Hydrodynamic stability of magnetic swimmers in an external field

Inspired by the dynamical behavior of magnetotactic bacteria, we present a minimal kinetic model for dilute suspensions of magnetic, self-propelled particles. Our kinetic theory couples a Fokker-Planck equation for active particles in an external magnetic field to the Stokes flow equation. Combining linear stability analysis and nonlinear 3D continuum simulations, we characterize the conditions under which instabilities occur. For sufficiently strong self-propulsion and magnetic field strengths, instabilities in density appear that make an orientationally aligned (polar) phase unstable. These hydrodynamic instabilities persist even for strong magnetic fields. The interplay between the hydrodynamic interactions and the coupling to an external magnetic field leads to emergent spatio-temporal patterns that depend on the type of swimmers. Examining the dynamics of pattern formation from initially homogeneous suspensions, we observe distinct types of instabilities for pusher and puller type swimmers. Pushers form wave-like structures perpendicular to the field that travel in its direction while pullers form wave-like lanes along the field.