Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions.

From incompressible flows to electrostatics, harmonic functions can provide solutions to many two-dimensional problems and, similarly, the director field of a planar nematic can be determined using complex analysis. We derive a closed-form solution for a quasi-steady state director field induced by an arbitrarily large set of point defects and circular inclusions with or without fixed rotational degrees of freedom, and compute the forces and torques acting on each defect or inclusion. We show that a complete solution must include two types of singularities, generating a defect winding number and its spiral texture, which have a direct effect on defect equilibrium textures and their dynamics.

Symmetrically pulsating bubbles swim in an anisotropic fluid by nematodynamics.

Swimming in low-Reynolds-number fluids requires the breaking of time-reversal symmetry and centrosymmetry. Microswimmers, often with asymmetric shapes, exhibit nonreciprocal motions or exploit nonequilibrium processes to propel. The role of the surrounding fluid has also attracted attention because viscoelastic, non-Newtonian, and anisotropic properties of fluids matter in propulsion efficiency and navigation.

Defect Line Coarsening and Refinement in Active Nematics.

Active matter is naturally out of equilibrium which results in the emergence of diverse dynamic steady states, including the omnipresent chaotic state known as the active turbulence. However, much less is known how active systems dynamically depart out of these configurations, such as get excited or damped to a different dynamic steady state. In this Letter, we demonstrate the coarsening and refinement dynamics of topological defect lines in three-dimensional active nematic turbulence.

Continuous generation of topological defects in a passively driven nematic liquid crystal.

Synthetic active matter is emerging as the prime route for the realisation of biological mechanisms such as locomotion, active mixing, and self-organisation in soft materials. In particular, passive nematic complex fluids are known to form out-of-equilibrium states with topological defects, but their locomotion, activation and experimental realization has been developed and understood to only a limited extent. Here, we report that the concentration-driven flow of small molecules triggers turbulent flow in the thin film of a nematic liquid crystal that continuously generates pairs of topological defects with an integer topological charge.

Topological defect-propelled swimming of nematic colloids.

Topological defects on colloids rotating in nematic liquid crystals form far-from-equilibrium structures that perform complex swim strokes in which the defects periodically extend, depin, and contract. These defect dynamics propel the colloid, generating translation from rotation. The swimmer's speed and direction are determined by the topological defect's polarity and extent of elongation.

Nematic bits and universal logic gates.

Liquid crystals (LCs) can host robust topological defect structures that essentially determine their optical and elastic properties. Although recent experimental progress enables precise control over nematic LC defects, their practical potential for information storage and processing has yet to be explored. Here, we introduce the concept of nematic bits (nbits) by exploiting a quaternionic mapping from LC defects to the Poincaré-Bloch sphere.

Spectral energy analysis of bulk three-dimensional active nematic turbulence.

We perform energy spectrum analysis of the active turbulence in a 3D bulk active nematic using continuum numerical modelling. Specifically, we calculate the spectra of the two main energy contributions - kinetic energy and nematic elastic energy - and combine this with the geometrical analysis of the nematic order and flow fields, based on direct defect tracking and calculation of autocorrelations. We show that the active nematic elastic energy is concentrated at scales corresponding to the effective defect-to-defect separation, scaling with activity as ∼ζ0.

Three-Dimensional Active Defect Loops.

We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modeling, that they are governed by the local profile of the orientational order surrounding the defects. Analyzing a continuous span of defect loop profiles, ranging from radial and tangential twist to wedge ±1/2 profiles, we show that the distinct geometries can drive material flow perpendicular or along the local defect loop segment, whose variation around a closed loop can lead to net loop motion, elongation, or compression of shape, or buckling of the loops. We demonstrate a correlation between local curvature and the local orientational profile of the defect loop, indicating dynamic coupling between geometry and topology.

Field generated nematic microflows via backflow mechanism.

Generation of flow is an important aspect in microfluidic applications and generally relies on external pumps or embedded moving mechanical parts which pose distinct limitations and protocols on the use of microfluidic systems. A possible approach to avoid moving mechanical parts is to generate flow by changing some selected property or structure of the fluid. In fluids with internal orientational order such as nematic liquid crystals, this process of flow generation is known as the backflow effect.

Microfluidic control over topological states in channel-confined nematic flows.

Compared to isotropic liquids, orientational order of nematic liquid crystals makes their rheological properties more involved, and thus requires fine control of the flow parameters to govern the orientational patterns. In microfluidic channels with perpendicular surface alignment, nematics discontinuously transition from perpendicular structure at low flow rates to flow-aligned structure at high flow rates. Here we show how precise tuning of the driving pressure can be used to stabilize and manipulate a previously unresearched topologically protected chiral intermediate state which arises before the homeotropic to flow-aligned transition.

Sculpting stable structures in pure liquids.

Pure liquids in thermodynamic equilibrium are structurally homogeneous. In liquid crystals, flow and light pulses are used to create reconfigurable domains with polar order. Moreover, through careful engineering of concerted microfluidic flows and localized optothermal fields, it is possible to achieve complete control over the nucleation, growth, and shape of such domains.

Active nematic emulsions.

The formation of emulsions from multiple immiscible fluids is governed by classical concepts such as surface tension, differential chemical affinity and viscosity, and the action of surface-active agents. Much less is known about emulsification when one of the components is active and thus inherently not constrained by the laws of thermodynamic equilibrium. We demonstrate one such realization consisting in the encapsulation of an active liquid crystal (LC)-like gel, based on microtubules and kinesin molecular motors, into a thermotropic LC.

Cross-talk between topological defects in different fields revealed by nematic microfluidics.

Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors and biological materials. Although topological defects and their mutual interactions have been extensively studied, little is known about the interplay between defects in different fields-especially when they coevolve-within the same physical system. Here, using nematic microfluidics, we study the cross-talk of topological defects in two different material fields-the velocity field and the molecular orientational field.

Relevance of saddle-splay elasticity in complex nematic geometries.

We demonstrate the relevance of saddle-splay elasticity in nematic liquid crystalline fluids in the context of complex surface anchoring conditions and the complex geometrical confinement. Specifically, nematic cells with patterns of surface anchoring and colloidal knots are shown as examples where saddle-splay free energy contribution can have a notable role which originates from nonhomogeneous surface anchoring and the varying surface curvature. Patterned nematic cells are shown to exhibit various (meta)stable configurations of nematic field, with relative (meta)stability depending on the saddle-splay.

Electric field generation of Skyrmion-like structures in a nematic liquid crystal.

Skyrmions are particle-like topological objects that are increasingly drawing attention in condensed matter physics, where they are connected to inversion symmetry breaking and chirality. Here we report the generation of stable Skyrmion-like structures in a thin nematic liquid crystal film on chemically patterned patchy surfaces. Using the interplay of material elasticity and surface boundary conditions, we use a strong electric field to quench the nematic liquid crystal from a fully aligned phase to vortex-like nematic liquid crystal structures, centered on patterned patches, which carry two different sorts of topological defects.