Active nematics contain topological defects which under sufficient activity move, create and annihilate in a chaotic quasi-steady state, called active turbulence. However, understanding active defects under confinement is an open challenge, especially in three-dimensions. Here, we demonstrate the topology of three-dimensional active nematic turbulence under the spherical confinement, using numerical modelling. In such spherical droplets, we show the three-dimensional structure of the topological defects, which due to closed confinement emerge in the form of closed loops or surface-to-surface spanning line segments. In the turbulent regime, the defects are shown to be strongly spatially and time varying, with ongoing transformations between positive winding, negative winding and twisted profiles, and with defect loops of zero and non-zero topological charge. The timeline of the active turbulence is characterised by four types of bulk topology-linked events --- breakup, annihilation, coalescence and cross-over of the defects --- which we discuss could be used for the analysis of the active turbulence in different three-dimensional geometries. The turbulent regime is separated by a first order structural transition from a low activity regime of a steady-state vortex structure and an offset single point defect. We also demonstrate coupling of surface and bulk topological defect dynamics by changing from strong perpendicular to inplane surface alignment. More generally, this work is aimed to provide insight into three-dimensional active turbulence, distinctly from the perspective of the topology of the emergent three-dimensional topological defects.
We study the response of optically trapped achiral and chiralised nematic liquid crystal droplets to linear as well as circular polarised light. We find that there is internal dissipation in rotating achiral nematic droplets trapped in glycerine. We also demonstrate that some chiralised droplets rotate under linearly polarised light. The best fit to our data on chiralised droplets indicates that rotational frequency of these droplets with radius R is approximately proportional to1/R^2, rather than to 1/R^3.
Inverse nematic emulsions in which surfactant-coated water droplets are dispersed in a nematic host fluid have distinctive properties that set them apart from dispersions of two isotropic fluids or of nematic droplets in an isotropic fluid. We present a comprehensive theoretical study of the distortions produced in the nematic host by the dispersed droplets and of solvent mediated dipolar interactions between droplets that lead to their experimentally observed chaining. A single droplet in a nematic host acts like a macroscopic hedgehog defect. Global boundary conditions force the nucleation o…
The emergence of new techniques for the fabrication of nematic droplets with nontrivial topology provides new routes for the assembly of responsive devices. Here we perform a numerical study of spherical nematic droplets on fibres. We analyse the equilibrium textures and find that, under certain conditions,the nematic can avoid the nucleation of topological defects. We consider in detail a homeotropic nematic droplet wrapped around a fibre with planar anchoring. We investigate the effect of an electric field on the texture of this droplet such type of system. In the presence of a DC field, the…
We stabilize nematic droplets with handles against surface-tension-driven instabilities using a yield-stress material as outer fluid and study the complex nematic textures and defect structures that result from the competition between topological constraints and the elasticity of the nematic liquid crystal. We uncover a surprisingly persistent twisted configuration of the nematic director inside the droplets when tangential anchoring is established at their boundaries, which we explain after considering the influence of saddle-splay on the elastic free energy. For toroidal droplets, we find th…
Active matter comprised of self-propelled interacting units holds a major promise for extraction of useful work from its seemingly chaotic out-of-equilibrium dynamics. Streamlining active matter to produce work is especially important at microscale, where the viscous forces prevail over inertia and the useful modes of transport require very specific non-reciprocal type of motion. Here we report that microscopic active droplets representing aqueous dispersions of swimming bacteria Bacillus subtilis show unidirectional propulsion when placed in an inactive nematic medium. Random motion of bacter…
Aqueous dispersions of exfoliated, bile-salt stabilized single-wall carbon nanotubes exhibit a first order transition to a nematic liquid-crystalline phase. The nematic phase presents itself in the form of micron-sized nematic droplets also known as tactoids, freely floating in the isotropic host dispersion. The nematic droplets are spindle shaped and have an aspect ratio of about four, irrespective of their size. We attribute this to a director field that is uniform rather than bipolar, which is confirmed by polarization microscopy. It follows that the ratio of the anchoring strength and the …
Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains (Poulin et al., Science 275, 1770 (1997)). The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements …
One objective of active matter science is to unveil principles by which chaotic microscale dynamics could be transformed into useful work. A nematic liquid crystal environment offers a number of possibilities, one of which is a directional motion of an active droplet filled with an aqueous dispersion of swimming bacteria. In this work, using the responsiveness of the nematic to the electric field and light, we demonstrate how to control the direction and speed of active droplets. The dielectric response of nematic to the electric field causes two effects: (i) reorientation of the overall direc…
To model a nematic emulsion consisting of a surfactant-coated water droplet dispersed in a nematic host, we performed a molecular dynamics simulation of a droplet immersed in a system of 2048 Gay-Berne ellipsoids in a nematic phase. Strong radial anchoring at the surface of the droplet induced a Saturn ring defect configuration, consistent with theoretical predictions for very small droplets. A surface ring configuration was observed for lower radial anchoring strengths, and a pair of point defects was found near the poles of the droplet for tangential anchoring. We also simulated the falling …
Suspended droplets of cholesteric (chiral nematic) liquid crystals spontaneously rotate in the presence of a heat flux due to a temperature gradient, a phenomenon known as Lehmann effect. So far, it is not clear whether this effect is due to the chirality of the phase and the molecules or only to the chirality of the director field. Here, we report the continuous rotation in a temperature gradient of nematic droplets of a lyotropic chromonic liquid crystal featuring a twisted bipolar configuration. The achiral nature of the molecular components leads to a random handedness of the spontaneous t…
Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological charge, the particles are either confined to a two-dimensional circular cavity with homeotropic boundary or to the surface of a three-dimensional sphere. Both systems exhibit half-integer topological point defects. The isotropic defect core has a radius of the order of one particle length and is surrounded by free-standing density oscillations. The effective …
We investigated the effect of a photovoltaic field generated on the surface of iron-doped lithium niobate crystals on droplets of a ferroelectric nematic liquid crystalline and a standard nematic liquid crystalline material deposited on this surface. When such assembly is illuminated with a laser beam, a wide range of dynamic phenomena are initiated. Droplets located outside the laser spot are dragged in the direction of the illuminated area, while droplets located inside the illuminated region tend to bridge each other and rearrange into tendril-like structures. In the ferroelectric nematic p…
For the first time we observed formation of small satellite droplets from the bridge at droplet coalescence. Investigations were made using a Hele-Shaw cell in the two-phase region at nematic-isotropic phase transition. In previous works on coalescence it was considered that before start of coalescence there exists a bridge between the outer fluid connecting regions on the two sides of the droplets (outer bridge). After start of coalescence a bridge connecting the two droplets appears (droplet bridge) and the outer bridge is broken. For the first time we have shown that there are coalescence p…
In this paper, a Freedericksz-like positional transition is found for a spherical micro-droplet suspended in a nematic liquid crystal cell in the presence of an external electric field. Based on the numerical calculation of elastic energy using Green function method, the equilibrium position of micro-droplet is decided through a competition between the buoyant force and the effective force built by the elastic energy gradient existing inside the nematic liquid crystal(NLC) cell. It is shown that the elastic energy dominates the kinetics of micro-droplet until the external field applied reaches…
The quasistationary spreading of a circular liquid drop on a solid substrate typically obeys the so-called Tanner law, with the instantaneous base radius R(t) growing with time as R ~ t^{1/10} -- an effect of the dominant role of capillary forces for a small-sized droplet. However, for droplets of nematic liquid crystals, a faster spreading law sets in at long times, so that R ~ t^alpha with alpha significantly larger than the Tanner exponent 1/10. In the framework of the thin film model (or lubrication approximation), we describe this "acceleration" as a transition to a qualitatively differen…
Here we study theoretically the dynamics of a 2D and a 3D isotropic droplet in a nematic liquid crystal under a shear flow. We find a large repertoire of possible nonequilibrium steady states as a function of the shear rate and of the anchoring of the nematic director field at the droplet surface. We first discuss homeotropic anchoring. For weak anchoring, we recover the typical behaviour of a sheared isotropic droplet in a binary fluid, which rotates, stretches and can be broken by the applied flow. For intermediate anchoring, new possibilities arise due to elastic effects in the nematic flui…
Active forces occurring within cells can drive crucial biological processes that involve spontaneous organization and shape change, such as cell division. Motivated by recent in vitro experiments of nematic droplets of cytoskeletal filaments and motors that self-organize and divide, we present a minimal hydrodynamic model that combines the nonequilibrium kinetics of motor-filament interactions with equilibrium nematic phase separation. The motors organize within droplets and structure filaments into polarized aster defects. At large motor activity, they can even deform or divide the droplet, o…
We study droplets of chromonic liquid crystals squeezed between parallel plates inducing degenerate tangential anchoring on the nematic director. In the coexistence regime, where droplets in the nematic phase are at equilibrium with the surrounding melt, our two-dimensional theoretical model predicts a regime of shape bistability for sufficiently large bipolar droplets, where tactoids (pointed shapes) and discoids (smooth shapes) coexist in equilibrium. This phenomenon has not yet been observed. Two-dimensional droplets of disodium cromoglycate (DSCG) have been the object of a thorough experim…
From the mitotic spindle up to tissues and biofilms, many biological systems behave as active droplets, which often break symmetry and change shape spontaneously. Here, I show that active nematic droplets can experience a fingering instability. I consider an active fluid that acquires nematic order through anchoring at the droplet interface, and I predict its morphological stability in terms of three dimensionless parameters: the anchoring angle, the penetration length of nematic order compared to droplet size, and an active capillary number. Droplets with extensile (contractile) stresses and …
We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamics flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.
Dynamic simulations of the isotropic-nematic phase transformation of liquid crystal droplets under homeotropic anchoring are found to predict chiral symmetry-breaking dynamics. These observations occur when using material parameters for pentyl-cyanobiphenyl (5CB) but not under the single elastic constant approximation of this material, frequently used in simulation. The twisting dynamic process occurs during the relaxation of the domain from an unstable radial texture to a stable uniform texture and involves simultaneous defect loop motion and twisting of the bulk nematic texture.
We investigate condensation of a long confined chiral nematic polymer inside a spherical enclosure, mimicking condensation of DNA inside a viral capsid. The Landau-de Gennes nematic free energy {\sl Ansatz} appropriate for nematic polymers allows us to study the condensation process in detail with different boundary conditions at the enclosing wall that simulate repulsive and attractive polymer-surface interactions. Increasing the chirality, we observe a transformation of the toroidal condensate into a closed surface with an increasing genus, akin to the ordered domain formation observed in cr…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in its vicinity; this topological defect is cancelled by nearby defect structures in the surrounding liquid crystal, so as to give a uniform director field at large distances. We observe three defect structures for different particle sizes: a quadrupolar one with a ring defect surrounding the particle in the equatorial plane; a dipolar one with a satellite def…
Two-dimensional nematics possess peculiar properties that have been studied recently using computer simulation and various theoretical models. Here we review our own contribution to the field using density-functional theory, and present some preliminary simulation results on confined two-dimensional nematics. First we discuss the possible stable bulk phases and phase diagrams and the relation between phases and particle geometry. We then explore the adsorption properties on a single substrate and the confinement effects that arise when the fluid is confined between parallel walls. Next, confin…
Tactoids are pointed, spindle-like droplets of nematic liquid crystal in an isotropic fluid. They have long been observed in inorganic and organic nematics, in thermotropic phases as well as lyotropic colloidal aggregates. The variational problem of determining the optimal shape of a nematic droplet is formidable and has only been attacked in selected classes of shapes and director fields. Here, by considering a novel class of admissible solutions for a bipolar droplet, we study the prevalence in the population of all equilibrium shapes of each of the three that may be optimal (tactoids primar…
We theoretically investigate under what conditions the director field in a spindle-shaped nematic droplet or tactoid obtains a twisted, parity-broken structure. By minimizing the sum of the bulk elastic and surface energies, we show that a twisted director field is stable if the twist and bend elastic constants are small enough compared to the splay elastic constant, but only if the droplet volume is larger than some minimum value. We furthermore show that the transition from an untwisted to a twisted director-field structure is a sharp function of the various control parameters. We predict th…
We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no…
The effect of rough walls on the phase behaviour of a confined liquid crystal (LC) fluid is studied using constant pressure Monte Carlo simulations. The LC is modelled as a fluid of soft ellipsoidal molecules and the rough walls are represented as a hard wall with a number of molecules randomly embedded in them. It is found that the isotropic-nematic (IN) transition is shifted to higher pressures for rougher walls.
Ferrofluids are strongly paramagnetic liquids. We study the behavior of ferrofluid droplets confined between two parallel plates with a weak applied field parallel to the plates. The droplets elongate under the applied field to reduce their demagnetizing energy and reach an equilibrium shape where the magnetic forces balance against the surface tension. This elongation varies logarithmically with aspect ratio of droplet thickness to its original radius, in contrast to the behavior of unconfined droplets. Experimental studies of a ferrofluid/water/surfactant emulsion confirm this prediction.
A spontaneous buckling transition in thin layers of monodomain nematic liquid crystalline gel was observed by polarized light microscopy. The coupling between the orientational ordering of liquid crystalline solvent and the translational ordering of crosslinked polymer backbones inside the nematic gel contributes to such buckling transition. As the nematic mesogens become more ordered when the gel is cooled down from a higher gelation temperature, the polymeric backbones tend to elongate along the direction parallel to the nematic director, which is perpendicular to the rigid glass surfaces in…
We present computer simulations of long thin hard spherocylinders in a narrow planar slit. We observe a transition from the isotropic to a nematic phase with quasi-long-range orientational order upon increasing the density. This phase transition is intrinsically two dimensional and of the Kosterlitz-Thouless type. The effective two-dimensional density at which this transition occurs increases with plate separation. We qualitatively compare some of our results with experiments where microtubules are confined in a thin slit, which gave the original inspiration for this work.
We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer {\sl via} the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy {\sl ansatz} is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and …
Nematic drops suspended in the isotropic phase of the same substance were subjected to alternating electrical fields of varying frequency. The system was carefully kept in the isotropic-nematic coexistance region, which was broadened due to small amounts of non-mesogenic additives. Whereas the droplets remained spherical at low (order of 10 Hz) and high frequencies (in the kHz range), at intermediate frequencies, we observed a marked flattening of the droplet in the plane perpendicular to the applied field. The deformation of the liquid crystal (LC) droplets occurred both in substances with po…
In experiments, an individual chemically active liquid crystal (LC) droplet submerged in the bulk of a surfactant solution may self-propel along a straight, helical, or random trajectory. In this paper, we develop a minimal model capturing all three types of self-propulsion trajectories of a drop in the case of a nematic LC with homeotropic anchoring at LC-fluid interface. We emulate the director field within the drop by a single preferred polarization vector that is subject of two reorientation mechanisms, namely, the internal flow-induced displacement of the hedgehog defect and the droplet's…
We use numerical modelling to study the flow patterns of an active nematic confined in a cylindrical capillary, considering both planar and homeotropic boundary conditions. We find that active flow emerges not only along the capillary axis but also within the plane of the capillary, where radial vortices are formed. If topological defects are imposed by the boundary conditions, they act as local pumps driving the flow. At higher activity we demonstrate escape of the active defects and flow into the third dimension, indicating the importance of dimensionality in active materials. We argue that …
Sessile droplets of a ferroelectric nematic liquid crystalline material were exposed to surface electric fields produced by pyroelectric and photogalvanic (photovoltaic) effects in X-cut iron-doped lithium niobate crystals. The resulting dynamic processes were monitored by polarization optical (video)microscopy (POM). During heating/cooling cycles, at first, the droplets change their shape from spherical to extended ellipsoidal. Then they start to move rapidly along the surface electric field, i.e., along the crystal's polar axis (c-axis). During this motion, several droplets merge into runnin…
We develop the scaled particle theory to describe the thermodynamic properties and orientation ordering of a binary mixture of hard spheres (HS) and hard spherocylinders (HSC) confined in a disordered porous medium. Using this theory the analytical expressions of the free energy, the pressure and the chemical potentials of HS and HSC have been derived. The improvement of obtained results is considered by introducing the Carnahan-Starling-like and Parsons-Lee-like corrections. Phase diagrams for the isotropic-nematic transition are calculated from the bifurcation analysis of the integral equati…
Motivated by recent experiments on the rod-like virus bacteriophage fd, confined to circular and annular domains, we present a theoretical study of structural transitions in these geometries. Using the continuum theory of nematic liquid crystals, we examine the competition between bulk elasticity and surface anchoring, mediated by the formation of topological defects. We show analytically that bulk defects are unstable with respect to defects sitting at the boundary. Moreover, in case of an annulus, whose topology does not require the presence of topological defects, under weak anchoring condi…
We numerically investigate the morphology and disclination line dynamics of active nematic droplets in three dimensions. Although our model only incorporates the simplest possible form of achiral active stress, active nematic droplets display an unprecedented range of complex morphologies. For extensile activity finger-like protrusions grow at points where disclination lines intersect the droplet surface. For contractile activity, however, the activity field drives cup-shaped droplet invagination, run-and-tumble motion or the formation of surface wrinkles. This diversity of behaviour is explai…
Within the macroscopic Landau-de Gennes approach, we examine the Gaussian normal mode fluctuations of semi-infinite nematic liquid crystals in a regime of critical wetting. It is argued that surface free-energy potentials that strongly suppress the long-range nematic order favor the appearance of bound biaxial nematic-director fluctuation modes, located in the domain occupied by the thermodynamic phase wetting the wall. Instead, substrates enhancing the orientational order promote the existence of uniaxial nematic-director local excitations. Close to the phase coexistence temperature both type…
We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter $S\simeq1$. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in …
The deformation and break-up of Newtonian/viscoelastic droplets are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and finite difference schemes, the former used to model two immiscible fluids with variable viscous ratio, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We quantify the droplet response by changing the polymer relaxation time $τ…
