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We present numerical simulations of a particle trapped at the isotropic-nematic liquid crystal (Iso-N) interface. We use our recent model, based on a phase-field approach [see Qiu et al., Phys. Rev. E 103, 022706 (2021)10.1103/PhysRevE.103.022706], to couple the capillary forces acting on the interface with the elastic stresses in the nematic phase along with topological defects. A range of floating configurations are first investigated as a function of the contact angle and various anchoring conditions at the fluid interface. The results show that the response of the system is driven by the existence of an anchoring conflict at the contact line. Substantial particle displacements and/or interfacial deformations may occur in this case even for moderate anchoring strengths. These findings highlight the coupling between elastic and capillary forces. In a second part, we compute drag forces exerted on a particle that moves along the Iso-N interface for several contact angles and a moderate Ericksen number. Because of the coupling between the velocity and order parameter fields, topological defects are swept downstream of the particle by the flow and sometimes escape from the particle or merge with the interface. We also find linear force-velocity laws, with drag forces at the Iso-N interface being slightly greater than their isotropic counterparts due to director distortions. We discuss these results in light of past studies on the behavior of particles being dragged in the bulk of a liquid crystal matrix.

International audience; We use dynamic numerical simulations to investigate the role of particle rotation in pairwise capillary interactions of particles trapped at a fluid interface. The fluid interface is modeled with a phase-field method which is coupled to the Navier-Stokes equations to solve for the flow dynamics. Numerical solutions are found using a finite element scheme in a bounded two-dimensional geometry. The interfacial deformations are caused by the buoyant weight of the particles, which are allowed to both translate and rotate due to the capillary and viscous forces and torques at play. The results show that the capillary attraction is faster between freely rotating particles than if particle rotation is inhibited, and the higher the viscosity mismatch, the greater the effect. To explain this result, we analyze the drag force exerted on the particles and find that the translational drag force on a rotating particle is always less than its non-rotating counterpart due to attenuated velocity gradients in the vicinity of the particle. We also find that the influence of interfacial deformations on particle rotation is minute.

Extremely small amounts of surface-active contaminants are known to drastically modify the hydrodynamic response of the water-air interface. Surfactant concentrations as low as a few thousand molecules per square micron are sufficient to eventually induce complete stiffening. In order to probe the shear response of a water-air interface, we design a radial flow experiment that consists in an upward water jet directed to the interface. We observe that the standard no-slip effect is often circumvented by an azimuthal instability with the occurence of a vortex pair. Supported by numerical simulations, we highlight that the instability occurs in the (inertia-less) Stokes regime and is driven by surfactant advection by the flow. The latter mechanism is suggested as a general feature in a wide variety of reported and yet unexplained observations.

We use dynamic numerical simulations to investigate the role of particle rotation in pairwise capillary interactions of particles trapped at a fluid interface. The fluid interface is modeled with a phase-field method which is coupled to the Navier-Stokes equations to solve for the flow dynamics. Numerical solutions are found using a finite element scheme in a bounded two-dimensional geometry. The interfacial deformations are caused by the buoyant weight of the particles, which are allowed to both translate and rotate due to the capillary and viscous forces and torques at play. The results show that the capillary attraction is faster between freely rotating particles than if particle rotation is inhibited, and the higher the viscosity mismatch, the greater the effect. To explain this result, we analyze the drag force exerted on the particles and find that the translational drag force on a rotating particle is always less than its non-rotating counterpart due to attenuated velocity gradients in the vicinity of the particle. We also find that the influence of interfacial deformations on particle rotation is minute.

WOS:000401378800010; International audience; The two-beam levitator (TBL) is a standard optical setup made of a couple of counter-propagating beams. Note worthily, TBLs allow the manipulation and trapping of particles at long working distances. While much experience has been accumulated in the trapping of single spherical particles in TBIs, the behaviors of asymmetrical particles turn out to be more complex, and even surprising. Here, we report observations with prolate ellipsoidal polystyrene particles, with varying aspect ratio and ratio of the two beam powers. Generalizing the earlier work by Mihiretie et al. in single beam geometries [JQSRT 126, 61 (2013)], we observe that particles may be either static, or permanently oscillating, and that the two-beam geometry produces new particle responses: some of them are static, but non-symmetrical, while others correspond to new types of oscillations. A two-dimensional model based on ray-optics qualitatively accounts for these configurations and for the "primary" oscillations of the particles. Furthermore, levitation powers measured in the experiments are in fair agreement with those computed from GLMT (Generalized Lorentz Mie Theory), MLFMA (Multilevel Fast Multipole Algorithm) and approximate ray-optics methods. (C) 2017 Elsevier Ltd. All rights reserved.

International audience; We numerically investigate the influence of interfacial deformations on the drag force exerted on a particle straddling a fluid interface. We perform finite element simulations of the two-phase flow system in a bounded two-dimensional geometry. The fluid interface is modeled with a phase-field method which is coupled to the Navier-Stokes equations to solve for the flow dynamics. The interfacial deformations are caused by the buoyant weight of the particle, which results in curved menisci. We compute drag coefficients as a function of the three-phase contact angle, the viscosity ratio of the two fluids, and the particle density. Our results show that, for some parameter values, large drag forces are not necessarily correlated with large interfacial distortions and that a lower drag may actually be achieved with non-flat interfaces rather than with unperturbed ones.

International audience; We study the features of a radial Stokes flow due to a submerged jet directed toward a liquid-air interface. The presence of surface-active impurities confers to the interface an in-plane elasticity that resists the incident flow. Both analytical and numerical calculations show that a minute amount of surfactants is enough to profoundly alter the morphology of the flow. The hydrodynamic response of the interface is affected as well, shifting from slip to no-slip boundary condition as the surface compressibility decreases. We argue that the competition between the divergent outward flow and the elastic response of the interface may actually be used as a practical way to detect and quantify a small amount of impurities.

International audience; We investigate the radial thermocapillary flow driven by a laser-heated microbead in partial wetting at the water-air interface. Particular attention is paid to the evolution of the convective flow patterns surrounding the hot sphere as the latter is increasingly heated. The flow morphology is nearly axisymmetric at low laser power P. Increasing P leads to symmetry breaking with the onset of counter-rotating vortex pairs. The boundary condition at the interface, close to no-slip in the low-P regime, turns about stress-free between the vortex pairs in the high-P regime. These observations strongly support the view that surface-active impurities are inevitably adsorbed on the water surface where they form an elastic layer. The onset of vortex pairs is the signature of a hydrodynamic instability in the layer response to the centrifugal forced flow. Interestingly, our study paves the way for the design of active colloids able to achieve high-speed self-propulsion via vortex pair generation at a liquid interface.

International audience; We briefly report experimental observations of striped patterns in the menisci of free-standing smectic C films. The results were obtained with a mesogenic compound that transits directly from the nematic phase to the smectic C phase, without an intermediate smectic A phase. In this case, it is shown that stripes do not correspond to undulations of the smectic free surface and smectic layers, as was indeed evidenced in previous studies with other compounds and different phasesequences. Hence, our results show that the nature of striped patterns in free-standing films depends on the phase sequence of the considered materials. Further experimental and theoretical works are still required to fully elucidate the physical mechanisms that drive the onset of patterns in such systems

We report an experimental investigation of the structure of periodic patterns observed in the meniscus of free-standing smectic films. Combination of polarizing optical microscopy and phase shifting interferometry enabled us to obtain new information on the structure of the meniscus, and in particular, on the topography of the smectic-air interface. We investigate the profile of the undulations in the striped structure in the thin part of the meniscus, change of the stripe period with the meniscus thickness and subsequent transition into a two-dimensional structure. It is shown that the two-dimensional structure has an unusual complex profile of "egg-box" type. The striped texture occurs upon cooling from the nontilted smectic-A to the smectic-C* phase, whereas the two-dimensional pattern is present in both phases. We discuss the possible origin of the modulated structures, the role of the dislocations in the meniscus, the elasticity of smectic layers, and the mechanical stress induced by dislocations.

We present experiments and numerical simulations to investigate the collective behavior of submicrometer-sized particles immersed in a nematic micellar solution. We use latex spheres with diameters ranging from 190 to 780 nm and study their aggregation properties due to the interplay of the various colloidal forces at work in the system. We found that the morphology of aggregates strongly depends on the particle size, with evidence for two distinct regimes: the biggest inclusions clump together within minutes into either compact clusters or V-like structures that are completely consistent with attractive elastic interactions. On the contrary, the smallest particles form chains elongated along the nematic axis, within comparable timescales. In this regime, Monte Carlo simulations, based on a modified diffusion-limited cluster aggregation model, strongly suggest that the anisotropic rotational Brownian motion of the clusters combined with short-range depletion interactions dominate the system coarsening; elastic interactions no longer prevail. The simulations reproduce the sharp transition between the two regimes on increasing the particle size. We provide reasonable estimates to interpret our data and propose a likely scenario for colloidal aggregation. These results emphasize the growing importance of the diffusion of species at suboptical-wavelength scales and raise a number of fundamental issues.

8 pages; International audience; Radiation pressure forces from a moderately focused vertical laser beam are used to levitate transparent particles, a few micrometers in size. Having recalled basic results about levitation of spheres, and applications to long-working distance trapping, we turn to ellipsoid-shaped particles. Experiments are carried out with polystyrene particles, inside a glass chamber filled with water. The particles are lifted up to contact with the chamber top surface. We examine particle equilibrium in such conditions and show that the system ''bifurcates'' between static on-axis equilibrium with short ellipsoids, to sustained oscillations with longer ones. A similar Hopf bifurcation is found using a simple ray-optics model of the laser-ellipsoid interaction, providing a qualitative account of the observed oscillations.

International audience; A micrometer-sized spherical particle classically equilibrates at the water?air interface in partial wetting configuration, causing about no deformation to the interface. In condition of thermal equilibrium, the particle just undergoes faint Brownian motion, well visible under a microscope. We report experimental observations when the particle is made of a light-absorbing material and is heated up by a vertical laser beam. We show that, at small laser power, the particle is trapped in on-axis configuration, similarly to 2-dimensional trapping of a transparent sphere by optical forces. Conversely, on-axis trapping becomes unstable at higher power. The particle escapes off the laser axis and starts orbiting around the axis. We show that the laser-heated particle behaves as a microswimmer with velocities on the order of several 100 ?m/s with just a few milliwatts of laser power.

This article reviews recent findings on the formation of ordered colloidal structures from bulk demixing in liquid crystalline materials. In contrast to classical phase separations, which lead to randomly distributed macrodomains of various sizes, demixing in liquid crystals leads to remarkably uniform droplets that form ordered arrays of either infinitely long straight chains (nematic phase) or highly curved chains (cholesteric phase). This distinctive behaviour arises from the presence of topological defects and elastic distortions around the inclusions formed during the separation. These distortions induce long‐range attractions and short‐range repulsions. These forces direct the ordering of microdomains and stabilize them against coalescence, thereby limiting the coarsening mechanism of the separation. We show that the ordering can be controlled on a large scale by simply controlling the macroscopic alignment of the liquid crystal. We also discuss the influence of an electric field and demonstrate mar...

This experimental paper deals with phase separations of binary mixtures composed of a continuous liquid crystal phase and an isotropic dispersed phase. In contrast to isotropic binary mixtures, the investigated mixtures do not lead to a full phase separation but to a self-ordering of colloidal particles, as reported earlier (Loudet, J. C. et al. Nature 2000, 407, 611). We present here further aspects of such phase separations which include the kinetics of the phase separation, the origin of the formation of dislocation-like patterns, the influence of surfactants, chiral additives, and temperature on the formed colloidal structures. The present results show that (i) the dislocations in chain arrays can be seen as kinetically frozen defects, (ii) temperature can be used to control the size of the domains formed upon demixing, (iii) a slight change in surface chemistry, via the addition of surfactants, profoundly alters the formed colloidal structures, and (iv) chiral additives allow the formation of unique helical pearl chains which reflect the symmetry of the liquid crystal phase they are embedded in.

We study experimentally the dynamics of a topological defect located around a colloidal particle suspended in a thermotropic nematic liquid crystal. The considered defect consists of a disclination loop encircling the particle at the equator. Under specific conditions, it is shown that this disclination continuously shrinks to a hedgehog defect located in the immediate vicinity of the particle. This phenomenon corresponds to a transition between an elastic quadrupolar configuration and an elastic dipolar configuration. We performed a basic numerical calculation to get an estimate of the dissipated energy during the transition; we compare the results with theoretical predictions that describe the elastic energy of particles surrounded by defects.

We review recent findings about the behavior of emulsions made of droplets suspended in liquid crystalline materials. By contrast to classical emulsions, which are usually made of isotropic oils and water, liquid crystal emulsions exhibit a variety of structures result in the ordering of the continuous phase. The droplets induce the formation of topological defects and distortions that lead to strong and anisotropic elastic forces between the particles. These elastic forces govern the stability and the ordering of the particles. This is observed in aqueous emulsions as well as in non-aqueous emulsions obtained from phase separation phenomena. It is shown that phase separations in liquid crystals can lead to the formation of highly ordered arrays of uniformly sized droplets. More generally, ordered structures seen in liquid crystal emulsions are of interest as examples of topologicallv-controlled organizations; they are also of potential practical importance as a novel way to control both the stab...

International audience; We report numerical calculations on the mechanical effects of light on micrometer-sized dielectric ellipsoids immersed in water. We used a simple two-dimensional ray-optics model to compute the radiation pressure forces and torques exerted on the object as a function of position and orientation within the laser beam. Integration of the equations of motion, written in the Stokes limit, yields the particle dynamics that we investigated for different aspect ratios k. Whether the beam is collimated or focused, the results show that above a critical aspect ratio kC, the ellipsoids cannot be stably trapped on the beam axis; the particle never comes to rest and rather oscillates permanently in a back-and-forth motion involving both translationand rotation in the vicinity of the beam. Such oscillations are a direct evidence of the non-conservative character of optical forces. Conversely, stable trapping can be achieved for k < kC with the particle standing idle in a vertical position. These predictions are in very good qualitative agreement with experimental observations. The physical origin of the instability may be understood from the force and torque fields whose structures greatly depend on the ellipsoid aspect ratio and beam diameter. The oscillations arise from a non-linear coupling of the forces and torques and the torque amplitude was identified as the bifurcation control parameter. Interestingly, simulations predict that sustained oscillations can be suppressed throughthe use of two coaxial counterpropagating beams, which may be of interest whenever a static equilibrium is required as in basic force and torque measurements or technological applications.

We report on the formation of edge dislocations in two-dimensional crystals of colloidal chains of particles suspended in a nematic solvent. The systems are obtained from a phase separation of a binary mixture composed of a polymer and a liquid crystal. The colloidal structures are governed by elastic interactions mediated by the nematic matrix. Since the latter one breaks the rotational invariance symmetry, distortions around dislocations cannot be appropriately described by existing theories. We develop a simple elastic model which accounts for this symmetry breaking to gain information on factors governing the chains interaction. We find that rotation and compression/dilatation moduli of the chains are of the same order of magnitude. We also calculate the energies of single and pairs of dislocations. The results should be relevant for other layered systems such as smectics, cholesterics and surfactant lamellar phases in the presence of an external field.

We study nonaqueous emulsions that are composed of liquid crystal and silicone oils. New surfactant molecules are specifically synthesized to stabilize these emulsions. The behavior of the present surfactants is reminiscent of the behavior of classical surfactants used for aqueous emulsions. Depending on their affinity for the liquid crystal or the silicone oils, they may either stabilize silicone in liquid crystal emulsions or stabilize liquid crystal in silicone emulsions. Stabilization of nonaqueous liquid crystal emulsions may be potentially useful as a new method for making electrooptical display instruments known as polymer dispersed liquid crystal devices. It also presents a way to impart specific optical properties to silicone materials traditionally used in various coating applications and in cosmetics.

We report the experimental observation of anisotropic diffusion of polystyrene particles immersed in a lyotropic liquid crystal with two different anchoring conditions. Diffusion is shown to obey the Stokes-Einstein law for particle diameters ranging from 190 nm up to 2 micron. In the case of prolate micelles, the beads diffuse four times faster along the director than in perpendicular directions. In the theory part we present a perturbative approach to the Leslie-Ericksen equations and relate the diffusion coefficients to the Miesovicz viscosity parameters.We provide explicit formulas for the cases of uniform director field and planar anchoring conditions which are then discussed in view of the data. As a general rule, we find that the inequalities {\eta}b < {\eta}a < {\eta}c, satisfied by various liquid crystals of rodlike molecules, imply Dpar > Dperp., Comment: 5 pages, 3 figures

Colloidal particles dispersed in a partially ordered medium, such as a liquid crystal (LC) phase, disturb its alignment and are subject to elastic forces. These forces are long-ranged, anisotropic and tunable through temperature or external fields, making them a valuable asset to control colloidal assembly. The latter is very sensitive to the particle geometry since it alters the interactions between the colloids. We here present a detailed numerical analysis of the energetics of elongated objects, namely prolate ellipsoids, immersed in a nematic host. The results, complemented with qualitative experiments, reveal novel LC configurations with peculiar topological properties around the ellipsoids, depending on their aspect ratio and the boundary conditions imposed on the nematic order parameter. The latter also determine the preferred orientation of ellipsoids in the nematic field, because of elastic torques, as well as the morphology of particles aggregates., 31 pages, 11 figures

6 pages; International audience; We report on optical levitation of dielectric particles, of prolate ellipsoidal shape, a few tens of micrometers in length, in a low-aperture laser beam. Ellipsoids of moderate aspect ratio (k3) cannot be kept immobile, and rather undergo sustained oscillating motions, comprising both lateral and angular excursions around the beam axis; hence the name "tumble". The observed tumbling motion, a straightforward manifestation of the non-conservative character of radiation pressure forces, is explained through a 2-dimensional ray optics model of the interaction of light with an ellipsoid.

International audience; This work reports a detailed numerical study of the behavior of ellipsoid-shaped particles adsorbed at fluid interfaces. Former experiments have shown that micrometer-sized prolate ellipsoids aggregate under the action of strong and long-ranged capillary interactions. The latter are due to nonplanar contact lines and to the resulting deformations of the interface in the vicinity of the trapped objects. We first consider the case of a single ellipsoid and examine in detail the influence of contact angle and ellipsoid aspect ratio on interfacial distortions. We then focus on two contacting ellipsoids and study the optimum packing configuration depending on their size and/or aspect ratio mismatch. We thoroughly explore the variety of contact configurations between both ellipsoids and provide corresponding energy maps. Whereas the side-by-side configuration is the most stable state for identical ellipsoids, we find that the mismatched pair adopts an "arrow" configuration in which a finite angle exists between the particles long axes. Such arrows are actually seen in experiments with micron-sized ellipsoids and similarly with millimeter-sized mosquito eggs. These results complement our previous work (J.C. Loudet, B. Pouligny, EPL 85, 28003 (2009)) and highlight the importance of geometrical factors to explain the morphology of aggregated structures at fluid interfaces.

Using optical microscopy, phase shifting interferometry and atomic force microscopy, we demonstrate the existence of undulated structures in the meniscus of ferroelectric smectic-C* films. The meniscus is characterized by a periodic undulation of the smectic-air interface, which manifests itself in a striped pattern. The instability disappears in the untilted smectic-A phase. The modulation amplitude and wavelength both depend on meniscus thickness. We study the temperature evolution of the structure and propose a simple model that accounts for the observed undulations., Submitted to PRL

Some binary mixtures exist as a single phase at high temperatures and as two phases at lower temperatures; rapid cooling therefore induces phase separation that proceeds through the initial formation of small particles and subsequent growth and coarsening. In solid and liquid media, this process leads to growing particles with a range of sizes, which eventually separate to form a macroscopically distinct phase. Such behaviour is of particular interest in systems composed of an isotropic fluid and a liquid crystal, where the random distribution of liquid-crystal droplets in an isotropic polymer matrix may give rise to interesting electro-optical properties. Here we report that a binary mixture consisting of an isotropic fluid and a liquid crystal forming the continuous phase does not fully separate into two phases, but self-organizes into highly ordered arrays of monodisperse colloidal droplet chains. We find that the size and spatial organization of the droplets are controlled by the orientational elasticity of the liquid-crystal phase and the defects caused by droplets exceeding a critical size. We expect that our approach to forming monodisperse, spatially ordered droplets in liquid crystals will allow the controlled design of ordered composites that may have useful rheological and optical properties.

6 pages; International audience; Anisotropic particles adsorbed at a water-air interface are known to aggregate due to capillary interactions. We show that the packing configuration of a pair of prolate ellipsoids critically depends on their relative size and/or aspect ratio mismatch. While identical particles simply pack side-by-side, particles of slightly different sizes are observed to systematically selfassemble into characteristic arrows, i.e. with a finite angle between their axes. The occurrence of such arrows cannot be explained within the far-field approximation of interacting polar quadrupoles. A numerical analysis is worked out which allows us to explore the near-field characteristics of the capillary interaction. Results clearly show the destabilization of the side-by-side configuration due to a size mismatch, in agreement with experimental observations.

4 pages; International audience; We experimentally study the behavior of micrometer-sized prolate ellipsoidal particles dispersed in a nematic liquid crystal. The latter is an aqueous solution of rodlike micelles. When embedded into such a solvent, ellipsoids with small enough aspect ratios aggregate to form anisotropic structures oriented at an angle with respect to the local background director (as already observed for spheres). This is, however, no longer the case when the aspect ratio reaches a well-defined value: above that value, the ellipsoids remain well dispersed and apparently do no interact with each other, even over very long periods of time (several months). Therefore, there exists a transition from an aggregated to a nonaggregated state as a function of aspect ratio and for a given particle concentration. This behavior has not been predicted so far and we put forward simple calculations to rationalize our observations.

We experimentally and theoretically investigate the shapes of contact lines on the surfaces of micrometer-sized polystyrene ellipsoids at the water-air interface. By combining interferometry and optical trapping, we directly observe quadrupolar symmetry of the interface deformations around such particles. We then develop numerical solutions of the partial wetting problem for ellipsoids, and use these solutions to deduce the shapes of the corresponding contact lines and the values of the contact angles, theta(c)(k), as a function of the ellipsoid aspect ratio k. Surprisingly, theta(c) is found to decrease for increasing k suggesting that ellipsoid microscopic surface properties depend on ellipsoid aspect ratio.

We report on the behavior of micron-sized prolate ellipsoids trapped at an oil-water interface. The particles experience strong, anisotropic, and long-ranged attractive capillary interactions which greatly exceed the thermal energy ${k}_{B}T$. Depending on surface chemistry, the particles aggregate into open structures or chains. Using video microscopy, we extract the pair interaction potential between ellipsoids and show it exhibits a power law behavior over the length scales probed. Our observations can be explained using recent calculations, if we describe the interfacial ellipsoids as capillary quadrupoles.

We present recent findings on the formation of ordered emulsions from bulk demixing in liquid crystalline materials. In contrast to classical phase separations, which lead to randomly distributed macrodomains of various sizes, demixing in liquid crystals leads to remarkably uniform droplets that form ordered arrays. This distinctive behavior arises from the presence of topological defects and elastic distortions around the inclusions formed during the separation. These distortions induce long-range attractions and short-range repulsions. These forces direct the ordering of the microdomains and stabilize them against coalescence; limiting thereby the coarsening mechanism of the separation. We show that the ordering can be controlled on a large-scale by simply controlling the macroscopic alignment of the liquid crystal. We also discuss the influence of an external electric field and demonstrate marked differences with classical emulsions and colloids in isotropic fluids.

We report observations of polystyrene spheroidal particles that undergo different types of sustained oscillatory motion when exposed to one, or two, moderately focused Gaussian beams. Simulations predict some of the observed oscillatory regimes.

We present a statistical mechanical treatment relating the macroscopic adhesion energy of two surfaces, which can be obtained by micropipette aspiration studies, to the microscopic adhesion energy between individual bonds. The treatment deals with the case of weak reversible bonds, so that the equilibrium partition function has significance. This description is coherent with previous theories. Experiment and theory are compared to probe the nature of weak bonds in membranes, where local equilibria can be obtained. The case of a bead and a vesicle decorated by nucleosides was considered.