Modelization of dispersion of swimming bacteria in Poiseuille flow
Résumé
This work reports 3D Langevin simulations of swimming bacteria modelled as an active Brownian rod experiencing rotational and translational motion when subject to Poiseuille flow. We perform the simulations for large number of particles, and sufficiently long time so that effective steady state longitudinal, transverse dispersion coefficients and mixing time across the gap can be determined. The influence of the particle aspect ratio, flow velocity, gap size and the competition between the Brownian motion and the swimming characteristics of the particle on the macroscopic dispersion coefficient is studied. Three different regimes are observed : (i) at low shear rate, rotational diffusion dominates, and classical Taylor dispersion regime is observed (ii) an intermediate regime where reorientation of the bacteria by the shear increases the mixing time in the gap and in turn increases longitudinal dispersion, (iii) a final "new" Taylor regime where mixing in the gap is set by the Brownian thermal diffusion. Three Péclet numbers are identified to capture the transition and the range of observation of those regimes.