Lift force in odd compressible fluids
Phys. Rev. E, 108 (2):
L023101 (Aug 2, 2023)DOI: 10.1103/PhysRevE.108.L023101
Abstract
When a body moves through a fluid, it can experience a force orthogonal to its movement called lift force.
Odd viscous fluids break parity and time-reversal symmetry, suggesting the existence of an odd lift force on
tracer particles, even at vanishing Reynolds numbers and for symmetric geometries. It was previously found
that an incompressible odd fluid cannot induce lift force on a tracer particle with no-slip boundary conditions,
making signatures of odd viscosity in the two-dimensional bulk elusive. By computing the response matrix for a
tracer particle, we show that an odd compressible fluid can produce an odd lift force. Using shell localization, we
provide analytic expressions for the drag and odd lift forces acting on the tracer particle in a steady state and also
at finite frequency. Importantly, we find that the existence of an odd lift force in a steady state requires taking into
account the nonconservation of the fluid mass density due to the coupling between the two-dimensional surface
and the three-dimensional bulk fluid.