Collective motion in microswimmer suspensions

The main distinction of active matter from its passive counterpart is the ability to extract energy from the environment (consume food) and convert it into directed motion. One of the most striking consequences of this distinction is the appearance of collective motion in self-propelled particles suspended in a fluid observed experiments and simulations: at low densities particles move around in an apparently uncorrelated fashion, while at higher densities they organise into jets and vortices comprising many individual swimmers. Although this problem received significant attention in recent years, the precise origin of the transition is poorly understood. In this work, we develop theoretical tools, both analytical and numerical, to address this problem. We will study the minimal model of self-propelling particles immersed in an incompressible viscous fluid. Our approach is based on Kinetic theory - a probabilistic description of many-particle systems with both positional and orientational degree of freedom. The emphasis is put on the rˆole of hydrodynamic interactions, which are long-ranged in nature and result in nematic alignment between the individual particles. We aim to understand the properties of microswimmer suspensions when passing through the instability threshold leading to collective motion, as well as the collective motion itself. Our results, although derived for a minimal model, can be directly tested in experments, and numerical simulations. We carry out detailed linear stability analysis, and show that the exact type of instability in microswimmer suspensions depends on the geometry of the system. The collective motion regime is assessed at the mean-field level, where statistical properties of this highly non-linear state are measured using large-scale pseudo-spectral simulations. Moreover, we develop Kinetic theory that goes beyond the commonly assumed mean-field approximation, and directly incorporates both correlations stemming from the tumbling effects, as well as the self-propulsion mechanism. The results presented in this work shed light on the collective behaviour of large number of microorganisms, and serve as a solid basis for further research.