Microswimmer-induced chaotic mixing

Efficient mixing, typically characterized by chaotic advection, is hard to achieve in low Reynolds number conditions because of the linear nature of the Stokes equation that governs the motion. Here we show that low-Reynolds-number swimmers moving on quasi-periodic orbits can result in considerable stretching and folding of fluid elements. We accurately follow packets of tracers within the fluid domain and show that their trajectories become chaotic as the swimmers trajectory densely fills its invariant torus. The mixing process is demonstrated in two dimensions using the Quadroar swimmer that autonomously propels and tumbles along quasiperiodic orbits with multi-loop turning trajectories. We demonstrate and discuss that the streamlines of the flow induced by the Quadroar closely resemble the oscillatory flow field of the green alga C. reinhardtii. Our findings can thus be utilized to understand the interactions of microorganisms with their environments, and to design autonomous robotic mixers that can sweep and mix an entire volume of complex-geometry containers.