Emerging patterns from the collective dynamics of microswimmers in an external field
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Abstract
In recent years, the focus in soft matter physics has shifted gradually from equilibrium towards non-equilibrium systems. In particular, active particles that transform ambient energy into directed motion, have become a popular testbed for out-of-equilibrium statistical physics. From the collective dynamics of active particles fascinating phenomena emerge, such as pattern formation, unusual rheological properties, and transitions between ordered and disordered states. Some envisioned future applications of active particles, such as micro-scale targeted drug delivery, require some form of external control to influence the particles' dynamics and behaviour. Such a control could possibly be provided by an external (magnetic) field. Furthermore, experiments on active magnetotactic bacteria (MTB) in an external magnetic field have demonstrated intriguing pattern formation. Although not well understood, they have indicated the importance of hydrodynamic interactions for the dynamics of MTB.
In this thesis, we develop 3D kinetic theories of a dilute suspension of active magnetic microswimmers to study their collective dynamics and pattern formation in an external field. To solve the arising non-linear equations numerically, we develop a novel hybrid simulation method that, using a stochastic sampling technique, integrates a Brownian dynamics solver on the particle level with a continuum pseudo-spectral method to calculate interactions between particles.
We show that, for weakly magnetized microswimmers, the interplay between long-ranged hydrodynamic interactions and the external field can lead to distinct patterns for pusher- and puller-type microswimmers. A linear stability analysis of the homogeneous steady state not only predicts accurately the regime in which pattern formation occurs, but reveals that the mechanism of the pattern formation is driven by bend and splay instabilities. These instabilities lead to a partial depolarization and reduce the average speed of the swimmers. In particular, pullers undergoing a splay instability collectively create a flow against their average direction of motion parallel to the external field, resulting in a self-inflicted and significant reduction of their effective speed.
For active particles that are strongly magnetized, magnetic dipole-dipole interactions have to be considered. Even in the absence of an external magnetic field, they can cause a spontaneous magnetization --- similar to passive magnetic systems. Moreover, the dipole-dipole interactions can lead to instabilities of the polarized homogeneous steady state that, after a transient, highly ordered pattern formation, result in a condensation of the particles into polarized travelling clusters.