Stokes flows in three-dimensional fluids with odd viscosity

Tali Khain, Colin Scheibner, Vincenzo Vitelli

Published 2020-11-16Version 1

The Stokeslet is the fundamental Green's function associated with point forces in viscous flows. It prescribes how the work done by external forces is balanced by the energy dissipated through velocity gradients. In ordinary fluids, viscosity is synonymous with energy dissipation. Yet, in fluids with broken microscopic time-reversal symmetry, the viscosity tensor can acquire a dissipationless contribution called odd viscosity. As the ratio between odd and dissipative viscosity diverges, energy balance requires that the resulting flow gradients become singular. Here, we find that these singularities give rise to additional contributions to the Stokeslet flow that persist even when the odd viscosity is small. In this limit, we solve for the flow past a sphere and illustrate the distinct effects of odd shear and rotational viscosities. When applied to many-body sedimentation, our analysis reveals the emergence of non-reciprocal hydrodynamic interactions and chiral modifications to particle trajectories.