Rheotaxis of chiral bacteria: from single-cell behavior to a population-level description

Due to their morphology, the dynamics of bacteria suspended in media can exhibit complex behaviors. In the presence of a shear, swimming bacteria experience a drift perpendicular to the shear plane. This drift, termed rheotaxis, is studied here semi-analytically, numerically and experimentally. We find the dependency of bacterial orientation and bacterial speed on the shear rate, in the presence of rotational diffusion. This enables us to show that the drift speed of bacteria perpendicular to the shear is predominantly due to bacterial propulsion, and not rheotactic forces. Comparing the drift speed of bacteria and diffusion leads to the definition of a P\'{e}clet number. The rheotactic effect increases with the shear, reaching a plateau at very large P\'{e}clet numbers, in good agreement with experiments of rheotaxis performed in microfluidic droplets.