Induced diffusion of tracers in a bacterial suspension: theory and experiments

Abstract

The induced diffusion of tracers in a bacterial suspension is studied theoretically and experimentally at low bacterial concentrations. Considering the swimmer-tracer hydrodynamic interactions at low-Reynolds number and using a kinetic theory approach, it is shown that the induced diffusion coefficient is proportional to the swimmer concentration, their mean velocity and a coefficient β, as observed experimentally. The coefficient β scales as the tracer-swimmer cross section times the mean square displacement produced by single scatterings. The displacements depend on the swimmer propulsion forces. Considering simple swimmer models (acting on the fluid as two monopoles or as a force dipole) it is shown that β increases for decreasing swimming efficiencies. Close to solid surfaces the swimming efficiency degrades and, consequently, the induced diffusion increase. Experiments on W wild-type Escherichia coli in a Hele-Shaw cell under buoyant conditions are performed to measure the induced diffusion on tracers near surfaces. The modification of the suspension pH vary the swimmers' velocity in a wide range allowing to extract the β coefficient with precision. It is found that the solid surfaces modify the induced diffusion: decreasing the confinement height of the cell, β increases by a factor 4. The theoretical model reproduces this increase although there are quantitative differences, probably attributed to the simplicity of the swimmer models.

Unusual swelling of a polymer in a bacterial bath

“…5(c) and represents indeed a reasonable upper bound at which the ballistic regime ceases to exist. Finally, as a further extreme reference, we have included the case N = 1 of a single segment, representing a passive tracer in a bath of active particles as studied recently [74,75]. In this case, the ballistic regime is not very visible, since the collison time of active particles with the tracer is short.…”

Motion of two micro-wedges in a turbulent bacterial bath

“…This effect has been used to rectify the motion of swimmers [44,45,46,47,48] and to build sorting [49,50,51,52] as well as trapping devices [53,54,55]. Furthermore the motion of passive but mobile particles submersed in an active fluid has been studied, starting with spherical and curved tracers [56,57,58] to long deformable chains [59]. Using asymmetric cogwheels a spontaneous directed rotation [60,61,62] can be extracted out of active bath.…”

Fluid Mixing by Curved Trajectories of Microswimmers

“…As a result particles and biofilaments suspended in the fluid diffuse more quickly, thus helping to ensure an enhanced nutrient supply. Following the early studies of mixing in concentrated microswimmer suspensions [1][2][3], recent experiments have demonstrated enhanced diffusion in dilute suspensions of Chlamydomonas reinhardtii, Escherichia coli and selfpropelled particles [4][5][6][7][8]. Simulations have found similar behaviour [9][10][11] and microfluidic devices exploiting the enhanced transport due to motile organisms have been suggested [12,13].…”

“…The last term, i.e. the function I d,2 (a/λ), arises from the re-scaled lower integration limit in (7). (Convergence of the integral at the upper limit does not pose problems.)…”