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

TL;DR

This paper analytically investigates the steady distributions and bifurcation behavior of sinking spheroids and gyrotactic microorganisms in shear flows, revealing an analogy to chemotactic collapse phenomena.

Contribution

It introduces a unified analytical framework for understanding streamer formation in suspensions and draws a novel analogy to chemotactic collapse in Keller-Segel models.

Findings

Bifurcation depends on a single parameter related to particle concentration.

Streamer structures form and blow up when the parameter exceeds a threshold.

The singularity is analogous to chemotactic collapse in biological systems.

Abstract

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.