Swimming the chaotic seas: invariant manifolds, tori, and the transport of swimmers in vortex flows

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 both

invariant tori and so-called 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. The invariant tori, on

the other hand, lead both to trapping within vortex cells and

ballistic transport between vortex cells. Our theoretical framework

is applied to experiments on algae in microfluidic channels.