Asymmetric pattern formation in microswimmer suspensions induced by orienting fields

TL;DR

This study investigates how external orienting fields influence pattern formation in microswimmer suspensions, revealing a transition from vortex lattices to asymmetric stripe patterns driven by symmetry-breaking effects.

Contribution

The paper extends a hydrodynamic model by incorporating external aligning fields, demonstrating their impact on pattern symmetry and stability in microswimmer suspensions.

Findings

External fields induce asymmetric, traveling stripe patterns.

Transition observed between vortex lattice and stripe patterns.

Weakly nonlinear analysis describes pattern formation under certain conditions.

Abstract

This paper studies the influence of orienting external fields on pattern formation, particularly mesoscale turbulence, in microswimmer suspensions. To this end, we apply a hydrodynamic theory that can be derived from a microscopic microswimmer model [Phys. Rev. E 97, 022613 (2018)]. The theory combines a dynamic equation for the polar order parameter with a modified Stokes equation for the solvent flow. Here, we extend the model by including an external field that exerts an aligning torque on the swimmers (mimicking the situation in chemo-, photo-, magneto- or gravitaxis). Compared to the field-free case, the external field breaks the rotational symmetry of the vortex dynamics and leads instead to strongly asymmetric, traveling stripe patterns, as demonstrated by numerical solution and linear stability analysis. We further analyze the emerging structures using a reduced model which involves only an (effective) microswimmer velocity field. This model is significantly easier to handle analytically, but still preserves the main features of the asymmetric pattern formation. We observe an underlying transition between a square vortex lattice and a traveling stripe pattern. These structures can be well described in the framework of weakly nonlinear analysis, provided the strength of nonlinear advection is sufficiently weak.