Stokes flows in three-dimensional fluids with odd and parity-violating viscosities

TL;DR

This paper investigates how parity-violating and odd viscosities influence three-dimensional Stokes flows, revealing new azimuthal flow patterns and potential experimental signatures in symmetric fluid systems.

Contribution

It systematically characterizes all parity-violating viscosities compatible with cylindrical symmetry and analyzes their effects on classical Stokes flow solutions.

Findings

Parity-violating viscosities induce azimuthal flows in symmetric systems.

Azimuthal flows alter particle trajectories and cloud dynamics.

Presence of azimuthal flows can serve as experimental probes for parity-violating viscosities.

Abstract

The Stokes equation describes the motion of fluids when inertial forces are negligible compared to viscous forces. In this article, we explore the consequence of parity-violating and non-dissipative (i.e. odd) viscosities on Stokes flows in three dimensions. Parity-violating viscosities are coefficients of the viscosity tensor that are not invariant under mirror reflections of space, while odd viscosities are those which do not contribute to dissipation of mechanical energy. These viscosities can occur in systems ranging from synthetic and biological active fluids to magnetised and rotating fluids. We first systematically enumerate all possible parity-violating viscosities compatible with cylindrical symmetry, highlighting their connection to potential microscopic realizations. Then, using a combination of analytical and numerical methods, we analyze the effects of parity-violating viscosities on the Stokeslet solution, on the flow past a sphere or a bubble, and on many-particle sedimentation. In all the cases we analyze, parity-violating viscosities give rise to an azimuthal flow even when the driving force is parallel to the axis of cylindrical symmetry. For a few sedimenting particles, the azimuthal flow bends the trajectories compared to a traditional Stokes flow. For a cloud of particles, the azimuthal flow impedes the transformation of the spherical cloud into a torus and the subsequent breakup into smaller parts that would otherwise occur. The presence of azimuthal flows in cylindrically symmetric systems (sphere, bubble, cloud of particles) can serve as a probe for parity-violating viscosities in experimental systems.