Odd viscosity in chiral active fluids

Debarghya Banerjee,Anton Souslov,Vincenzo Vitelli,Alexander G Abanov

doi:10.1038/s41467-017-01378-7

Abstract

We study the hydrodynamics of fluids composed of self-spinning objects such as chiral grains or colloidal particles subject to torques. These chiral active fluids break both parity and time-reversal symmetries in their non-equilibrium steady states. As a result, the constitutive relations of chiral active media display a dissipationless linear-response coefficient called odd (or equivalently, Hall) viscosity. This odd viscosity does not lead to energy dissipation, but gives rise to a flow perpendicular to applied pressure. We show how odd viscosity arises from non-linear equations of hydrodynamics with rotational degrees of freedom, once linearized around a non-equilibrium steady state characterized by large spinning speeds. Next, we explore odd viscosity in compressible fluids and suggest how our findings can be tested in the context of shock propagation experiments. Finally, we show how odd viscosity in weakly compressible chiral active fluids can lead to density and pressure excess within vortex cores.

Highlights

We study the hydrodynamics of fluids composed of self-spinning objects such as chiral grains or colloidal particles subject to torques
Odd viscosity was neglected in previous hydrodynamic theories of active rotors[11,21,22,23,24,25] that implicitly consider only rotors with small spinning frequency near equilibrium—a regime for which the antisymmetric stress dominates over the odd viscosity
We construct a hydrodynamic description of “dry” chiral active fluids based on a constitutive relation that explicitly accounts for an odd viscosity term

Summary

Introduction

We study the hydrodynamics of fluids composed of self-spinning objects such as chiral grains or colloidal particles subject to torques. Conservation of angular momentum dictates that the stress tensor σij of any medium with vanishing bulk external torque must be symmetric under the exchange of its two indices i and j This conclusion, does not apply to chiral active fluids composed of self-spinning constituents (Fig. 1a) that are driven by active torques[16,17,18,19,20,21]. We show how such chiral active fluids break both parity and time-reversal symmetries in their steady states, giving rise to a dissipationless linear-response coefficient called odd (or Hall) viscosity ηoijklð1⁄4 ÀηoklijÞ in their constitutive relations. Violation of Onsager reciprocity originates from the breaking of microscopic reversibility out of equilibrium, a feature inherent to active matter[33,34] In this case, an odd viscosity can emerge as a linear-response coefficient calculated around the non-equilibrium steady state of a purely classical system. On general grounds[28,29], it can be shown that odd viscosity is proportional to the non-vanishing net angular momentum density that exists within the active fluid in steady state

Objectives

Methods

Results

Conclusion