Invariant manifolds and barriers blocking swimming microbes in vortex flows*

We present experiments on the motion of bacteria in laminar vortex chain and vortex array flows. The flows are generated by magnetohydrodynamic forcing in an acrylic, microfluidic cell, and the bacteria are a strain of bacillus subtilis mutated to express green fluorescent protein (GFP). A generalized theory of active mixing predicts "swimming invariant manifolds" (SwIMs) that split from the passive manifolds and act as one-way barriers that block the motion of smooth-swimming microbes. The same theory predicts "burning invariant manifolds" (BIMs) for the special case of bacteria that swim in a direction perpendicular to their semi-major axis; these BIMs also act as one-way barriers blocking the motion of reaction fronts in the same flow. We track the bacteria in the flow and: (1) identify curves in the flow across which the smooth-swimming bacteria cannot cross and compare those barriers to the SwIMs and BIMs predicted by the theory; (2) investigate role of BIMs as barriers that block even tumbling microbes; and (3) measure variations in the microbe density that are predicted by the theory.