Lift force in odd compressible fluids

TL;DR

This paper derives the response matrix for a tracer in a 2D compressible fluid with odd viscosity, revealing that such fluids can generate an odd lift force, unlike incompressible fluids.

Contribution

It provides analytic expressions for drag and lift forces in odd compressible fluids, highlighting the role of non-conservation of mass density in steady-state lift.

Findings

Odd compressible fluids can produce an odd lift force.

Analytic formulas for drag and lift forces are derived.

Steady-state lift depends on mass density non-conservation.

Abstract

We compute the response matrix for a tracer particle in a compressible fluid with odd viscosity living on a two-dimensional surface. Unlike the incompressible case, we find that an odd compressible fluid can produce an odd lift force on a tracer particle. Using a "shell localization" formalism, 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 non-conservation of the fluid mass density due to the coupling between the two-dimensional surface and the three-dimensional bulk fluid.