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A sequence of transcritical bifurcations in a suspension of gyrotactic microswimmers in vertical pipe

Published online by Cambridge University Press:  03 September 2020

Lloyd Fung Open the ORCID record for Lloyd Fung [Opens in a new window]  and
Yongyun Hwang Open the ORCID record for Yongyun Hwang [Opens in a new window]
Lloyd Fung*
Affiliation:
Department of Aeronautics, Imperial College London, LondonSW7 2AZ, UK
Yongyun Hwang
Affiliation:
Department of Aeronautics, Imperial College London, LondonSW7 2AZ, UK
*
†Email address for correspondence: lloyd.fung@imperial.ac.uk
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Abstract

Kessler (Nature, vol. 313, 1985, pp. 218–220) first showed that plume-like structures spontaneously appear from both stationary and flowing suspensions of gyrotactic microswimmers in a vertical pipe. Recently, it has been shown that there exist multiple steady, axisymmetric and axially uniform solutions to such a system (Bees & Croze, Proc. R. Soc. A, vol. 466, 2010, pp. 2057–2077). In the present study, we generalise this finding by reporting that a countably infinite number of such solutions emerge as the Richardson number increases. Linear stability, weakly nonlinear and fully nonlinear analyses are performed, revealing that each of the solutions arises from the destabilisation of a uniform suspension. The countability of the solutions is due to the finite flow domain, while the transcritical nature of the bifurcation is because of the cylindrical geometry, which breaks the horizontal symmetry of the system. It is further shown that there exists a maximum threshold of achievable downward flow rate for each solution if the flow is to remain steady, as varying the pressure gradient can no longer increase the flow rate from the solution. All of the solutions found are unstable, except for the one arising at the lowest Richardson number, implying that they would play a role in the transient dynamics in the route from a uniform suspension to the fully developed gyrotactic pattern.

JFM classification

Biological Fluid Dynamics: Bioconvection Biological Fluid Dynamics: Micro-organism dynamics Nonlinear Dynamical Systems: Bifurcation
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , R2
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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