Collective Behaviour of Swimming Micro-organisms

Abstract

The occurrence and mechanism of bioconvection patterns in suspensions of upswimming micro-organisms are described, and the linear stability theory for bioconvection in an otherwise uniform dilute suspension is outlined for the case of algae which swim upwards because they are bottom-heavy. Particular attention is paid to the effect of the stress generated in the suspension by the force-dipole exerted by each swimming cell. Coherent structures are also observed in concentrated suspensions, of bacteria in particular, and it is postulated that these come about solely through the hydrodynamic interactions between cells. We examine the deterministic swimming of model organisms which interact hydrodynamically but do not exhibit intrinsic randomness except in their initial positions and orientations. A micro-organism is modelled as a squirming, inertia-free sphere with prescribed tangential surface velocity. Pairwise interactions have been computed using the boundary element method, and the results stored in a database. The movement of a number of identical squirmers is computed by the Stokesian Dynamics method, with the help of the database of interactions. It is found that the spreading in three dimensions is correctly described as a diffusive process after a sufficiently long time. Scaling arguments are used to estimate this time-scale and the diffusitivities. These depend strongly on volume fraction and mode of squirming. However, in two dimensions the squirmers show a definite tendency to aggregation.