Swimming bacteria in a Poiseuille flow : the quest for active Betherton-Jeffery trajectories

Using a 3D Lagrangian tracking technique, we determine the swimming trajectories of E.coli in a Poiseuille flow. We identify many trajectories displaying the qualitative features of an “active Bretherton-Jeffery” model featuring an axi-symmetric self-propelled ellipsoid swimming in a flow. By deriving closed-forms for two phase-portraits involving one spatial and two angular coordinates as well as, the mean angular shift displayed by the families of cycloid trajectories, we show that for a smooth swimmer mutant, a quantitative mapping with the actual experimental trajectories can be made. Furthermore we show that from cycloid trajectories, the effective aspect ratio of the swimmer can be extracted. This analysis also allows to highlight the crucial influence of Brownian rotation noise, on the swimmer trajectories.