Analogy between streamers in sinking spheroids, gyrotactic plumes and chemotactic collapse

In a dilute suspension where sinking spheroids or motile gyrotactic microorganisms 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 dist...

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Bibliographic Details
Published in:arXiv.org 2023-03
Main Author: Fung, Lloyd
Format: Article
Language:English
Subjects:
Bifurcations
Exact solutions
Flow profiles
Mathematical models
Microorganisms
Parallel flow
Parameters
Spheroids
Vertical distribution
Online Access:Get full text
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Summary:In a dilute suspension where sinking spheroids or motile gyrotactic microorganisms 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 this analogy entails.
ISSN:2331-8422
DOI:10.48550/arxiv.2301.07164