Hydrodynamic instabilities in active cholesteric liquid crystals

Abstract

Abstract. We describe the basic properties and consequences of introducing active stresses, with principal direction along the local director, in cholesteric liquid crystals. The helical ground state is found to be linearly unstable to extensile stresses, without threshold in the limit of infinite system size, whereas contractile stresses are hydrodynamically screened by the cholesteric elasticity to give a finite threshold. This is confirmed numerically and the non-linear consequences of instability, in both extensile and contractile cases, are studied. We also consider the stresses associated to defects in the cholesteric pitch (λ lines) and show how the geometry near to the defect generates threshold-less flows reminiscent of those for defects in active nematics. At large extensile activity λ lines are spontaneously created and can form steady-state patterns sustained by constant active flows.

Mechanically induced Helfrich-Hurault effect in a confined lamellar system with finite surface anchoring

“…In particular [18,19] explored the case of non-linear undulations where the instability show a transition from sinusoidal to a chevron structure. Napoli and Nobili [20], extended the classical results valid for infinitesimal imposed strain (see equation 40) to the most general case valid for an imposed finite dilatative strain (see equation 391 ), capable therefore to cover cases were the specimen thickness d can be comparable to the characteristic length λ. Analogous observed instabilities are reported in [21,22]. The former refers to active cholesteric liquid crystals where buckling can be induced by both extensile or contractile applied stresses.…”

Three-Dimensional Active Defect Loops

“…Especially, it is important to realise that defect lines and loops in three-dimensional active nematics can exhibit a full span of different local orientational profiles -of ±1/2 wedge, twist and mixed type -which results in profoundly different local self-propulsion velocities, both in the directions perpendicular and along the defect loop segment. There are many natural directions for extension of our work, including to a detailed com- parison of topologically charged and uncharged loops [11] and to defects in active cholesterics [31,32]. The significance of two-dimensional topological defects to biological systems such as cell cultures and tissues has been wellestablished in recent years [5][6][7]; active defect loops may provide similar insights to fully three-dimensional biological tissues, fluids and processes.…”

Topological states in chiral active matter: Dynamic blue phases and active half-skyrmions

“…Combining active stresses of self-propelled particles with two-dimensional helical ordering in the blue phase provides a framework for studying non-equilibrium topological states in active matter. Compared to the few existing theoretical works that treat chiral active materials 31,35,[45][46][47] , we explicitly introduce topological states in chiral liquid crystals and connect the director structure to the resulting dynamics. We show that half-skyrmions are stable to contractile stresses, but that there is an active instability threshold for extensile active particles analogous to the pitch-splay mode in active cholesterics.…”

“…In chiral nematics however, the cholesteric order contributes a passive bend term that acts to screen the nematic splay mode. Instability only sets in when the activity exceeds a threshold, and only for extensile activity 31 . Due to the cholesteric order in half-skyrmions, it can therefore be expected that a half-skyrmion is unstable to extensile stresses above a finite threshold in activity, but stable to contractile stresses.…”