Pattern Formation in a Suspension of Swimming Microorganisms: Nonlinear Aspects

Abstract

Convection in a suspension of motile microorganisms with upward drift is studied using nonlinear stability theory. The organisms move with Reynolds number much less than unity and do not leave the fluid. Hence, the condition of zero flux on horizontal boundaries must be imposed and this produces, in linear theory, a critical wave number of zero. For slightly supercritical conditions, a band of small wave numbers is excited. The generic case is not Boussinesq and the onset of motion occurs through a subcritical bifurcation, a result consistent with observation of cultures of microorganisms near the onset of instability. We develop a stationary model for the dense clusters of organisms that form. In this model, the momentum transferred to the fluid by a cluster of organisms interacts with the horizontal boundaries, and the resulting recirculation of the fluid can maintain the integrity of the clusters. The observed spacing of aggregates is consistent with the stationary solution which maximizes the mean cluster volume.