Dissipative effects in odd viscous Stokes flow around a single sphere

Odd viscosity (OV) is a transport coefficient in, for example, fluids of self-spinning (active) particles or electrons in an external magnetic field. The key feature of OV is that it does not contribute to dissipation in two spatial dimensions. In contrast, we explicitly show that in the three-dimensional case, OV can contribute indirectly to dissipation by modifying the fluid flow. We quantify the dissipation rate of a single spherical particle moving through a fluid with OV via an exact analytical solution of the generalised stationary creeping flow equations. Our results provide a novel way to quantify the effects of OV by measuring the solid-body motion of a single spherical particle. Moreover, we explicitly demonstrate how complex fluids can be designed in terms of their rheological properties by mixing passive particles with self-spinning active particles.