Lévy fluctuations and mixing in dilute suspensions of algae and bacteria
- 23 February 2011
- journal article
- Published by The Royal Society in Journal of The Royal Society Interface
- Vol. 8 (62), 1314-1331
- https://doi.org/10.1098/rsif.2010.0545
Abstract
Swimming micro-organisms rely on effective mixing strategies to achieve efficient nutrient influx. Recent experiments, probing the mixing capability of unicellular biflagellates, revealed that passive tracer particles exhibit anomalous non-Gaussian diffusion when immersed in a dilute suspension of self-motile Chlamydomonas reinhardtii algae. Qualitatively, this observation can be explained by the fact that the algae induce a fluid flow that may occasionally accelerate the colloidal tracers to relatively large velocities. A satisfactory quantitative theory of enhanced mixing in dilute active suspensions, however, is lacking at present. In particular, it is unclear how non-Gaussian signatures in the tracers' position distribution are linked to the self-propulsion mechanism of a micro-organism. Here, we develop a systematic theoretical description of anomalous tracer diffusion in active suspensions, based on a simplified tracer-swimmer interaction model that captures the typical distance scaling of a microswimmer's flow field. We show that the experimentally observed non-Gaussian tails are generic and arise owing to a combination of truncated Lévy statistics for the velocity field and algebraically decaying time correlations in the fluid. Our analytical considerations are illustrated through extensive simulations, implemented on graphics processing units to achieve the large sample sizes required for analysing the tails of the tracer distributions.Keywords
This publication has 36 references indexed in Scilit:
- Fidelity of adaptive phototaxisProceedings of the National Academy of Sciences, 2010
- Bacterial ratchet motorsProceedings of the National Academy of Sciences, 2010
- Swimmer-tracer scattering at low Reynolds numberSoft Matter, 2010
- Swimming bacteria power microscopic gearsProceedings of the National Academy of Sciences, 2009
- Statistical mechanics and hydrodynamics of bacterial suspensionsProceedings of the National Academy of Sciences, 2009
- Introduction: 100years of Brownian motionChaos: An Interdisciplinary Journal of Nonlinear Science, 2005
- Functional characterization of generalized Langevin equationsJournal of Physics A: General Physics, 2004
- Lévy Distribution of Single Molecule Line Shape Cumulants in GlassesPhysical Review Letters, 2000
- Aging in Out-of-Equilibrium Dynamics of Models for Granular MediaPhysical Review Letters, 1999
- Lagrangian path integrals and fluctuations in random flowPhysical Review E, 1994