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

Fung, Lloyd, Bearon, Rachel N ORCID: 0000-0001-8461-0823 and Hwang, Yongyun (2020) Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe. JOURNAL OF FLUID MECHANICS, 902. a26-.

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Official URL: http://dx.doi.org/10.1017/jfm.2020.614

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 Generalised 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.

Item Type:	Article
Uncontrolled Keywords:	bioconvection, micro-organism dynamics, suspensions
Depositing User:	Symplectic Admin
Date Deposited:	13 Oct 2020 09:42
Last Modified:	17 Mar 2024 07:18
DOI:	10.1017/jfm.2020.614
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3073975