Anisotropic mesoscale turbulence and pattern formation in microswimmer suspensions induced by orienting external fields

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 (Reinken et al 2018 Phys. Rev. E 97, 022613). 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 anisotropic 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.