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

Published online by Cambridge University Press:  24 July 2013

G. L. Miño ,
J. Dunstan ,
A. Rousselet ,
E. Clément  and
R. Soto
G. L. Miño
Affiliation:
PMMH-ESPCI, UMR 7636, CNRS–ESPCI–Université Paris 6 and Paris 7, 10 rue Vauquelin, 75005 Paris, France
J. Dunstan
Affiliation:
Departamento de Física, FCFM, Universidad de Chile, Casilla 487-3, Santiago, Chile Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
A. Rousselet
Affiliation:
PMMH-ESPCI, UMR 7636, CNRS–ESPCI–Université Paris 6 and Paris 7, 10 rue Vauquelin, 75005 Paris, France
E. Clément
Affiliation:
PMMH-ESPCI, UMR 7636, CNRS–ESPCI–Université Paris 6 and Paris 7, 10 rue Vauquelin, 75005 Paris, France
R. Soto*
Affiliation:
Departamento de Física, FCFM, Universidad de Chile, Casilla 487-3, Santiago, Chile
*
†Email address for correspondence: rsoto@dfi.uchile.cl
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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 $\beta $, as observed experimentally. This paper shows that $\beta $ increases as a result of the interaction with solid surfaces. The coefficient $\beta $ scales as the tracer–swimmer cross-section times the mean square displacement produced by single scattering events, which depends 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 $\beta $ increases for decreasing swimming efficiencies. Close to solid surfaces, the swimming efficiency degrades and, consequently, the induced diffusion increases. Experiments on 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 varies the swimmers’ velocity over a wide range, allowing the $\beta $ coefficient to be extracted with precision. It is found that solid surfaces modify the induced diffusion: decreasing the confinement height of the cell, $\beta $ increases by a factor of 4. The theoretical model reproduces this increase, although there are quantitative differences, probably attributed to the simplicity of the swimmer models and to the estimates for the parameters that model E. coli.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Micro-organism dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 729 , 25 August 2013 , pp. 423 - 444
Copyright
©2013 Cambridge University Press 

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