Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe
File(s)
Accepted version
Author(s)
Fung, Lloyd
Bearon, Rachel
Hwang, Yongyun
Type
Journal Article
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.
Date Issued
2020-11-10
Date Acceptance
2020-07-20
Citation
Journal of Fluid Mechanics, 2020, 902 (A26), pp.1-34
ISSN
0022-1120
Publisher
Cambridge University Press
Start Page
1
End Page
34
Journal / Book Title
Journal of Fluid Mechanics
Volume
902
Issue
A26
Copyright Statement
© The Author(s), 2020. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Identifier
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/bifurcation-and-stability-of-downflowing-gyrotactic-microorganism-suspensions-in-a-vertical-pipe/C70D70887A9924B69C39F7BC77A0D0ED
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
bioconvection
micro-organism dynamics
suspensions
GENERALIZED TAYLOR DISPERSION
SWIMMING MICROORGANISMS
BIOCONVECTION PATTERNS
GROWTH
FLOW
PARTICLES
MODEL
INSTABILITY
ORIENTATION
RHEOLOGY
physics.flu-dyn
physics.flu-dyn
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status
Published online
Date Publish Online
2020-11-10