Sedimentation in a chiral fluid with odd viscosity*

Chiral particles do not sediment in the same way as spherical ones. We ask, what if the fluid is chiral instead of the particle? In particular, we explore the modifications to Stokes flow due to coefficients of the viscosity tensor which are parity-violating (not invariant under mirror reflections of space) and non-dissipative (i.e. odd). We find that, in the Stokeslet flow, as well as in other cylindrically symmetric systems, the velocity field acquires an azimuthal component due to the additional viscosity coefficients. When treating each sedimenting particle as a Stokeslet, we show that the hydrodynamic interaction between two particles is changed as the azimuthal flow bends the particle trajectories in a manner not present in a standard fluid. For a spherical cloud of thousands of particles, the azimuthal flow impedes the transformation into a torus and the subsequent breakup that would otherwise occur. The basic mechanisms explored here are relevant for sedimentation in fluids under rotation, a magnetic field, and in fluids with internal activity, in which parity-violating viscosities have been experimentally demonstrated.