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Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe

Published online by Cambridge University Press:  16 September 2020

Lloyd Fung Open the ORCID record for Lloyd Fung [Opens in a new window] ,
Rachel N. Bearon  and
Yongyun Hwang Open the ORCID record for Yongyun Hwang [Opens in a new window]
Lloyd Fung*
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
Rachel N. Bearon
Affiliation:
Department of Mathematical Sciences, University of Liverpool, LiverpoolL69 7ZL, UK
Yongyun Hwang
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
*
†Email address for correspondence: lloyd.fung@imperial.ac.uk
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Abstract

In the experiment that first demonstrated gyrotactic behaviour of bottom-heavy swimming microalgae (e.g. Chlamydomonas), Kessler (Nature, vol. 313, 1985, pp. 218–220) showed that a beam-like structure, often referred to as a gyrotactic plume, would spontaneously appear from a suspension of gyrotactic swimmers in a downflowing pipe. Such a plume is prone to an instability to form blips. This work models the gyrotactic plume as a steady parallel basic state and its subsequent breakdown into blips as an instability, employing both the generalized Taylor dispersion (GTD) theory and the Fokker–Planck model for comparison. Upon solving for the basic state, it is discovered that the steady plume solution undergoes sophisticated bifurcations. When there is no net flow, there exists a non-trivial solution of the plume structure other than the stationary uniform suspension, stemming from a transcritical bifurcation with the average cell concentration. When a net downflow is prescribed, there exists a cusp bifurcation. Furthermore, there is a critical concentration at which the cell concentration at the centre would blow up for the GTD model. The subsequent stability analysis using the steady plume solution shows that the Fokker–Planck model is inconsistent with what was experimentally observed, as it predicts stabilisation of axisymmetric blips at high concentration of the plume and destabilisation of the first non-axisymmetric mode at low flow rates.

JFM classification

Biological Fluid Dynamics: Bioconvection Biological Fluid Dynamics: Micro-organism dynamics Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A26
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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