Abstract:
We present a mathematical and computational model to trace the dynamics of thousands of self-motile slender micro-swimmers that interact directly and via the fluid flow in which they are suspended. Through linear analysis and full nonlinear simulations we show that the swimming mechanism, the swimmer concentration and system size are important in the overall suspension dynamics. When put in a background flow much larger in scale and speed than the individual swimmers, hydrodynamical interactions of “Pusher” swimmers (like bacteria) or “Puller” swimmers (like algae chlamydomonas) and effective volume concentration determine whether the swimmers get trapped in large vortices or can collaboratively escape the flow barriers.
In the second part of the talk I will discuss the continuum theory resulting from the aforementioned model and apply it to the case when micro-swimmers interact hydrodynamically as well as via chemical signals. This kinetic theory couples run-and-tumble based chemotaxis, which by itself leads to colony aggregation, with the flow fields generated by collective swimming. The stability of isotropic suspensions reveals separate branches of chemotactic and hydrodynamic instability, the first driving aggregation, and the second driving orientational ordering in “Pusher” suspensions. Simulations of the long-time nonlinear dynamics of chemotactic suspensions show aggregation and growth in swimmer density. Including hydrodynamic interactions can limit and modify the aggregation dynamics. For Pusher suspensions particularly, chemotactic aggregation can lead to destabilizing time-dependent flows with fragmented regions of aggregation.