We first describe theory and simulations of hydrodynamically interacting microorganisms, using very simple models of the individual organisms. In the dilute limit, simple arguments reveal the dependence of swimmer and tracer velocities and diffusivities on concentration. As concentration increases, we show that cases exist in which the swimming motion generates large-scale flows and dramatically enhanced transport in the fluid. A physical argument supported by a mean field theory sheds light on the origin of these effects.
The second part of the talk focuses on the dynamics of the flagellar bundling process, using a mathematical model that incorporates the fluid motion generated by each flagellum as well as the finite flexibility of the flagella. The initial stage of bundling is driven purely by hydrodynamics, while the final state of the bundle is determined by a nontrivial and delicate balance between hydrodynamics and elasticity. As the flexibility of the flagella increases a regime is found where, depending on initial conditions, one finds bundles that are either tight, with the flagella in mechanical contact, or loose, with the flagella intertwined but not touching. That is, multiple coexisting states of bundling are found. The parameter regime at which this multiplicity occurs is comparable to the parameters for a number of bacteria.
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