Screw Symmetry, Chiral Hydrodynamics and Odd Instability in Active Cholesterics

Abstract

Active cholesterics are chiral in both their structure, which has continuous screw symmetry, and their active stresses, which include contributions from torque dipoles. Both expressions of chirality give rise to curl forces in the hydrodynamics, which we derive from the active Ericksen-Leslie equations using a geometric approach. This clarifies the hydrodynamics of continuous screw symmetry and provides an example of generalised odd elastic forces that originate from an equilibrium free energy. We discuss also the nonlinear structure of the active hydrodynamics in terms of the Eulerian displacement field of the cholesteric pseudolayers. For the active instability, screw symmetry generates a contribution of chiral activity to the linearised pseudolayer hydrodynamics that is absent in materials with chiral activity but achiral structure. When the two forms are sufficiently antagonistic, this term produces a new active instability with threshold and characteristic wavevector distinct from those of the active Helfrich-Hurault instability in chiral active smectics. Finally, we comment on the isotropic chiral hydrodynamics of materials with three-dimensional screw symmetry.

12 pages, 3 figures

References in corpus (26)

• The Mechanics and Statistics of Active Matter
• Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles
• Odd dynamics of living chiral crystals
• Odd Viscosity and Odd Elasticity
• Stresses in lipid membranes
• On the structure of blue phase III
• Odd viscosity in two-dimensional incompressible fluids
• Review: Topology of solitons and singular defects in chiral liquid crystals
• Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity
• Limit cycles turn active matter into robots
• Contractile and chiral activities co-determine the helicity of swimming droplet trajectories
• The geometry of thresholdless active flow in nematic microfluidics
• Live Soap: Order, Fluctuations and Instabilities in Active Smectics
• Umbilic Lines in Orientational Order
• Hydrodynamic instabilities in active cholesteric liquid crystals
• Nonlinear smectic elasticity of a helical state in cholesterics and helimagnets
• Active cholesterics: odder than odd elasticity
• Self-organized swimming with odd elasticity
• Helical Nanofilaments and the High Chirality Limit of Smectics-A
• Helfrich-Hurault elastic instabilities driven by geometrical frustration
• Point Defects, Chirality and Singularity Theory in Cholesteric Liquid Crystal Droplets
• Odd elastohydrodynamics: non-reciprocal living material in a viscous fluid
• Intrinsic Geometry and Director Reconstruction for Three-Dimensional Liquid Crystals
• Contact Topology and the Structure and Dynamics of Cholesterics
• Hydrodynamics of chiral liquids and suspensions
• Chirality and odd mechanics in active columnar phases