Odd viscous flow past a sphere at low but nonzero Reynolds numbers

TL;DR

This paper investigates how odd viscosity influences flow past a sphere at low Reynolds numbers, revealing that while lift force vanishes, a non-zero torque can arise due to the interplay of odd viscosity and convection.

Contribution

It extends understanding of odd viscosity effects in low Reynolds number flows past spheres, overcoming theoretical hurdles with asymptotic matching and reciprocal theorem techniques.

Findings

Lift force vanishes in the considered flow regime.

A stream-induced non-vanishing torque arises due to odd viscosity and convection.

The analysis includes cases with and without axial symmetry.

Abstract

Measuring lift force on symmetrically shaped obstacles immersed in laminar flow is the quintessential way of signalling odd viscosity. For flow past cylinders, such a lift force does not arise when incompressibility and no-slip boundary conditions hold, whereas for spheres, a lift force was found in Stokes flow, applying to cases where the Reynolds number is negligible and convection can be ignored. When considering the role of convection at low but nonzero Reynolds numbers, two arising hurdles are the Whitehead paradox and the breaking of axial symmetry, which are overcome by asymptotic matching and the Lorentz reciprocal theorem respectively. We also consider the case where axial symmetry is retained because the translation of the sphere is aligned with the anisotropy vector of odd viscosity. We find that while lift vanishes, the interplay between odd viscosity and convection gives rise to a stream-induced non-vanishing torque.