Slip-induced odd viscous flow past a cylinder

In fluids with broken parity and time-reversal symmetry, odd viscosity introduces the possibility of unique behaviors such as lift force on an obstacle in a symmetric geometry. As incompressible odd viscous fluids are known to not show lift on cylinders under no-slip boundary conditions, this study examines the effect of a finite slip length. While it follows from the Lorentz reciprocal theorem that lift does not arise at first order in slip length, we find that lift does arise at second order upon solving for the fluid profile explicitly. Extending to Oseen flow, we derive a fluid profile that offers new insights into lift force on a cylinder at low Reynolds numbers.