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In a dilute suspension where sinking spheroids or motile gyrotacticmicroorganisms are modelled as orientable and negatively buoyant particles, wehave found analytical solutions to their steady distributions under anyarbitrary continuous vertical shear flow. The two-way coupling between theirdistribution and the vertical flow is nonlinear, enabling the uniform basestate to bifurcate into a structure reminiscent of the streamers in settlingspheroid suspensions and gyrotactic plumes. This bifurcation depends on asingle parameter that is proportional to the average number of particles on ahorizontal cross section. In a three-dimensional axisymmetric system, the plumestructure blows up when the parameter is above a threshold. We discuss how thissingularity is analogous to the chemotactic collapse of a Keller-Segel model,and the significance this analogy entails.

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