Spherical squirmers: models for swimming micro-organisms

In 1952, Lighthill introduced the simplest possible model of a swimming micro-organism of finite size, intended as a model of a single-celled protozoan covered in beating cilia. The model consisted of a sphere, on the surface of which material points undergo small-amplitude oscillations. In 1971, Lighthill's student, John Blake, completed the calculations and applied the theory to various species of ciliate. Subsequently we, and many others, have used the even simpler (though less realistic) model of a steady squirmer, a sphere whose surface moves tangentially with time-independent velocity. In this article we survey: - low-Reynolds-number locomotion, nutrient uptake and optimisation of individual squirmers; - hydrodynamic interactions between pairs of steady squirmers and their influence on clustering, self-diffusion and rheology in suspensions of squirmers, including the effect of being bottom-heavy; - measurements and modelling of metachronal waves in Volvox, the only truly spherical multi-celled organism, culminating in predictions of the mean swimming speed and angular velocity of free-swimming Volvox. The predictions are compared with experiment.