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The trapping in high-shear regions of slender bacteria undergoing chemotaxis in a channel

  • R. N. Bearon (a1) and A. L. Hazel (a2)
Abstract

Recently published experimental observations of slender bacteria swimming in channel flow demonstrate that the bacteria become trapped in regions of high shear, leading to reduced concentrations near the channel’s centreline. However, the commonly used advection–diffusion equation, formulated in macroscopic space variables and originally derived for unbounded homogeneous shear flow, predicts that the concentration of bacteria is uniform across the channel in the absence of chemotactic bias. In this paper, we instead use a Smoluchowski equation to describe the probability distribution of the bacteria, in macroscopic (physical) and microscopic (orientation) space variables. We demonstrate that the Smoluchowski equation is able to predict the trapping phenomena and compare the full numerical solution of the Smoluchowski equation with experimental results when there is no chemotactic bias and also in the presence of a uniform cross-channel chemotactic gradient. Moreover, a simple analytic approximation for the equilibrium distribution provides an excellent approximate solution for slender bacteria, suggesting that the dominant effect on equilibrium behaviour is flow-induced modification of the bacteria’s swimming direction. A continuum framework is thus provided to explain how the equilibrium distribution of slender chemotactic bacteria is altered in the presence of spatially varying shear flow. In particular, we demonstrate that while advection is an appropriate description of transport due to the mean swimming velocity, the random reorientation mechanism of the bacteria cannot be simply modelled as diffusion in physical space.

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Corresponding author
Email address for correspondence: rbearon@liv.ac.uk
References
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Bearon, R. N. 2003 An extension of generalized Taylor dispersion in unbounded homogeneous shear flows to run-and-tumble chemotactic bacteria. Phys. Fluids 15 (6), 15521563.
Bearon, R. N., Hazel, A. L. & Thorn, G. J. 2011 The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields. J. Fluid Mech. 680, 602635.
Bearon, R. N. & Pedley, T. J. 2000 Modelling run-and-tumble chemotaxis in a shear flow. Bull. Math. Biol. 62 (4), 775791.
Berg, H. C. 1993 Random Walks in Biology. Princeton University Press.
Frankel, I. & Brenner, H. 1993 Taylor dispersion of orientable Brownian particles in unbounded homogeneous shear flows. J. Fluid Mech. 255, 129156.
Guazzelli, E. & Morris, J. F. 2012 A Physical Introduction to Suspension Dynamics. Cambridge University Press.
Heil, M. & Hazel, A. L. 2006 oomph-lib – An object-oriented multi-physics finite-element library in fluid structure interaction. In Lecture Notes on Computational Science and Engineering (ed. Schafer, M. & Bungartz, H.-J.), pp. 1949. Springer.
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.
Locsei, J. T. & Pedley, T. J. 2009 Run and tumble chemotaxis in a shear flow: the effect of temporal comparisons, persistence, rotational diffusion, and cell shape. Bull. Math. Biol. 71, 10891116.
Lushi, E., Goldstein, R. E. & Shelley, M. J. 2012 Collective chemotactic dynamics in the presence of self-generated fluid flows. Phys. Rev. E 86, 040902.
Manela, A. & Frankel, I. 2003 Generalized Taylor dispersion in suspensions of gyrotactic swimming micro-organisms. J. Fluid Mech. 490, 99127.
O’Malley, S. & Bees, M. A. 2012 The orientation of swimming biflagellates in shear flows. Bull. Math. Biol. 74, 232255.
Pedley, T. J. 2010 Instability of uniform micro-organism suspensions revisited. J. Fluid Mech. 647, 335359.
Pedley, T. J. & Kessler, J. O. 1990 A new continuum model for suspensions of gyrotactic microorganisms. J. Fluid Mech. 212, 155182.
Pedley, T. J. & Kessler, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24, 313358.
Rusconi, R., Guasto, J. S. & Stocker, R. 2014 Bacterial transport suppressed by fluid shear. Nat. Phys. 10 (3), 212217.
Saintillan, D. & Shelley, M. J. 2013 Active suspensions and their nonlinear models. C. R. Phys. 14 (6), 497517.
Stocker, R. 2011 Reverse and flick: hybrid locomotion in bacteria. Proc. Natl Acad. Sci. USA 108 (7), 26352636.
Taylor, J. R. & Stocker, R. 2012 Trade-offs of chemotactic foraging in turbulent water. Science 338 (6107), 675679.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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