Liquid crystal microfluidics for tunable flow shaping

Electrically-driven modulation of flow patterns in liquid crystal microfludics

The flow of liquid crystals in the presence of electric fields is investigated as a possible means of flow control. The Beris-Edwards model is coupled to a free energy incorporating electric field effects. Simulations are conducted in straight channels and in junctions. Our findings reveal that local flow mediation can be achieved by the application of spatially varying electric fields. In rectangular straight channels, we report a two-stream velocity profile arising in response to the imposed electric field. Furthermore, we observe that the flow rate in each stream scales inversely with the Miesowicz viscosities, leading to the confinement of 70% of the throughput to one half of the channel. Similar flow partitioning is also demonstrated in channel junction geometries, where we show that using external fields provides a novel avenue for flow modulation in microfluidic circuits.

Control of liquid crystals combining surface acoustic waves, nematic flows, and microfluidic confinement

The optical properties of liquid crystals serve as the basis for display, diagnostic, and sensing technologies. Such properties are generally controlled by relying on electric fields. In this work, we investigate the effects of microfluidic flows and acoustic fields on the molecular orientation and the corresponding optical response of nematic liquid crystals. Several previously unknown structures are identified, which are rationalized in terms of a state diagram as a function of the strengths of the flow and the acoustic field. The new structures are interpreted by relying on calculations with a free energy functional expressed in terms of the tensorial order parameter, using continuum theory simulations in the Landau-de Gennes framework. Taken together, the findings presented here offer promise for the development of new systems based on combinations of sound, flow, and confinement.

Engineering Nano/Microscale Chiral Self-Assembly in 3D Printed Constructs

Helical hierarchy found in biomolecules like cellulose, chitin, and collagen underpins the remarkable mechanical strength and vibrant colors observed in living organisms. This study advances the integration of helical/chiral assembly and 3D printing technology, providing precise spatial control over chiral nano/microstructures of rod-shaped colloidal nanoparticles in intricate geometries. We designed reactive chiral inks based on cellulose nanocrystal (CNC) suspensions and acrylamide monomers, enabling the chiral assembly at nano/microscale, beyond the resolution seen in printed materials. We employed a range of complementary techniques including Orthogonal Superposition rheometry and in situ rheo-optic measurements under steady shear rate conditions. These techniques help us to understand the nature of the nonlinear flow behavior of the chiral inks, and directly probe the flow-induced microstructural dynamics and phase transitions at constant shear rates, as well as their post-flow relaxation. Furthermore, we analyzed the photo-curing process to identify key parameters affecting gelation kinetics and structural integrity of the printed object within the supporting bath. These insights into the interplay between the chiral inks self-assembly dynamics, 3D printing flow kinematics and photo-polymerization kinetics provide a roadmap to direct the out-of-equilibrium arrangement of CNC particles in the 3D printed filaments, ranging from uniform nematic to 3D concentric chiral structures with controlled pitch length, as well as random orientation of chiral domains. Our biomimetic approach can pave the way for the creation of materials with superior mechanical properties or programable photonic responses that arise from 3D nano/microstructure and can be translated into larger scale 3D printed designs.

Curvature-mediated programming of liquid crystal microflows

Despite the recognized role of liquid crystal microfluidics in generating programmable, self-organized and guided flow properties, to date, the flow behavior of LCs within curved channels remains unexplored. Using experiments and numerical simulations, we demonstrate that the curvature of microscale conduits allow programming of liquid crystal (LC) flows. Focusing on a nematic LC flowing through U- and L-shaped channels - two simple yet fundamental curved flow paths - with rectangular cross-section, our results reveal that the curvature of flow path can trigger transverse flow-induced director gradients. The emergent director field feeds back into the flow field, ultimately leading to LC flows controlled by the channel curvature. This curvature-mediated flow control, identified by polarizing optical microscopy and supported by the nematofluidic solutions, offers concepts in LC microfluidic valves, wherein the throughput distribution is determined by the Ericksen number and variations in local curvature. Finally, this work leverages curvature to amplify (suppress) LC transport through flow-aligned (homeotropic) regions emerging within channels with bends, in a programmable manner. Our results demonstrating the dependence of the dynamic flow-director coupling on the local curvature will have far-reaching ramifications in advancing the understanding of LC-based passive and active biological systems under real life geometrical constraints.

Bio-inspired microfluidics: A review

Biomicrofluidics, a subdomain of microfluidics, has been inspired by several ideas from nature. However, while the basic inspiration for the same may be drawn from the living world, the translation of all relevant essential functionalities to an artificially engineered framework does not remain trivial. Here, we review the recent progress in bio-inspired microfluidic systems via harnessing the integration of experimental and simulation tools delving into the interface of engineering and biology. Development of "on-chip" technologies as well as their multifarious applications is subsequently discussed, accompanying the relevant advancements in materials and fabrication technology. Pointers toward new directions in research, including an amalgamated fusion of data-driven modeling (such as artificial intelligence and machine learning) and physics-based paradigm, to come up with a human physiological replica on a synthetic bio-chip with due accounting of personalized features, are suggested. These are likely to facilitate physiologically replicating disease modeling on an artificially engineered biochip as well as advance drug development and screening in an expedited route with the minimization of animal and human trials.

Spatio-temporal programming of lyotropic phase transition in nanoporous microfluidic confinements

HYPOTHESIS

The nanoporous polydimethylsiloxane (PDMS) surfaces of a rectangular microfluidic channel, selectively uptakes water molecules, concentrating the solute molecules in an aqueous phase, that could drive phase transitions. Factors such as surface wettability, channel geometry, the surface-to-volume ratio, and surface topography of the confinements could play a key role in tuning the phase transitions spatio-temporally.

EXPERIMENTS

Using a lyotropic chromonic liquid crystal as model biological material, confined within nanoporous microfluidic environments, we study molecular assembly driven by nanoporous substrates. By combining timelapse polarized imaging, quantitative image processing, and a simple mathematical model, we analyze the phase transitions and construct a master diagram capturing the role of surface wettability, channel geometry and embedded topography on programmable lyotropic phase transitions.

FINDINGS

Intrinsic PDMS nanoporosity and confinement cross-section, together with the imposed wettability regulate the rate of the N-M phase transition; whereas the microfluidic geometry and embedded topography enable phase transition at targeted locations. We harness the emergent long-range order during N-M transition to actuate elasto-advective transport of embedded micro-cargo, demonstrating particle manipulation concepts governed by tunable phase transitions. Our results present a programmable physical route to material assembly in microfluidic environment, and offer a new paradigm for assembling genetic components, biological cargo, and minimal synthetic cells.

Dynamic Flow Control over Optical Properties of Liquid Crystal-Quantum Dot Hybrids in Microfluidic Devices

In this paper, we report developing approaches to tuning the optical behavior of microfluidic devices by infusing smart hybrids of liquid crystal and quantum dots into microchannel confinement. We characterize the optical responses of liquid crystal-quantum dot composites to polarized and UV light in single-phase microflows. In the range of flow velocities up to 10 mm/s, the flow modes of microfluidic devices were found to correlate with the orientation of liquid crystals, dispersion of quantum dots in homogeneous microflows and the resulting luminescence response of these dynamic systems to UV excitation. We developed a Matlab algorithm and script to quantify this correlation by performing an automated analysis of microscopy images. Such systems may have application potential as optically responsive sensing microdevices with integrated smart nanostructural components, parts of lab-on-a-chip logic circuits, or diagnostic tools for biomedical instruments.

Weak-anchoring effects in a thin pinned ridge of nematic liquid crystal

A theoretical investigation of weak-anchoring effects in a thin two-dimensional pinned static ridge of nematic liquid crystal resting on a flat solid substrate in an atmosphere of passive gas is performed. Specifically, we solve a reduced version of the general system of governing equations recently derived by Cousins et al. [Proc. R. Soc. A 478, 20210849 (2022)10.1098/rspa.2021.0849] valid for a symmetric thin ridge under the one-constant approximation of the Frank-Oseen bulk elastic energy with pinned contact lines to determine the shape of the ridge and the behavior of the director within it. Numerical investigations covering a wide range of parameter values indicate that the energetically preferred solutions can be classified in terms of the Jenkins-Barratt-Barbero-Barberi critical thickness into five qualitatively different types of solution. In particular, the theoretical results suggest that anchoring breaking occurs close to the contact lines. The theoretical predictions are supported by the results of physical experiments for a ridge of the nematic 4^{'}-pentyl-4-biphenylcarbonitrile (5CB). In particular, these experiments show that the homeotropic anchoring at the gas-nematic interface is broken close to the contact lines by the stronger rubbed planar anchoring at the nematic-substrate interface. A comparison between the experimental values of and the theoretical predictions for the effective refractive index of the ridge gives a first estimate of the anchoring strength of an interface between air and 5CB to be (9.80±1.12)×10^{-6}Nm^{-1} at a temperature of (22±1.5)^{∘}C.

Controllable particle migration in liquid crystal flows

We observe novel positional control of a colloidal particle in microchannel flow of a nematic liquid crystal. Lattice Boltzmann simulations show multiple equilibrium particle positions, the existence and position of which are tunable using the driving pressure, in direct contrast to the classical Segré-Silberberg effect in isotropic liquids. In addition, particle migration in nematic flow occurs an order of magnitude faster. These new equilibria are determined through a balance of elastic forces, hydrodynamic lift and drag as well as order-flow interactions through the defect structure around the particle.

Young and Young-Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states

Motivated by the need for greater understanding of systems that involve interfaces between a nematic liquid crystal, a solid substrate and a passive gas that include nematic–substrate–gas three-phase contact lines, we analyse a two-dimensional static ridge of nematic resting on a solid substrate in an atmosphere of passive gas. Specifically, we obtain the first complete theoretical description for this system, including nematic Young and Young–Laplace equations, and then, making the assumption that anchoring breaking occurs in regions adjacent to the contact lines, we use the nematic Young equations to determine the continuous and discontinuous transitions that occur between the equilibrium states of complete wetting, partial wetting and complete dewetting. In particular, in addition to continuous transitions analogous to those that occur in the classical case of an isotropic liquid, we find a variety of discontinuous transitions, as well as contact-angle hysteresis, and regions of parameter space in which there exist multiple partial wetting states that do not occur in the classical case.

Single-Shot Quantitative Polarization Imaging of Complex Birefringent Structure Dynamics

Polarization light microscopes are powerful tools for probing molecular order and orientation in birefringent materials. While a number of polarization microscopy techniques are available to access steady-state properties of birefringent samples, quantitative measurements of the molecular orientation dynamics on the millisecond time scale have remained a challenge. We propose polarized shearing interference microscopy (PSIM), a single-shot quantitative polarization imaging method, for extracting the retardance and orientation angle of the laser beam transmitting through optically anisotropic specimens with complex structures. The measurement accuracy and imaging performance of PSIM are validated by imaging a birefringent resolution target and a bovine tendon specimen. We demonstrate that PSIM can quantify the dynamics of a flowing lyotropic chromonic liquid crystal in a microfluidic channel at an imaging speed of 506 frames per second (only limited by the camera frame rate), with a field-of-view of up to 350 × 350 μm² and a diffraction-limit spatial resolution of ~2 μm. We envision that PSIM will find a broad range of applications in quantitative material characterization under dynamical conditions.

Lattice Boltzmann and Jones matrix calculations for the determination of the director field structure in self-propelling nematic droplets

Nematic droplets immersed in aqueous surfactant solutions can show a self-propelled motion induced by a Marangoni flow in the droplet surface. In addition to the self-propulsion, the Marangoni flow induces within the droplet a convective flow which considerably influences the nematic director field of the droplet. We report numerical simulations aiming at the determination of the director field in the self-propelling droplet. The convective flow and the resulting structure of director field are described by a lattice Boltzmann model. The reliability of the obtained structures is proved by subsequent Jones matrix calculations which enable the direct comparison of experimental polarizing microscopy images of self-propelling droplets with calculated images based on the simulated structures.

Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

New Liquid Crystal Assemblies Based on Cyano-Hydrogen Bonding Interactions

A new selection of supramolecular liquid crystal complexes based on complementary molecules formed via hydrogen-bonding interactions is reported. All prepared complexes were prepared from 4-n-alkoxybenzoic acid (An) and N-4-cyanobenzylidene-4-n-(hexyloxy)benzenamine (I). FT-IR, temperature gradient NMR, Mass Spectrometer and Chromatography spectroscopy were carried out to confirm the -CN and -COOH H-bonded complexation by observing their Fermi-bands and the effects of the 1H-NMR signals as well as its elution signal from HPLC. Moreover, binary phase diagrams were established for further confirmation. All formed complexes (I/An) were studied by the use of differential scanning calorimetry and their phase properties were validated through the use of polarized optical microscopy Results of mesomorphic characterization revealed that all presented complexes exhibited enantiotropic mesophases and their type was dependent on the terminal lengths of alkoxy chains. Also, the mesomorphic temperature ranges decreased in the order I/A6 > I/A8 > I/A10 > I/A16 with linear dependency on the chain length. Finally, the density functional theory computational modeling has been carried out to explain the experimental findings. The relation between the dimensional parameters was established to show the effect of the aspect ratio on the mesophase range and stability. The normalized entropy of the clearing transitions (∆S/R) was calculated to illustrate the molecular interaction enhancements with the chain lengths.

Directing the far-from-equilibrium assembly of nanoparticles in confined liquid crystals by hydrodynamic fields

The assembly of nematic colloids relies on long-range elastic interactions that can be manipulated through external stimuli. Confinement and the presence of a hydrodynamic field alter the defect structures and the energetic interactions between the particles. In this work, the assembly landscape of nanoparticles embedded in a nematic liquid crystal confined in a nanochannel under a pressure-driven flow is determined. The dynamics of the liquid crystal tensor alignment field is determined through a Poisson-Bracket framework, namely the Stark-Lubensky equations, coupled with the zero-Reynolds momentum equations and the liquid crystal Landau-de Gennes free energy functional. A second order semi-implicit time integration and a three-dimensional Galerkin finite element method are used to resolve flow and nematic fields under several conditions. In general, the zero Reynolds flow displaces the defects around the particles in the upstream direction and renders the surface anchoring ineffective when the flow strength dominates over the nematic elasticity. More importantly, the potential of mean force for particle assembly is non-monotonic independent of surface anchoring. Our results show that the confinement length scale determines the repulsion/attraction transition between colloids, while the flow strength modifies the static defect structure surrounding the particles and determines the magnitude of the energetic barrier for successful assembly. In the attractive regime, the particles move at different rates through the nematic until one particle eventually catches up with the other. This process occurs against or along the direction of flow depending on the flow strength. Ultimately, these results provide a template for engineering and controlling the transport and assembly of nanoparticles under far-from equilibrium conditions in anisotropic media.

Transient flow-driven distortion of a nematic liquid crystal in channel flow with dissipative weak planar anchoring

Motivated by the one-drop-filling (ODF) method for the industrial manufacturing of liquid crystal displays, we analyze the pressure-driven flow of a nematic in a channel with dissipative weak planar anchoring at the boundaries of the channel. We obtain quasisteady asymptotic solutions for the director angle and the velocity in the limit of small Leslie angle, in which case the key parameters are the Ericksen number and the anchoring strength parameter. In the limit of large Ericksen number, the solution for the director angle has narrow reorientational boundary layers and a narrow reorientational internal layer separated by two outer regions in which the director is aligned at the positive Leslie angle in the lower half of the channel and the negative Leslie angle in the upper half of the channel. On the other hand, in the limit of small Ericksen number, the solution for the director angle is dominated by splay elastic effects with viscous effects appearing at first order. As the Ericksen number varies, there is a continuous transition between these asymptotic behaviors, and in fact the two asymptotic solutions capture the behavior rather well for all values of the Ericksen number. The steady-state value of the director angle at the boundaries and the timescale of the evolution toward this steady-state value in the asymptotic limits of large and small Ericksen number are determined. In particular, using estimated parameter values for the ODF method, it is found that the boundary director rotation timescale is substantially shorter than the timescale of the ODF method, suggesting that there is sufficient time for significant transient flow-driven distortion of the nematic molecules at the substrates from their required orientation to occur.

Novel optofluidic concepts enabled by topological microfluidics-INVITED

The coupling between flow and director orientation of liquid crystals (LCs) has been long utilized to devise wide-ranging applications spanning modern displays, medical and environmental solutions, and bio-inspired designs and applications. LC-based optofluidic platforms offer a non-invasive handle to modulate light and material fields, both locally and dynamically. The flow-driven reorientation of the LC molecules can tailor distinct optical and mechanical responses in microfluidic confinements, and harness the coupling therein. Yet the synergy between traditional optofluidics with isotropic fluids and LC microfluidics remains at its infancy. Here, we discuss emerging optofluidic concepts based on Topological Microfluidics, leveraging microfluidic control of topological defects and defect landscapes. With a specific focus on the role of surface anchoring and microfluidic geometry, we present recent and ongoing works that harness flow-controlled director and defect configurations to modulate optical fields. The flow-induced optical attributes, and the corresponding feedback, is enhanced in the vicinity of the topological defects which geenerate distinct isotropic opto-material properties within an anisotropic matrix. By harnessing the rich interplay of confining geometry, anchoring and micro-scale nematodynamics, topological microfluidics offers a promising platform to ideate the next generation of optofluidic and optomechnical concepts.

Time Dependent Lyotropic Chromonic Textures in Microfluidic Confinements

Nematic and columnar phases of lyotropic chromonic liquid crystals (LCLCs) have been long studied for their fundamental and applied prospects in material science and medical diagnostics. LCLC phases represent different self-assembled states of disc-shaped molecules, held together by noncovalent interactions that lead to highly sensitive concentration and temperature dependent properties. Yet, microscale insights into confined LCLCs, specifically in the context of confinement geometry and surface properties, are lacking. Here, we report the emergence of time dependent textures in static disodium cromoglycate (DSCG) solutions, confined in PDMS-based microfluidic devices. We use a combination of soft lithography, surface characterization, and polarized optical imaging to generate and analyze the confinement-induced LCLC textures and demonstrate that over time, herringbone and spherulite textures emerge due to spontaneous nematic (N) to columnar M-phase transition, propagating from the LCLC-PDMS interface into the LCLC bulk. By varying the confinement geometry, anchoring conditions, and the initial DSCG concentration, we can systematically tune the temporal dynamics of the N- to M-phase transition and textural behavior of the confined LCLC. Overall, the time taken to change from nematic to the characteristic M-phase textures decreased as the confinement aspect ratio (width/depth) increased. For a given aspect ratio, the transition to the M-phase was generally faster in degenerate planar confinements, relative to the transition in homeotropic confinements. Since the static molecular states register the initial conditions for LC flows, the time dependent textures reported here suggest that the surface and confinement effects—even under static conditions—could be central in understanding the flow behavior of LCLCs and the associated transport properties of this versatile material.

Investigation of Shear-Driven and Pressure-Driven Liquid Crystal Flow at Microscale: A Quantitative Approach for the Flow Measurement

The liquid crystal-based method is a new technology developed for flow visualizations and measurements at microscale with great potentials. It is the priority to study the flow characteristics before implementation of such a technology. A numerical analysis has been applied to solve the simplified dimensionless two-dimensional Leslie-Ericksen liquid crystal dynamic equation. This allows us to analyze the coupling effect of the LC's director orientation and flow field. We will be discussing two classic shear flow cases at microscale, namely Couette and Poiseuille flow. In both cases, the plate drag speed in the state of Couette flow are varied as well as the pressure gradients in Poiseuille flow state are changed to study their effects on the flow field distributions. In Poiseuille flow, with the increase of applied pressure gradient, the influence of backflow significantly affects the flow field. Results show that the proposed method has great advantages on measurement near the wall boundaries which could complement to the current adopted flow measurement technique. The mathematical model proposed in this article could be of great potentials in the development of the quantitatively flow measurement technology.

Flow-induced order-order transitions in amyloid fibril liquid crystalline tactoids

Liquid crystalline droplets, also known as tactoids, forming by nucleation and growth within the phase diagram region where isotropic and nematic phases coexist, challenge our understanding of liquid crystals under confinement due to anisotropic surface boundaries at vanishingly small interfacial tension, resulting in complex, non-spherical shapes. Little is known about their dynamical properties, since they are mostly studied under quiescent, quasi-equilibrium conditions. Here we show that different classes of amyloid based nematic and cholesteric tactoids undergo order–order transitions by flow-induced deformations of their shape. Tactoids align under extensional flow, undergoing extreme deformation into highly elongated prolate shapes, with the cholesteric pitch decreasing as an inverse power-law of the tactoids aspect ratio. Free energy functional theory and experimental measurements are combined to rationalize the critical elongation above which the director-field configuration of tactoids transforms from bipolar and uniaxial cholesteric to homogenous and to debate on the thermodynamic nature of these transitions.

Tactoids are liquid crystal droplets with nearly vanishing interfacial tension. Almohammadi et al. show using a microfluidic focusing device how to manipulate them gently enough to facilitate the study of amyloid liquid crystal phase transitions subject to non-equilibirum forcing and shape changes.

Polarization holographic microscope slide for birefringence imaging of anisotropic samples in microfluidics

Birefringence is an important optical property of anisotropic materials arising from anisotropies of tissue microstructures. Birefringence parameters have been found to be important to understand optical anisotropic architecture of many materials and polarization imaging has been applied in many researches in the field of biology and medicine. Here, we propose a scheme to miniaturize a double-channel polarization holographic interferometer optics to create a polarization holographic microscope slide (P-HMS) suitable for integrating with microfluidic lab-on-a-chip (LoC) systems. Based on the P-HMS combined with a simple reconstruction algorithm described in the paper, we can not only simultaneously realize holographic imaging of two orthogonal polarization components of dynamic samples in a microfluidic channel but also quantitative measurement of 2D birefringence information, both including the birefringence phase retardation and optic-axis orientation. This chip interferometer allows for off-axis double-channel polarization digital holographic recording using only a single illumination beam without need of any beam splitter or mirror. Its quasi-common path configuration and self-aligned design also make it tolerant to vibrations and misalignment. This work about the P-HMS could play a positive role in promoting the application of birefringence imaging in microfluidic LoC technology.

Binary Liquid Crystal Mixtures Based on Schiff Base Derivatives with Oriented Lateral Substituents

Binary mixtures of the laterally substituted Schiff base/ester derivatives, namely 4-((2- or 3-) substituted phenyl imino methyl) phenyl-4”-alkoxy benzoates, Ia–d, were prepared and mesomorphically studied by differential scanning calorimetry (DSC) and their mesophases identified by polarized optical microscopy (POM). The lateral group (1-naphthyl, 2-F, 2-Br, 3-F in Ia–d, respectively) is attached to different positions of the phenyl Schiff moiety. The mixtures investigated were made from two differently shaped compounds that differ from each other in the polarity, size, orientation, and relative positions of the lateral group. The results revealed that the binary mixture Ia/Ib (bearing the naphthyl and 2-flouro substituents) exhibited the SmA phase, which covered the whole composition range. For the mixtures Ib/Id (2-F and 2-Br), the isomeric lateral F-group in compound Ib distributed the SmA arrangement of Id. In the Ic/Id mixture bearing two positionally and structurally different substituents, the addition of Ic to Id resulted in solid binary mixtures where its behavior may be attributed to the negligible steric effect of the small electronegative fluorine atom compared to the Br atom. Density functional theory (DFT) theoretical calculations were carried out to estimate the geometrical parameters of individual components and to show the effect of these parameters in the mesophase behavior of the binary system, where the higher dipole moment of Id (6 Debye) may be the reason for its high π–π molecular stacking, which influences its mesophase range and stability.

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. We characterize the mechanisms underlying the transition and construct a phenomenological model to describe the critical behaviour and the phase diagram of the observed chiral flow state, and evaluate the effect of a forced symmetry breaking by introduction of a chiral dopant. Finally, we induce transitions on demand through channel geometry, application of laser tweezers, and careful control of the flow rate.

It is interesting phenomenon that chiral order can emerge in intrinsically achiral liquid crystals. Here Čopar et al. demonstrate achiral-to-chiral transition of the nematic liquid crystals flow in microfluidic channels and their behaviour, stability, and dependence on geometric and material parameters.

Active nematic-isotropic interfaces in channels

We use numerical simulations to investigate the hydrodynamic behavior of the interface between nematic (N) and isotropic (I) phases of a confined active liquid crystal. At low activities, a stable interface with constant shape and velocity is observed separating the two phases. For nematics in homeotropic channels, the velocity of the interface at the NI transition increases from zero (i) linearly with the activity for contractile systems and (ii) quadratically for extensile ones. Interestingly, the nematic phase expands for contractile systems while it contracts for extensile ones, as a result of the active forces at the interface. Since both activity and temperature affect the stability of the nematic, for active nematics in the stable regime the temperature can be tuned to observe static interfaces, providing an operational definition for the coexistence of active nematic and isotropic phases. At higher activities, beyond the stable regime, an interfacial instability is observed for extensile nematics. In this regime defects are nucleated at the interface and move away from it. The dynamics of these defects is regular and persists asymptotically for a finite range of activities. We used an improved hybrid model of finite differences and the lattice Boltzmann method with a multi-relaxation-time collision operator, the accuracy of which allowed us to characterize the dynamics of the distinct interfacial regimes.

Multiparticle collision dynamics for tensorial nematodynamics

Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this variety of dynamics. We have generalized the particle-based multiparticle collision dynamics (MPCD) method to model the dynamics of nematic liquid crystals. Following the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)1063-651X10.1103/PhysRevE.58.7475] of nematics, the spatial and temporal variations of the nematic director field and order parameter are described by a tensor order parameter. The key idea is to assign tensorial degrees of freedom to each MPCD particle, whose mesoscopic average is the tensor order parameter. This nematic MPCD method includes backflow effect, velocity-orientation coupling, and thermal fluctuations. We validate the applicability of this method by testing (i) the nematic-isotropic phase transition, (ii) the flow alignment of the director in shear and Poiseuille flows, and (iii) the annihilation dynamics of a pair of line defects. We find excellent agreement with existing literature. We also investigate the flow field around a force dipole in a nematic liquid crystal, which represents the leading-order flow field around a force-free microswimmer. The anisotropy of the medium not only affects the magnitude of velocity field around the force dipole, but can also induce hydrodynamic torques depending on the orientation of dipole axis relative to director field. A force dipole experiences a hydrodynamic torque when the dipole axis is tilted with respect to the far-field director. The direction of hydrodynamic torque is such that the pusher- (or puller-) type force dipole tends to orient along (or perpendicular to) the director field. Our nematic MPCD method can have far-reaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium.

Flow-driven disclination lines of nematic liquid crystals inside a rectangular microchannel

For nematic liquid crystals (LCs), a disclination line is formed when the director of the LCs changes abruptly. In this study, we demonstrate an approach to form dynamic disclination lines by flowing the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) in rectangular microchannels with a large aspect ratio. The dynamic disclination line moves gradually from the side toward the centre of the microchannel when the Ericksen number reaches 8.5. At the critical Ericksen number, influence of the anchoring energy on the side wall extends to the centre of the microchannel and determines the final position of the dynamic disclination line. As a result, the orientation of the LC is influenced by surface defects of the side wall. This phenomenon can be used to detect minute surface defects on the side wall and is potentially useful for visual sensing applications that require high sensitivity.

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. Experiments, theory, and simulations indicate that the resulting structures can be stabilized indefinitely, provided the liquids are maintained in a controlled nonequilibrium state. The resulting sculpted liquids could find applications in microfluidic devices for selective encapsulation of solutes and particles into optically active compartments that interact with external stimuli.

Nematohydrodynamics for colloidal self-assembly and transport phenomena

HYPOTHESIS

Colloidal particles in a nematic liquid crystal (NLC) exhibit very different behaviour to that observed in an isotropic medium. Such differences arise principally due to the nematic-induced elastic stresses exerted due to the interaction of NLC molecules with interfaces, which compete with traditional fluid viscous stresses on the particle.

THEORY

A systematic mathematical analysis of particles in an NLC microfluidic channel is performed using the continuum Beris-Edwards framework coupled to the Navier-Stokes equations. We impose strong homeotropic anchoring on the channel walls and weak homeotropic anchoring on the particle surfaces.

FINDINGS

The viscous and NLC forces act on an individual particle in opposing directions, resulting in a critical location in the channel where the particle experiences zero net force in the direction perpendicular to the flow. For multi-particle aggregation we show that the final arrangement is independent of the initial configuration, but the path towards achieving equilibrium is very different. These results uncover new mechanisms for particle separation and routes towards self-assembly.

Multi-Scale Responses of Liquid Crystals Triggered by Interfacial Assemblies of Cleavable Homopolymers

Liquid crystals (LCs) offer the basis of stimuli-responsive materials that can amplify targeted molecular events into macroscopic outputs. However, general and versatile design principles are needed to realize the full potential of these materials. To this end, we report the synthesis of two homopolymers with mesogenic side chains that can be cleaved upon exposure to either H₂ O₂ (polymer P1) or UV light (polymer P2). Optical measurements reveal that the polymers dissolve in bulk LC and spontaneously assemble at nematic LC-aqueous interfaces to impose a perpendicular orientation on the LCs. Subsequent addition of H₂ O₂ to the aqueous phase or exposure of the LC to UV was shown to trigger a surface-driven ordering transition to a planar orientation and an accompanying macroscopic optical output. Differences in the dynamics of the response to each stimulus are consistent with sequential processing of P1 at the LC-aqueous interface (H₂ O₂ ) and simultaneous transformation of P2 within the LC (UV). The versatility of the approach is demonstrated by creating stimuli-responsive LCs as films or microdroplets, and by dissolving mixtures of P1 and P2 into LCs to create LC materials that respond to two stimuli. Overall, our results validate a simple and generalizable approach to the rational design of polymers that can be used to program stimuli-responsiveness into LC materials.

Shear-Induced Alignment of Anisotropic Nanoparticles in a Single-Droplet Oscillatory Microfluidic Platform

Flow-induced alignment of shape-anisotropic colloidal particles is of great importance in fundamental research and in the fabrication of structurally anisotropic materials; however, rheo-optical studies of shear-induced particle orientation are time- and labor-intensive and require complicated experimental setups. We report a single-droplet oscillatory microfluidic strategy integrated with in-line polarized light imaging as a strategy for studies of shear-induced alignment of rod-shape nanoparticles. Using an oscillating droplet of an aqueous isotropic suspension of cellulose nanocrystals (CNCs), we explore the effect of the shear rate and suspension viscosity on the flow-induced CNC alignment and subsequent relaxation to the isotropic state. The proposed microfluidic strategy enables high-throughput studies of shear-induced orientations in structured liquid under precisely controlled experimental conditions. The results of such studies can be used in the development of structure-anisotropic materials.

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. Specifically, we generate hydrodynamic stagnation points of different topological charges at the center of star-shaped microfluidic junctions, which then interact with emergent topological defects in the orientational field of the nematic director. We combine experiments and analytical and numerical calculations to show that a hydrodynamic singularity of a given topological charge can nucleate a nematic defect of equal topological charge and corroborate this by creating [Formula: see text], [Formula: see text], and [Formula: see text] topological defects in four-, six-, and eight-arm junctions. Our work is an attempt toward understanding materials that are governed by distinctly multifield topology, where disparate topology-carrying fields are coupled and concertedly determine the material properties and response.

Liquid crystals in micron-scale droplets, shells and fibers

The extraordinary responsiveness and large diversity of self-assembled structures of liquid crystals are well documented and they have been extensively used in devices like displays. For long, this application route strongly influenced academic research, which frequently focused on the performance of liquid crystals in display-like geometries, typically between flat, rigid substrates of glass or similar solids. Today a new trend is clearly visible, where liquid crystals confined within curved, often soft and flexible, interfaces are in focus. Innovation in microfluidic technology has opened for high-throughput production of liquid crystal droplets or shells with exquisite monodispersity, and modern characterization methods allow detailed analysis of complex director arrangements. The introduction of electrospinning in liquid crystal research has enabled encapsulation in optically transparent polymeric cylinders with very small radius, allowing studies of confinement effects that were not easily accessible before. It also opened the prospect of functionalizing textile fibers with liquid crystals in the core, triggering activities that target wearable devices with true textile form factor for seamless integration in clothing. Together, these developments have brought issues center stage that might previously have been considered esoteric, like the interaction of topological defects on spherical surfaces, saddle-splay curvature-induced spontaneous chiral symmetry breaking, or the non-trivial shape changes of curved liquid crystal elastomers with non-uniform director fields that undergo a phase transition to an isotropic state. The new research thrusts are motivated equally by the intriguing soft matter physics showcased by liquid crystals in these unconventional geometries, and by the many novel application opportunities that arise when we can reproducibly manufacture these systems on a commercial scale. This review attempts to summarize the current understanding of liquid crystals in spherical and cylindrical geometry, the state of the art of producing such samples, as well as the perspectives for innovative applications that have been put forward.

Optothermally driven colloidal transport in a confined nematic liquid crystal

We demonstrate transport of microparticles by rapid movement of a laser spot in a thin layer of a nematic liquid crystal. The transport is achieved by fluid flow, caused by two different mechanisms. The thermoviscous expansion effect induces colloidal transport in the direction opposite to the laser movement, whereas thermally induced local melting of the liquid crystal pulls the particles in the direction of the laser movement. We demonstrate control of colloidal transport by changing the speed of the laser trap movement and the laser power. We anticipate that complex optofluidic colloidal transport could be realized in the nematic liquid crystal using a channel-free optofluidic approach.

Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring

Liquid crystals (LCs) display many of the flow characteristics of liquids but exhibit long range orientational order. In the nematic phase, the coupling of structure and flow leads to complex hydrodynamic effects that remain to be fully elucidated. Here, we consider the hydrodynamics of a nematic LC in a hybrid cell, where opposite walls have conflicting anchoring boundary conditions, and we employ a 3D lattice Boltzmann method to simulate the time-dependent flow patterns that can arise. Due to the symmetry breaking of the director field within the hybrid cell, we observe that at low to moderate shear rates, the volumetric flow rate under Couette and Poiseuille flows is different for opposite flow directions. At high shear rates, the director field may undergo a topological transition which leads to symmetric flows. By applying an oscillatory pressure gradient to the channel, a net volumetric flow rate is found to depend on the magnitude and frequency of the oscillation, as well as the anchoring strength. Taken together, our findings suggest several intriguing new applications for LCs in microfluidic devices.

Connecting and disconnecting nematic disclination lines in microfluidic channels

Disclination lines in nematic liquid crystals can be used as "soft rails" for the transport of colloids or droplets through microfluidic channels [A. Sengupta, C. Bahr and S. Herminghaus, Soft Matter, 2013, 9, 7251]. In the present study we report on a method to connect and disconnect disclination lines in microfluidic channels using the interplay between anchoring, flow, and electric field. We show that the application of an electric field establishes a continuous disclination that spans across a channel region in which a disclination usually would not exist (because of different anchoring conditions), demonstrating an interruptible and reconnectable soft rail for colloidal transport.

Tunable optofluidic birefringent lens

An optofluidic birefringent lens is demonstrated using hydrodynamic liquid-liquid (L(2)) interfaces in a microchannel. The L(2) lens comprises a nematic liquid crystal (NLC) phase and an optically isotropic phase for the main stream and the surrounding sub-stream, respectively. When the optofluidic device is subjected to a sufficiently strong electric field perpendicular to the flow direction, NLCs are allowed to orient along the external field rather than the flow direction overcoming fluidic viscous stress. The characteristics of the optofluidic birefringence lens are investigated by experimental and numerical analyses. The difference between the refractive indices of the main stream and the sub-stream changes according to the polarization direction of incident light, which determines the optical behaviour of the lens. The incidence of s-polarized light leads to a short focal point, while p-polarized light has a relatively long focal distance from the same L(2) interface. The curvatures and focal lengths of the lens are successfully evaluated by a hydrodynamic theory of NLCs and a simple ray-tracing model.

Nonequilibrium quasi-long-range order of a driven random-field O(N) model

We investigate three-dimensional O(N) spin models driven with a uniform velocity over a random field. Within a spin-wave approximation, it is shown that in the strong driving regime the model with N=2 exhibits a quasi-long-range order in which the spatial correlation function decays in a power-law form. Furthermore, for the cases that N=2 and 3, we numerically demonstrate a nonequilibrium phase transition between the quasi-long-range order phase and the disordered phase, which turns out to resemble the Kosterlitz-Thouless transition in the two-dimensional pure XY model in equilibrium.

Nematic liquid crystals confined in microcapillaries for imaging phenomena at liquid-liquid interfaces

Here, we report the development of an experimental system based on liquid crystals (LCs) confined in microcapillaries for imaging interfacial phenomena. The inner surfaces of the microcapillaries were modified with octadecyltrichlorosilane to promote an escaped-radial configuration of LCs. We checked the optical appearance of the capillary-confined LCs under a crossed polarizing microscope and determined their arrangement based on side and top views. We then placed the capillary-confined LCs in contact with non-surfactant and surfactant solutions, producing characteristic textures of two bright lines and a four-petal shape, respectively. We also evaluated the sensitivity, stability, and reusability of the system. Our imaging system was more sensitive than previously reported LC thin film systems. The textures formed in microcapillaries were stable for more than 120 h and the capillaries could be reused at least 10 times. Finally, we successfully applied our system to image the interactions of phospholipids and bivalent metal ions. In summary, we developed a simple, small, portable, sensitive, stable, and reusable experimental system that can be broadly applied to monitor liquid-liquid interfacial phenomena. These results provide valuable information for designs using confined LCs as chemoresponsive materials in optical sensors.

The effect of anchoring on the nematic flow in channels

Understanding the flow of liquid crystals in microfluidic environments plays an important role in many fields, including device design and microbiology. We perform hybrid lattice-Boltzmann simulations of a nematic liquid crystal flowing under an applied pressure gradient in two-dimensional channels with various anchoring boundary conditions at the substrate walls. We investigate the relationship between the flow rate and the pressure gradient and the corresponding profile of the nematic director, and find significant departures from the linear Poiseuille relationship. We also identify a morphological transition in the director profile and explain this in terms of an instability in the dynamical equations. We examine the qualitative and quantitative effects of changing the type and strength of the anchoring. Understanding such effects may provide a useful means of quantifying the anchoring of a substrate by measuring its flow properties.

Liquid Crystal Foams Generated by Pressure-Driven Microfluidic Devices

Thermotropic liquid crystals possess superior foaming capability without the aid of surfactants because of the anisotropic molecular structures. We developed a T-junction microfluidic device to inject gas bubbles of uniform size into a liquid crystal in the nematic and the smectic phases. The bubble size is primarily determined by the dimension of microfluidic channel regardless of the phase, and air bubbles of a few tens of micrometer diameter were stably injected at the rate up to 110 Hz to the close packing density with a polydispersity less than 4%. It is shown that an efficient path to fabricate stable liquid crystal foams is to inject bubbles in the nematic phase, where the highest injection rate is possible, and promptly cool it down to the smectic phase.

Nematic director reorientation at solid and liquid interfaces under flow: SAXS studies in a microfluidic device

In this work we investigate the interplay between flow and boundary condition effects on the orientation field of a thermotropic nematic liquid crystal under flow and confinement in a microfluidic device. Two types of experiments were performed using synchrotron small-angle X-ray-scattering (SAXS). In the first, a nematic liquid crystal flows through a square-channel cross section at varying flow rates, while the nematic director orientation projected onto the velocity/velocity gradient plane is measured using a 2D detector. At moderate-to-high flow rates, the nematic director is predominantly aligned in the flow direction, but with a small tilt angle of ∼±11° in the velocity gradient direction. The director tilt angle is constant throughout most of the channel width but switches sign when crossing the center of the channel, in agreement with the Ericksen-Leslie-Parodi (ELP) theory. At low flow rates, boundary conditions begin to dominate, and a flow profile resembling the escaped radial director configuration is observed, where the director is seen to vary more smoothly from the edges (with homeotropic alignment) to the center of the channel. In the second experiment, hydrodynamic focusing is employed to confine the nematic phase into a sheet of liquid sandwiched between two layers of Triton X-100 aqueous solutions. The average nematic director orientation shifts to some extent from the flow direction toward the liquid boundaries, although it remains unclear if one tilt angle is dominant through most of the nematic sheet (with abrupt jumps near the boundaries) or if the tilt angle varies smoothly between two extreme values (∼90 and 0°). The technique presented here could be applied to perform high-throughput measurements for assessing the influence of different surfactants on the orientation of nematic phases and may lead to further improvements in areas such as boundary lubrication and clarifying the nature of defect structures in LC displays.

Effects of flow on topological defects in a nematic liquid crystal near a colloid

We perform molecular dynamics simulations of a nematic liquid crystal flowing around a colloidal particle. We study the flow-induced modifications of the topological defects in the liquid crystal due to the presence of the colloid. We show that flow distorts Boojum defects into an asymmetrically larger downstream lobe, and that Saturn ring defects are convected downstream along the flow direction, which is in agreement with experimental observations. Additionally, for a Janus colloid with both parallel and perpendicular patches, exhibiting a Boojum defect and a Saturn ring defect, we find that the Boojum defect facing the upstream direction is destroyed and the Saturn ring is convected downstream.