Bacteria dispersion in microchanel containing random obstacles

Dispersion of particles in porous media is a classical problem well studied where physical laws are well established and show good agreement with experimental observations. Recently, contrary to what is thought, observations revealed that self-propelled particles under flow, orient their swimming, what is designated by the term of rheotaxis. But less is known about what happen for self-propelled particles under flow in presence of obstacles. For this purpose, we developed a specific experimental setup in order to show the coupling of bacteria {\it E. Coli} RP437 strain swimming with the presence of obstacles in the dispersion process. We chose to develop a micro-fluidic device of rectangular section of $0.05~\mu m^2$ containing obstacles of different sizes($10-150~\mu m$) when a bacteria size is about $1~\mu m$. Thanks to the transparency of the flow we can track hundreds of trajectories of bacteria, the analysis of which revealed that their swimming influences the dispersion when the flow velocity is of the order of their swimming velocity ($10~ \mu m/s$).