Sedimentation, trapping, and rectification of dilute bacteria

TL;DR

This paper analyzes the behavior of dilute bacteria modeled as run-and-tumble particles, focusing on sedimentation, confinement, and rectification, providing analytic and numerical insights into their diffusive dynamics without interactions.

Contribution

It offers new analytic and numerical models for ideal bacteria dynamics under gravity, confinement, and rectification, highlighting differences from colloidal particles.

Findings

Bacteria exhibit sedimentation profiles similar to diffusive particles.

Rectification by funnel gates affects bacterial distribution and flow.

Models match some experimental observations of bacterial behavior.

Abstract

The run-and-tumble dynamics of bacteria, as exhibited by \textit{E. coli}, offers a simple experimental realization of non-Brownian, yet diffusive, particles. Here we present some analytic and numerical results for models of the ideal (low-density) limit in which the particles have no hydrodynamic or other interactions and hence undergo independent motions. We address three cases: sedimentation under gravity; confinement by a harmonic external potential; and rectification by a strip of `funnel gates' which we model by a zone in which tumble rate depends on swim direction. We compare our results with recent experimental and simulation literature and highlight similarities and differences with the diffusive motion of colloidal particles.