Numerical modeling of dispersion of swimming bacteria in a Poiseuille flow

This paper reports a numerical study of the dispersion of bacteria modeled as ac-tive Brownian ellipsoids placed in a plane Poiseuille flow. The longitudinal (along the flow direction) and transverse (along the direction perpendicular to the plane of flow) macroscopic dispersion coefficients are determined from the analysis of a large number of trajectories and their scaling is studied as function of the Peclet number Pe. Three different regimes are observed. (i) At low shear rate, rotational diffusion associated to the swimming activity of the bacteria dominates and classical Taylor dispersion regime is observed. In this regime, the longitudinal dispersion coefficient scales like Peclet square. (ii) An intermediate active regime, where the shear induces a reorientation of the bacteria. This increases the longitudinal dispersion that scales as Pe2+kappa, with kappa ranging between 1.5 and 2 for aspect ratio between 10 and 1. In this regime, the dispersion coefficient in the direction perpendicular to the plane of the flow decreases like log(1/Pe). (iii) A final new Taylor regime, where the diffusivity in the gap is set by the molecular diffusion coefficient. We also show that the active regime originates from the enhancement in the time taken by particles to diffuse across the channel gap. We further show that, decreasing the channel height delayed the transition to the active regime.