Drifting and twirling in a chiral active fluid at low Reynolds number*

Chiral fluids - such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids - flow in a different way than ordinary ones. Here, we ask: how does the flow bend around a moving obstacle in the fluid? In chiral fluids, the viscosity tensor acquires additional coefficients that are parity-violating (not invariant under mirror reflections of space) and non-dissipative (odd). This modifies the velocity field in the incompressible Stokes regime in three dimensions. For instance, a sedimenting sphere generates rotational motion in the flow. Nonetheless, due to the symmetry of the flow, the torque on the sphere is zero, so it does not rotate. More generally, in the low Reynolds number regime, the response of a rigid body to forces and torques is given by the mobility matrix, which depends on the viscous properties of the fluid and the geometry of the body. By analyzing the symmetries of the mobility matrix, we constrain the possible motions of a general rigid body immersed in a parity-violating fluid. To further explore the trajectories of differently shaped particles, we model each object with a collection of Stokeslets, which allows for a numerical approximation of the mobility matrix. Applied to the context of sedimentation, our work shows that non-chiral particles can begin to spin as they sink under gravity.