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 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.

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• Cell locomotion
• Chaotic advection
• Microfluidics
• Dynamical systems
• Living matter & active matter
• Microswimmers
• Self-propelled particles
• Lagrangian particle tracking
• Phase space dynamics