Barriers for active transport of bacteria in a microfluidic flow

We present experiments on the motion of swimming bacteria in a laminar, hyperbolic flow in a microfluidic cross channel. The bacteria used are a genetically-mutated ``smooth swimming''\footnote{R. Rusconi, J.S. Guasto and R. Stocker, Nature Physics {\bf 10}, 212 (2014).} bacillus subtilis. The movement of bacteria in the flow is bounded by {\em swimming invariant manifolds} (SWIMs) that act as one-way barriers. The SWIMs are similar to `burning invariant manifolds''\footnote{J. Mahoney, D. Bargteil, M. Kingsbury, K. Mitchell and T. Solomon, Europhys. Lett. {\bf 98}, 44005 (2012).} that act as one-way barriers that impede the motion of reaction fronts in a fluid flow. We explore the structure and bounding behavior of the SWIMs and how their separation from the passive manifolds depends on the bacteria swimming speed, normalized by the characteristic fluid speeds.