Emergence and control of patterns in active fluids

Active fluids like suspensions of bacteria, microtubule bundles and artificial microswimmers consist of individuals that are able to transform internal energy into a directed motion. The talk surveys a variety of surprising examples for spatiotemporal self-organisation of active matter like mechano-chemical waves in giant amoeba cells and mesoscale turbulence in suspension of swimmers.  Many efforts have been made to understand the influence of individual’s properties onto the emergence of pattern on the meso- or macroscale. In the talk, we first formulate “microscopic” equations of motion for a collection of active particles that interact through short-range alignment and long-range hydrodynamic interactions and are subject to rotational and translational noise. A derivation of “mesoscale” continuum equations from the equations of motion of this collection of interacting model swimmers will then be sketched. Depending on the symmetry of the interaction between swimmers the continuum equations obtained lead to polar or nematic order parameter equations coupled to the hydrodynamic equation of the surrounding fluid. As a result, the different symmetries lead to the emergence of different topological defect as well as different forms of collective motion and patterns. Here, the phenomenon of mesoscale turbulence is discussed in detail and compared to recent experiments. Finally, the topic of control of emerging patterns in swimmer suspensions by means of external fields and periodic arrays of obstacles is addressed.