Odd viscosity in Stokes flows

In standard fluids, the viscosity converts the mechanical energy provided by external forces into heat. If, however, a fluid breaks microscopic time-reversal symmetry, for example by being composed of active spinning particles, its viscosity tensor may acquire an additional “odd” contribution that does not dissipate energy. In this work, we elucidate the effect of odd viscosity on Stokes flows in three dimensions. Strikingly, we discover that the Stokeslet solution for fluids with cylindrical symmetry contains an azimuthal component of velocity that originates from singularities in the limit of vanishing dissipative viscosity. In the small odd viscosity limit, we directly solve for the viscous flow past a sphere and compare with the Stokeslet solutions. Our work reveals the significant effect of odd viscosity on flow at low Reynolds number and suggests sedimentation-based probes of odd viscosity in three dimensions.