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Spherical Squirmers

Prof. Tim Pedley, FRS

DAMTP, Cambridge

In 1952, James 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 in particular showed how to model the metachronal wave patterns exhibited by beating cilia. Subsequently we 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 talk we survey:

• low Reynolds number locomotion, nutrient uptake and optimisation of individual squirmers;

• measurements and modelling of metachronal waves in Volvox, the only truly spherical multi-celled organism;

• hydrodynamic interactions between pairs of steady squirmers and their influence on self-diffusion in suspensions.

We conclude with observations of small numbers of Volvox in time-dependent bound states – dancing