Chirotactic response of microswimmers in fluids with odd viscosity

Odd viscosity is a property of chiral active fluids with broken time-reversal and parity symmetries. We show that the flow of such a fluid around a rotating axisymmetric body is exactly solvable and use this solution to determine the orientational dynamics of surface-driven microswimmers. Swimmers with a force-dipole moment exhibit precession around the axis of the odd viscosity. In addition, pushers show bimodal chirotaxis, i.e., alignment parallel or antiparallel to the axis, while pullers orbit in a plane perpendicular to it. A chiral swimmer that itself has a broken parity symmetry can exhibit unimodal chirotaxis and always align in the same direction.