The flow of a nematic liquid crystal in a Hele-Shaw cell with an electrically controlled viscous obstruction is investigated using both a theoretical model and physical experiments. The viscous obstruction is created by temporarily electrically altering the viscosity of the nematic in a region of the cell across which an electric field is applied. The theoretical model is validated experimentally for a circular cylindrical obstruction, demonstrating user-controlled flow manipulation of an anisotropic liquid within a heterogeneous single-phase microfluidic device.

We examine the equilibrium configurations of a nematic liquid crystal with an immersed body in two dimensions. A complex variables formulation provides a means for finding analytical solutions in the case of strong anchoring. Local tractions, forces and torques on the body are discussed in a general setting. For weak (finite) anchoring strengths, an effective boundary technique is proposed which is used to determine asymptotic solutions. The energy-minimizing locations of topological defects on the body surface are also discussed. A number of examples are provided, including circular and triangular bodies, and a Janus particle with hybrid anchoring conditions. Analogies to classical results in fluid dynamics are identified, including d'Alembert's paradox, Stokes’ paradox and the Kutta condition for circulation selection.

Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Emphasis is placed on the formulation of objective rates that account for normal deformations whilst ensuring that tangential flows are Eulerian, and the use of the surface derivative (rather than the covariant derivative) in the nematic free energy, which elastically couples local order to out-of-plane bending of the surface. Focusing on surface geometry and its dynamical interplay with the hydrodynamics, several illustrative instabilities are then characterised. These include cases where the role of the Scriven–Love number and its nematic analogue are non-negligible, and where the active nematic forcing can be characterised by an analogue of the Föppl–von Kármán number. For the former, flows and changes to the nematic texture are coupled to surface geometry by viscous dissipation. This is shown to result in non-trivial relaxation dynamics for a nematic tube. For the latter, the nematic active forcing couples to the surface bending terms of the nematic free energy, resulting in extensile (active ruffling) and contractile (active pearling) instabilities in the tube shape, as well as active bend instabilities in the nematic texture. In comparison to the flat case, such bend instabilities now have a threshold set by the extrinsic curvature of the tube. Finally, we examine a topological defect located on an almost flat surface, and show that there exists a steady state where a combination of defect elasticity, activity and non-negligible spin connection drive a shape change in the surface.

Microorganisms can efficiently navigate in anisotropic complex fluids, but the precise swimming mechanisms remain largely unexplored. Their dynamics is determined by the interplay between multiple effects, including the fluid's orientation order, swimmer's undulatory gait and the finite length. Here, we extend the numerical study of the two-dimensional undulatory motions of a flexible swimmer in lyotropic liquid-crystalline polymers (LCPs) by Lin et al. (J. Fluid Mech., vol. 921, 2021, p. A25) to the scenario of arbitrary swimming directions with respect to the nematic director. The swimmer is modelled as a nearly inextensible yet flexible fibre with imposed travelling-wave-like actuation. We investigate the orientation-dependent swimming behaviours in nematic LCPs for an infinitely long sheet (i.e. Taylor's swimming sheet model) and finite-length swimmers. We demonstrate that the swimmer must be sufficiently stiff to produce undulatory deformations to gain net motions. Moreover, a motile finite-length swimmer can reorient itself to swim parallel with the nematic director, due to a net body torque arising from the asymmetric distribution of the polymer force along the body.

Microorganisms may exhibit rich swimming behaviours in anisotropic fluids, such as liquid crystals, which have direction-dependent physical and rheological properties. Here we construct a two-dimensional computation model to study the undulatory swimming mechanisms of microswimmers in a solution of rigid, rodlike liquid crystal polymers. We describe the fluid phase using Doi's $Q$-tensor model, and treat the swimmer as a finite-length flexible fibre with imposed propagating travelling waves on the body curvature. The fluid–structure interactions are resolved via an immersed boundary method. Compared with the swimming dynamics in Newtonian fluids, we observe non-Newtonian behaviours that feature both enhanced and retarded swimming motions in lyotropic liquid crystal polymers. We reveal the propulsion mechanism by analysing the near-body flow fields and polymeric force distributions, together with asymptotic analysis for an idealized model of Taylor's swimming sheet.

Composite, helical nanostructures formed using cooperative interactions of liquid crystals and Au nanoparticles were studied using a scanning transmission electron microscopy (STEM) mode. The investigated helical assemblies exhibit long-range hierarchical order across length scales, as a result of the crystallization (freezing) directed growth mechanism of nanoparticle-coated twisted nanoribbons and their ability to form organized bundles. Here, STEM methods were used to reproduce the 3D structure of the Au nanoparticle double helix.

Cryogenic transmission electron microscopy (cryo-TEM) has become a powerful tool for probing the structures of soft-matter materials at nanometer or sub-nanometer scale. For many complex molecular fluids (CMFs), the limiting factor in such studies is the preparation of a cryo-TEM specimen that represents the native structure. Plunge freezing of electron-transparent thin films has been widely used, but it is often influenced or even dominated by surface effects and mechanical disturbances of the CMF. In this article, we use liquid crystals as model CMF systems and present the general procedures and typical results of cryo-ultramicrotomy of rapidly frozen “bulk” samples.

We study the complex dynamics of a two-dimensional suspension comprising non-motile active particles confined in an annulus. A coarse-grained liquid crystal model is employed to describe the nematic structure evolution, and is hydrodynamically coupled with the Stokes equation to solve for the induced active flows in the annulus. For dilute suspensions, coherent structures are captured by varying the particle activity and gap width, including unidirectional circulations, travelling waves and chaotic flows. For concentrated suspensions, the internal collective dynamics features motile disclination defects and flows at finite gap widths. In particular, we observe an intriguing quasi-steady-state at certain gap widths during which $+1/2$-order defects oscillate around equilibrium positions accompanying travelling-wave flows that switch circulating directions periodically. We perform linear stability analyses to reveal the underlying physical mechanisms of pattern formation during a concatenation of instabilities.

Instabilities at the deformable free surface of a thin nematic liquid crystal film can develop interesting patterns when exposed to an external electrostatic field. A general linear stability analysis is performed involving the Ericksen–Leslie governing equations for the dynamics of the nematic film coupled with the anisotropic Maxwell stresses for the electric field to uncover the salient features of these instabilities. The study reveals the coexistence of twin instability modes: (i) long-wave interfacial mode – stimulated when the sole destabilizing influence of the electric field overcomes the Frank bulk elasticity and surface tension force, and (ii) finite-wavenumber mode – engendered by the combined destabilizing influence originating from the anisotropic electric field and Ericksen stress, for the films with positive dielectric anisotropy and weaker Frank bulk elasticity. The results reported here are in contrast with the same obtained from the more frequently employed long-wave approach. The air-to-liquid-crystal filling ratio between the electrodes as well as thermodynamic parameters such as the dielectric anisotropy, Frank elasticity, and director orientations across the film and boundaries are found to play crucial roles in the selection of modes, whereas kinetic parameters such as Leslie viscosity coefficients influence only the time scale of instability. Importantly, at higher field intensities a symmetry-breaking Fréedericksz-type transition of director orientations is found to happen, which also causes the transition of the dominant mode of instability from the long-wave to the finite-wavenumber mode for films with relatively lower values of Frank bulk elasticity and positive dielectric anisotropy.

The aspect ratio dependence of the electroconvection phenomenon in a suspended nematic liquid crystal film with a rectangular boundary is investigated. Two-dimensional global stability analysis is carried out on the coupled electrohydrodynamic system to calculate the instability boundary of the phenomenon for different aspect ratios. The calculated critical $R$ number (Rayleigh-like number) shows a rapidly decreasing trend in the low-aspect-ratio region (roughly $\unicode[STIX]{x1D6FE}<1.5$, where $\unicode[STIX]{x1D6FE}$ is defined as the aspect ratio of the film), and then the variation becomes slow until $\unicode[STIX]{x1D6FE}\approx 2.5$, where the critical $R$ number starts to increase slightly. Convective patterns of liquid films with different aspect ratios are also obtained from stability analysis and validated by particle image velocimetry measurement.

Defects in liquid crystals are of great practical importance and theoretical interest. Despite tremendous efforts, predicting the location and transition of defects under various topological constraint and external field remains to be a challenge. We investigate defect patterns of nematic liquid crystals confined in three-dimensional spherical droplet and two-dimensional disk under different boundary conditions, within the Landau-de Gennes model. We implement a spectral method that numerically solves the Landau-de Gennes model with high accuracy, which allows us to study the detailed static structure of defects. We observe five types of defect structures. Among them the 1/2-disclination lines are the most stable structure at low temperature. Inspired by numerical results, we obtain the profile of disclination lines analytically. Moreover, the connection and difference between defect patterns under the Landau-de Gennes model and the Oseen-Frank model are discussed. Finally, three conjectures are made to summarize some important characteristics of defects in the Landau-de Gennes theory. This work is a continuing effort to deepen our understanding on defect patterns in nematic liquid crystals.

We consider a coating flow of nematic liquid crystal (NLC) fluid film on an inclined substrate. Exploiting the small aspect ratio in the geometry of interest, a fourth-order nonlinear partial differential equation is used to model the free surface evolution. Particular attention is paid to the interplay between the bulk elasticity and the anchoring conditions at the substrate and free surface. Previous results have shown that there exist two-dimensional travelling wave solutions that translate down the substrate. In contrast to the analogous Newtonian flow, such solutions may be unstable to streamwise perturbations. Extending well-known results for Newtonian flow, we analyse the stability of the front with respect to transverse perturbations. Using full numerical simulations, we validate the linear stability theory and present examples of downslope flow of nematic liquid crystal in the presence of both transverse and streamwise instabilities.

We review the mathematical analysis of some uniaxial, liquid crystal phases. Firstly, we state the models for the two different studied phases: nematic and smectic-A liquid crystals. The spatial and temporal profiles of the liquid crystal configurations will be described by means of strongly nonlinear parabolic partial differential systems, which are presented at the same time. Then we will state some results about existence, regularity, time-periodicity and stability of solutions at infinite time for both models. It is our aim to show that, although nematic and smectic-A phases have different physical properties and are modelled by different nonlinear parabolic problems, there exists a common mathematical machinery to rewrite the models and obtain analytical results.

We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth-order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three-dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate.

We analyse the creeping flow generated by a spherical particle moving through a viscous fluid with nematic directional order, in which momentum diffusivity is anisotropic and which opposes resistance to bending. Specifically, we provide closed-form analytical expressions for the response function, i.e. the equivalent to Stokes’s drag formula for nematic fluids. Particular attention is given to the rotationally pseudo-isotropic condition defined by zero resistance to bending, and to the strain pseudo-isotropic condition defined by isotropic momentum diffusivity. We find the former to be consistent with the rheology of biopolymer networks and the latter to be closer to the rheology of nematic liquid crystals. These ‘pure’ anisotropic conditions are used to benchmark existing particle tracking microrheology methods that provide effective directional viscosities by applying Stokes’s drag law separately in different directions. We find that the effective viscosity approach is phenomenologically justified in rotationally isotropic fluids, although it leads to significant errors in the estimated viscosity coefficients. On the other hand, the mere concept of directional effective viscosities is found to be misleading in fluids that oppose an appreciable resistance to bending. Finally, we observe that anisotropic momentum diffusivity leads to asymmetric streamline patterns displaying enhanced (reduced) streamline deflection in the directions of lower (higher) diffusivity. The bending resistance of the fluid is found to modulate the asymmetry of streamline deflection. In some cases, the combined effects of both anisotropy mechanisms leads to streamline patterns that converge towards the sphere.