The Geometry of Swimming Invariant Manifolds Mediates Long-Range Transport of Micro-swimmers in a Vortex Array

We analyze the kinematics of micro-swimmers in an imposed microchannel flow consisting of alternating fluid vortices. These swimmers could be biological (e.g. bacteria or algae) or artificial (e.g. Janus particles). Using dynamical systems techniques, we show that transport from one vortex down the channel to another vortex is mediated by Swimming Invariant Manifolds (SwIMs); SwIMs have previously been emphasized as one-way barriers to swimmer transport, but they also form chutes which guide swimmer passage between vortices. The SwIM geometry thus plays a critical role in determining transport rates of swimmers between vortices. Here, the SwIM geometry is analysed via a two-dimensional surface-of-section, which simplifies the analysis and leads to a topological classification of swimmer orbits. Our theoretical framework is applied to experiments on algae in microfluidic channels.