Collective motion in microswimmer suspensions
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Date
15/03/2023Author
Škultéty, Viktor
Metadata
Abstract
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.