Analogy between streamers in sinking spheroids, gyrotactic plumes and chemotactic collapse
Author(s)
Fung, Lloyd
Type
Journal Article
Abstract
In a dilute suspension where sinking spheroids or motile gyrotactic micro-organisms are modelled as orientable and negatively buoyant particles, we have found analytical solutions to their steady distributions under any arbitrary continuous vertical shear flow. The two-way coupling between their distribution and the vertical flow is nonlinear, enabling the uniform base state to bifurcate into a structure reminiscent of the streamers in settling spheroid suspensions and gyrotactic plumes. This bifurcation depends on a single parameter that is proportional to the average number of particles on a horizontal cross-section. In a three-dimensional axisymmetric system, the plume structure blows up when the parameter is above a threshold. We discuss how this singularity is analogous to the chemotactic collapse of a Keller–Segel model, and the significance that this analogy entails.
Date Issued
2023-04-25
Date Acceptance
2023-03-17
Citation
Journal of Fluid Mechanics, 2023, 961
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
961
Copyright Statement
© The Author(s), 2023. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-ShareAlike licence (http://creativecommons.org/licenses/by-sa/4.0), which permits re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is used to distribute the re-used or adapted article and the original article is properly cited.
License URL
Subjects
bioconvection
BIOCONVECTION PATTERNS
collective behaviour
FLUCTUATIONS
GROWTH
INSTABILITY
Mechanics
PARTICLES
Physical Sciences
Physics
Physics, Fluids & Plasmas
Science & Technology
SUSPENSION
suspensions
Technology
Publication Status
Published
Article Number
A12
Date Publish Online
2023-04-18