Odd viscosity in chiral active fluids

Abstract: Chiral active fluids are materials composed of self-spinning rotors that continuously inject energy and angular momentum at the microscale. Out-of-equilibrium fluids with active-rotor constituents have been experimentally realized using nanoscale biomolecular motors, microscale active colloids, or macroscale driven chiral grains. Here, 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 viscosity in their constitutive relations. Odd viscosity couples pressure and vorticity leading, for example, to density modulations within a vortex profile. Moreover, chiral active fluids flow in the direction transverse to applied compression as in shock propagation experiments. We envision that this collective transverse response may be exploited to design self-assembled hydraulic cranks that convert between linear and rotational motion in microscopic machines powered by active-rotors fluids.

• The paper investigates how broken parity and time-reversal symmetries in chiral active fluids lead to odd viscosity, a non-dissipative transport coefficient.
• Due to active torques, the stress tensor in these fluids gains antisymmetric components, allowing odd viscosity to generate forces orthogonal to velocity gradients.
• The findings suggest potential experiments and applications leveraging odd viscosity in micro-scale devices, such as converting linear to rotational motion or altering vortex dynamics.

Overview of "Odd Viscosity in Chiral Active Fluids"

The study titled "Odd viscosity in chiral active fluids" explores the properties and behaviors of chiral active fluids—materials composed of self-spinning microscopic rotors that continuously generate energy and angular momentum. The focus is on understanding the implications of broken parity and time-reversal symmetries, which give rise to a novel dissipationless transport coefficient known as odd viscosity. This paper primarily addresses how odd viscosity affects the mechanical response of such fluids and explores potential applications in designing micro-machines.

Key Findings

• Symmetry Breaking and Odd Viscosity: Chiral active fluids, through their active constituents, break both parity ($P$) and time-reversal ($T$) symmetries. This results in the emergence of odd viscosity ($\eta^o$), a Hall-like transport coefficient that is antisymmetric and stands apart from conventional viscosity by being non-dissipative.
• Constitutive Relations: The stress tensor in traditional fluids is symmetric, adhering to angular momentum conservation principles. However, in chiral active fluids, due to active torques, the stress tensor acquires antisymmetric components, and odd viscosity manifests in the symmetric part. This distinction implies that, unlike regular viscosity, odd viscosity can generate forces orthogonal to velocity gradients, influencing the flow without dissipating energy.
• Vortex Dynamics: Analyzing a simple vortex scenario, the study finds that odd viscosity can lead to variations in density profiles, primarily within vortices. Effects include density pile-ups in the core of a vortex, a significant departure from typical inertial vortex behavior observed in conventional fluids.
• Ultrasonic Shocks: The paper extends the analysis to high Mach number scenarios, examining shock propagation. In the presence of odd viscosity, shocks exhibit transverse flow components, which are absent in traditional shocks, altering the typical shock structure and potentially leading to novel density and flow patterns.

Theoretical and Practical Implications

• Theoretical Development: The research provides a compelling theoretical framework to incorporate odd viscosity into the hydrodynamic equations of motion for chiral active fluids. This involves recalibrating constitutive relations to include the novel terms arising from the microscopic chiral nature of the rotors.
• Experimental Predictions: The study suggests potential experiments to exploit the unique transverse responses to odd viscosity, including using chiral active fluids in micro-scale hydraulic devices. This also hints at new pathways for designing self-assembling systems where chiral active media could convert linear to rotational motion efficiently.
• Future Directions: Extending this framework may prove essential to explore other non-equilibrium systems where symmetry breaking plays a critical role. Additionally, leveraging the insights gained could lead to novel material designs with bespoke properties for robotics and other adaptive technologies.

In conclusion, this study not only advances the understanding of chiral active fluids and their non-equilibrium dynamics but also opens new avenues for engineering applications. By revealing the subtleties of odd viscosity, it encourages further investigation into other active systems where fluid-structure interactions critically depend on chiral influences.