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The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields

Published online by Cambridge University Press:  13 June 2011

R. N. BEARON ,
A. L. HAZEL  and
G. J. THORN
R. N. BEARON*
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
A. L. HAZEL
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK
G. J. THORN
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
*
†Email address for correspondence: [email protected]
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Abstract

We compare the results of two-dimensional, biased random walk models of individual swimming micro-organisms with advection–diffusion models for the whole population. In particular, we consider the influence of the local flow environment (gyrotaxis) on the resulting motion. In unidirectional flows, the results of the individual and population models are generally in good agreement, even in flows in which the cells can experience a range of shear environments, and both models successfully predict the phenomena of gravitactic focusing. Numerical results are also compared with asymptotic expressions for weak and strong shear. Discrepancies between the models arise in two cases: (i) when reflective boundary conditions change the orientation distribution in the random walk model from that predicted by the long-term asymptotics used to derive the advection–diffusion model; (ii) when the spatial and temporal scales are not large enough for the advection–diffusion model to apply. We also use a simple two-dimensional flow containing a variety of flow regimes to explore what happens when there are localized regions in which the generalized Taylor dispersion theory used in the derivation of the population model does not apply. For spherical cells, we find good agreement between the models outside the ‘break-down’ regions, but comparison of the results within these regions is complicated by the presence of nearby boundaries and their influence on the random walk model. In contrast, for rod-shaped cells which are reorientated by both vorticity and strain, we see qualitatively different spatial patterns between individual and advection–diffusion models even in the absence of gyrotaxis, because cells are advected between regions of differing rates of strain.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 680 , 10 August 2011 , pp. 602 - 635
Copyright
Copyright © Cambridge University Press 2011

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