Transport barriers to self-propelled particles in fluid flows

TL;DR

This paper combines theory and experiments to identify invariant manifolds that act as one-way barriers, impeding the movement of microswimmers like bacteria in fluid flows, revealing key phase-space structures called SwIMs.

Contribution

It introduces the concept of swimming invariant manifolds (SwIMs) as phase-space separatrices that serve as one-way barriers in fluid flows, supported by experimental validation.

Findings

SwIMs act as one-way barriers in fluid flows.

Experiments with Bacillus subtilis bacteria confirm the theory.

Invariant manifolds influence long-term swimmer behavior.

Abstract

We present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble \emph{Bacillus subtilis} bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into $xy$-space, the edges of the SwIMs act as one-way barriers, consistent with the experiments.