Continuum or individual models for suspensions of swimming micro-organisms?

This article will track the fluid mechanics of collective behaviour in suspensions of swimming microorganisms from the beginning of the author’s collaboration with the late John Kessler in 1984, concentrating exclusively on motile algae, especially those that are bottom-heavy, so they swim upwards, and denser than water. Kessler’s laboratory experiments revealed bioconvection patterns in shallow chambers, and population focussing on the axis of downward pipeflow due to gyrotaxis. We developed a continuum model to explain the observations and this proved qualitatively and to some extent quantitatively, very satisfactory. However, the model incorporates a number of simplifying assumptions, which will be questioned and those that need to be modified (or abandoned) will be identified. In particular, when a suspension is not dilute, so that hydrodynamic cell–cell interactions are significant, the continuum model must be replaced by an individual-based model, and when applying a model to a suspension of real microorganisms in the presence of rigid boundaries, we need to enquire what boundary conditions should be applied to individual swimmers as well as collections of them. Recent results that will be discussed include (a) the prediction of negative apparent viscosity in suspensions of upswimming, bottom-heavy puller squirmers (not pushers) and (b) the observation that certain algal cells respond to the presence of a wall when they appear to be too far from it for contact, or even hydrodynamic interaction, to be possible.