Ballistic to diffusive transition for swimmers in a periodic vortex array.

Area of Science:

• Physics
• Fluid Dynamics
• Nonlinear Dynamics

Background:

• Understanding microswimmer transport is crucial for applications in targeted drug delivery and micro-robotics.
• Vortex arrays create complex flow patterns that significantly influence particle and swimmer dynamics.

Purpose of the Study:

• To investigate the transport mechanisms of rigid ellipsoidal swimmers in a periodic vortex array.
• To elucidate the relationship between swimming speed and transport behavior (ballistic vs. diffusive).

Main Methods:

• Numerical simulations of swimmer trajectories.
• Dynamical systems analysis using time-reversible Poincaré return maps.
• Ensemble simulations to analyze transport statistics and robustness to noise.

Main Results:

• Slower swimming speeds result in fast ballistic transport, characterized by stable periodic orbits and invariant tori.
• Faster swimming speeds lead to chaotic and diffusive transport due to period-doubling bifurcations.
• Ballistic transport is degraded by increasing rotational diffusion (noise).

Conclusions:

• The study reveals a counterintuitive speed-transport relationship in periodic vortex arrays.
• Dynamical systems analysis explains the transition from ballistic to diffusive transport.
• Ballistic transport regimes may be observable in experimental settings.