Swimming bacteria in Poiseuille flow: The quest for active Bretherton-Jeffery trajectories

¹ Laboratoire PMMH- ESPCI Paris, PSL Research University, Sorbonne Université and Denis Diderot 7, quai Saint- Bernard, Paris, France
² Laboratoire FAST, Univ. Paris- Sud, CNRS, Université Paris-Saclay - F-91405, Orsay, France
³ Physics Department, FCFM, Universidad de Chile - Av. Blanco Encalada 2008, Santiago, Chile

Received: 14 March 2019
Accepted: 27 May 2019

Abstract

Using a 3D Lagrangian tracking technique, we determine experimentally the trajectories of non-tumbling E. coli mutants swimming in a Poiseuille flow. We identify a typology of trajectories in agreement with a kinematic “active Bretherton-Jeffery” model, featuring an axi-symmetric self-propelled ellipsoid. In particular, we recover the “swinging” and “shear tumbling” kinematics predicted theoretically by Zöttl and Stark (Phys. Rev. Lett., 108 (2012) 218104). Moreover using this model, we derive analytically new features such as quasi-planar piecewise trajectories, associated with the high aspect ratio of the bacteria, as well as the existence of a drift angle around which bacteria perform closed cyclic trajectories. However, the agreement between the model predictions and the experimental results remains local in time, due to the presence of Brownian rotational noise.