Emergent hydrodynamics of chiral active fluids: vortices, bubbles and odd diffusion

TL;DR

This paper develops a hydrodynamic theory for chiral active fluids with non-conservative odd forces, predicting phenomena like vortices, bubbles, and odd diffusion, and validating these with simulations and potential experiments.

Contribution

It derives a continuum hydrodynamic model from microscopic Langevin equations for chiral active particles, revealing novel behaviors such as odd viscosity and inhomogeneous phases.

Findings

Prediction of odd diffusivity and edge currents.

Identification of a linear instability due to odd viscosity and torque density.

Observation of bubble-like structures and vortices in steady states.

Abstract

Starting from a microscopic multiparticle Langevin equation, we systematically derive a hydrodynamic description in terms of density and momentum fields for chiral active particles interacting via standard repulsive and nonlocal odd forces. These odd interactions are reciprocal but non-conservative: they are non-potential forces, as they act perpendicular to the vector joining any pair of particles. As a result, the torques that two particles exert on one another are non-reciprocal. The ensuing macroscopic continuum description consists of a continuity equation for the density and a generalized compressible Navier-Stokes equation for the fluid velocity. The latter includes a chirality-induced torque density term and an odd viscosity contribution. Our theory predicts the emergence of odd diffusivity, edge currents, and an inhomogeneous phase - characterized by bubble-like structures - recently observed in simulations. Specifically, the theory exhibits a linear instability arising from the interplay between odd viscosity and torque density, and admits steady-state inhomogeneous solutions featuring bubbles and vortices, in agreement with numerical simulations. Our findings can be tested experimentally in systems of granular spinners or rotating microorganisms suspended in a fluid.