Behavior of inclusions with different value and orientation of topological dipoles in ferroelectric smectic films

Cholesteric droplets in ferroelectric free-standing films with tunable anchoring on the droplet boundary are investigated. A droplet and satellite topological defect(s) form a topological dipole. We obtained droplets with different angles α between two radial lines from the droplet center to −1/2 topological defects. Droplets with parallel dipoles form linear chains in which the interparticle distances decrease with increasing the defect angle α. For the first time, the dependence of the interparticle distance on the angle between topological defects was measured. We can adjust the magnitude and orientation of topological dipoles formed by the droplets. For the first time, the droplets with antiparallel topological dipoles were prepared in a smectic film. Interaction of the droplets with parallel and antiparallel dipoles differs drastically. Formation of antiparallel dipoles leads to a decomposition of the droplet pairs and chains of droplets. Our observations may be used to change the magnitude, anisotropy of the interparticle interaction, and structures of inclusions in liquid crystal media. The article is published in the original.     

Smectic islands in antiferroelectric nanofilms

Heterochiral islands, in which topological dipoles are oppositely directed, are observed in freestanding antiferroelectric (SmC _A ^*) films. The topological dipoles in films with a transverse electric polarization and a planar molecule orientation at island boundaries are coplanar with an electric field. The topological dipoles in films with a longitudinal polarization and a planar orientation at island boundaries are perpendicular to an electric field. For a radial director orientation at island boundaries, the topological dipoles in films with a longitudinal polarization are coplanar with a field. Changing the orientation of an electric field, we can control the position of a topological defect at an island boundary and the orientation of a topological dipole. Heterochiral islands can form dimers with an anomalously small interisland distance.     

Different mechanisms of nucleation and self-organization of droplets in ferroelectric smectic membranes

New mechanisms of droplet nucleation and self-organization in ferroelectric membranes are described. The droplets may be accompanied by different number of topological defects (zero, one, two) whose location may be on the droplet boundary or in the membrane. Nucleation and self-organization of droplets with total topological charge S = 0 , S = + 1 and S = - 1 were investigated. We found that an S = - 1 topological defect may be the center of both droplet nucleation and chain formation. This mechanism of chaining drastically differs from the droplet self-organization described earlier which is realized by attraction of droplet-defect pairs. Our observations demonstrate new possibilities for manipulating the inclusions and their self-organization in smectic membranes.     

Water droplets in a spherically confined nematic solvent: A numerical investigation

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 to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998     

Stability of cellulose lyotropic liquid crystal emulsions

We studied a new kind of W/O emulsions based on a lyotropic liquid crystal as the aqueous droplet phase. The cholesteric phase, a solution hydroxypropyl cellulose in water was dispersed in the continuous oil matrix, paraffin oil or heptane. We made a specific choice of surfactant in order to impose director anchoring conditions at the oil-water interface and orient the liquid crystal inside the droplet. The strong anchoring conditions resulted in a topological defect inside the droplets of size above the critical value R^*. The defect elastic energy creates a barrier against droplet coalescence, the effect of topological size selection. We have studied the orientation of the director inside the droplets and their size distribution.     

Macroscopic vortex droplets in Bi2Sr2CaCu2O8 crystals pumped by an ac magnetic field

The formation of droplets (or breathers) of vortex matter in Bi(2)Sr(2)CaCu(2)O(8) crystals pumped by the low-frequency ac magnetic field is observed by magneto-optic imaging. The droplets nucleate at the points of crossing the planar defects. The magnetic flux in the droplet and the droplet size increase with time. When the flux in the droplet exceeds a critical value, the droplet shifts along the defect to the sample bulk and a new droplet with the opposite flux direction starts to nucleate at the same point. As a result, a beadlike structure of the droplets arises along the defect. A possible explanation of the phenomenon is proposed.     

Field dependent shape variation of magnetic fluid droplets on magnetic dots

The morphology of magnetic fluid droplets on magnetic thin film dots is studied experimentally, including the aspect ratio and the contact angle variation of the droplets. Under a uniform external magnetic field, the droplet's aspect ratio increases with the external field and with the diameter of the magnetic dot due to the concentrated magnetic flux inside the magnetic fluid droplet. Similar to the electrical wetting phenomenon, the induced magnetic dipoles in the magnetic film and in the magnetic fluid near the solid–liquid interface change the solid–liquid interfacial tension, and in consequence reduce the apparent contact angle of the magnetic fluid droplet.     

Landau quantization for an induced electric dipole in the presence of topological defects

In this contribution we investigate the non-relativistic quantum dynamics of induced electric dipoles in the presence of a topological defect. We propose an analog of Landau quantization for neutral atoms, where a electric dipole is induced by the electromagnetic field configuration. We investigate this system in the presence of a topological defect and show that it breaks the infinite degeneracy of Landau levels.     

Ferroelectricity in mixtures of mesogenic and nonmesogenic compounds

It is shown that by adding potassium nitrate (1 % by weight) to compensated cholesteric mixtures (cholesteryl chloride-cholesteryl myristate 63.63:36.37% by weight and cholesteryl laurate-cholesteryl chloride 35.65% by weight) or to smectic sitosteryl undecilenate, the mixtures exhibit ferroelectric behaviour. Values of P_s = 10-⁹ - 10-⁸ C/cm² were obtained in the high-temperature range. In compensated cholesteric mixtures, the spontaneous polarisation reached a minimum at a temperature corresponding to the cholesteric-nematic transition. The results are explained by assuming coupling between the dipoles of the antiferroelectric KNO₃ and the dipoles of the mesogenic compound.     

Direct numerical simulations of autoignition in turbulent two-phase flows

Three-dimensional direct numerical simulations (DNS) were carried out to investigate the impact of evaporation of droplets on the autoignition process under decaying turbulence. The droplets were taken as point sources and were tracked in a Lagrangian manner. Three cases with the same initial equivalence ratio but different initial droplet size were simulated and the focus was to examine the influence of the droplet evaporation process on the location of autoignition. It was found that an increase in the initial droplet size results in an increase in the autoignition time, that highest reaction rates always occur at a specific mixture fraction ξ_MR, as in purely gaseous flows, and that changes in the initial droplet size did not affect the value of ξ_MR. The conditional correlation coefficient between scalar dissipation rate and reaction rates was only mildly negative, contrary to the strongly negative values for purely gaseous autoigniting flows, possibly due to the continuous generation of mixture fraction by the droplet evaporation process that randomizes both the mixture fraction and the scalar dissipation fields.     

The apparent state of droplets on a rough surface

The factors influencing the state and wetting transition of droplets on a rough surface are both complex and obscure. The change in wetting is directly reflected by changes under the contact condition of the droplets with the surface. The recent study about the wettability of the superhydrophobic surface under the condensing condition arouses the new understanding about the apparent state of droplets on a rough surface. In this work, to validate the existence of droplets in an intermediate state, a microscale pillar topological polydimethylsiloxane (PDMS) surface was manufactured and its wettability under various conditions was studied. According to the experimental data, it is proposed that the wetting state of a rough surface may be embodied using the contact area ratio of a solid/liquid/gas droplet with the projective plane. A general calculation model for the apparent contact angle of droplets is given and expressed diagrammatically. It is found that the measured apparent contact angles of droplets at different states on the surface falls within the range predicted by our proposed equation. Supported by the National Natural Science Foundation of China (Grant No. 50606025)     

Visualization of aggregation process of dispersed water droplets and the effect of aggregation on secondary atomization of emulsified fuel droplets

The effect of aggregation of dispersed water droplets on secondary atomization of emulsified fuel droplets in a heating process was investigated. Secondary atomization was observed using a single droplet experiment in which a water-in-oil (W/O) emulsified fuel droplet prepared using colored water was heated by a halogen heater. The initial diameter of dispersed water droplets before heating was controlled, and the change in the diameter of dispersed water droplets was measured by image analysis. As a result, the aggregation process of dispersed water droplets in the heating process was successfully visualized. The dispersed water droplet diameter increased with an increase in W/O emulsified fuel droplet temperature. The occurrence probability of micro-explosion increased with an increase in the dispersed water droplet diameter in emulsified fuel droplets. It is suggested that the occurrence probability of micro-explosion can be increased by accelerating the aggregation and coalescence of dispersed water droplets below 430 K, which is the average temperature of the starting point of puffing.     

Nonane droplet combustion with and without buoyant convection: Flame structure, burning rate and extinction in air and helium

The burning and extinction characteristics of isolated small nonane droplets are examined in a buoyant convective environment and in an environment with no external axial convection (as created by doing experiments at low gravity) to promote spherical droplet flames. The ambience is air and a mixture of 30%O₂/70%He to assess the influence of soot formation. The initial droplet diameter (D_o) ranges from 0.4 to 0.95 mm. Measurements are reported of the extinction diameter and time to extinction, and of the evolution of droplet diameter, flame diameter, soot shell diameter, burning rate, and broadband radiative emissions.In a buoyancy-free environment for air larger droplets burn slower than smaller droplets for the range of D_o examined, which is attributed to the influence of soot. In the presence of a buoyant flow in air, no influence of D_o is observed on the burning rate while the buoyant flames are still heavily sooting. The effect of D_o is believed to be due to a combination of dominance of the nonluminous, nonsooting, portion of the buoyant flame around the forward half of the droplet on heat transport and the secondary role of the luminous wake portion of the flame. In a non-sooting helium inert at low gravity, no effect of D_o is found on the evolution of droplet diameter.Flame extinction is observed only in the 30%O₂/70%He ambience. For all of the observations, extinction appears to occur before the disappearance of the droplet which is then followed by a period of evaporation. The extinction diameter and time to extinction increases with D_o and an empirical correlation is presented for these two variables.     

Phase transition in ellipsoidal droplets of nematic liquid crystals

We developed a simple method for the calculation of the director field distribution in the droplets of nematic liquid crystals (LCs) of any shape, allowing for the interaction of LCs with the droplet surface, as well as the influence of constant electric field. In contrast to different approaches, the approach that is developed in the present paper does not require any simplifying suppositions about the structure of the LC director field. The elastic-continuum theory is used, complemented with the possibility of consideration of point and linear defects. Calculations are performed using the Monte Carlo method on a simple grid. The triangulation technique is used to take the boundary conditions of droplets of a complex shape into account. The developed approach can be used for investigation of the properties of polymer-dispersed liquid crystals (PDLCs). The topological phase transitions in the nematic LC 4-cyano-4′-pentyl-biphenyl (5CB) in spherical and ellipsoidal droplets are investigated in this paper.     

Coexistence of two colloidal crystals at the nematic-liquid-crystal-air interface

Glycerol droplets at a nematic-liquid-crystal-air interface form two different lattices--hexagonal and dense quasihexagonal--which are separated by the energy barrier and can coexist. Director distortions around each droplet form an elastic dipole. The first order transition between the two lattices is driven by a reduction of the dipole-dipole repulsion through reorientation of these dipoles. The elastic-capillary attraction is essential for the both lattices. The effect has a many-body origin.     

Stochastic modeling of atomizing spray in a complex swirl injector using large eddy simulation

Large-eddy simulation of an atomizing spray issuing from a gas-turbine injector is performed. The filtered Navier–Stokes equations with dynamic subgrid scale model are solved on unstructured grids to compute the swirling turbulent flow through complex passages of the injector. The collocated grid, incompressible flow algorithm on arbitrary shaped unstructured grids developed by Mahesh et al. (J. Comp. Phys. 197 (2004) 215–240) is used in this work. A Lagrangian point-particle formulation with a stochastic model for droplet breakup is used for the liquid phase. Following Kolmogorov’s concept of viewing solid particle-breakup as a discrete random process, the droplet breakup is considered in the framework of uncorrelated breakup events, independent of the initial droplet size. The size and number density of the newly produced droplets is governed by the Fokker–Planck equation for the evolution of the pdf of droplet radii. The parameters of the model are obtained dynamically by relating them to the local Weber number and resolved scale turbulence properties. A hybrid particle-parcel is used to represent the large number of spray droplets. The predictive capability of the LES together with Lagrangian droplet dynamics models to capture the droplet dispersion characteristics, size distributions, and the spray evolution is examined in detail by comparing it with the spray patternation study for the gas-turbine injector. The present approach is computationally efficient and captures the global features of the fragmentary process of liquid atomization in complex configurations.     

Ultrasonic surface acoustic wave-assisted separation of microscale droplets with varying acoustic impedance

In droplet-based microfluidic platforms, precise separation of microscale droplets of different chemical composition is increasingly necessary for high-throughput combinatorial chemistry in drug discovery and screening assays. A variety of droplet sorting methods have been proposed, in which droplets of the same kind are translocated. However, there has been relatively less effort in developing techniques to separate the uniform-sized droplets of different chemical composition. Most of the previous droplet sorting or separation techniques either rely on the droplet size for the separation marker or adopt on-demand application of a force field for the droplet sorting or separation. The existing droplet microfluidic separation techniques based on the in-droplet chemical composition are still in infancy because of the technical difficulties. In this study, we propose an acoustofluidic method to simultaneously separate microscale droplets of the same volume and dissimilar acoustic impedance using ultrasonic surface acoustic wave (SAW)-induced acoustic radiation force (ARF). For extensive investigation on the SAW-induced ARF acting on both cylindrical and spherical droplets, we first performed a set of the droplet sorting experiments under varying conditions of acoustic impedance of the dispersed phase fluid, droplet velocity, and wave amplitude. Moreover, for elucidation of the underlying physics, a new dimensionless number AR_D was introduced, which was defined as the ratio of the ARF to the drag force acting on the droplets. The experimental results were comparatively analyzed by using a ray acoustics approach and found to be in good agreement with the theoretical estimation. Based on the findings, we successfully demonstrated the simultaneous separation of uniform-sized droplets of the different acoustic impedance under continuous application of the acoustic field in a label-free and detection-free manner. Insomuch as on-chip, precise separation of multiple kinds of droplets is critical in many droplet microfluidic applications, the proposed acoustofluidic approach will provide new prospects for microscale droplet separation.     

Controlled Production of Emulsions Using a Crossflow Membrane

A method for manufacturing emulsions — crossflow membrane emulsification has been studied. This involves the formation of emulsions by breaking up the discontinuous phase into droplets in a controlled manner without the use of turbulent eddies. This is achieved by passing the discontinuous phase through a suitable microporous medium and injecting the droplets so formed directly into a moving continuous phase. This paper presents two examples of experimental data for droplet formation using a single pore (capillary tube) and a membrane tube. A high-speed video camera (up to 1000 frames per second) was used to record the formation of droplet from a single pore and thus measure droplet growth and the detachment processes as a function of process parameters such as transmembrane pressure drop, membrane pore size, continuous phase crossflow velocity etc. Real emulsions were prepared using a membrane tube.     

Flame structure and stabilization of lean-premixed sprays in a counterflow with low-volatility fuel

An experimental study was performed on the combustion of lean-premixed spays in a counterflow. n-Decane was used as a liquid fuel with low volatility. The flame structure and stabilization were discussed based on the flame-spread mechanism of a droplet array with a low-volatility fuel. The spray flame consisted of a blue region and a yellow luminous region. The flame spread among droplets and group-flame formation through the droplet interaction were observed on the premixed spray side, while envelope flames were also observed on the opposing airflow side. The blue-flame region consisted of premixed flames propagating in the mixture layer around each droplet, the envelope diffusion flames around each droplet, the lower parts of the group diffusion flame surrounding each droplet cluster, and the envelope flame around droplets passing through the group flame. The flame was stabilized within a specific range of the mean droplet diameter via a balance between the droplet velocity and the flame-spread rate of the premixed spray.     

Dipolar configuration in the ordered state of alkali cyanides

The electrostatic ground state energy of the fully ordered state in KCN and NaCN is evaluated. The main contribution is shown to arise from an indirect interaction of CN^- dipoles via induced dipoles due to lattice displacements. The resulting effective interaction has a maximum at wave vector $\text{q}\text{= (0,}\text{2π}\text{b}\text{, 0)}$, corresponding to an antiferroelectric state such that the dipole at the centre of the orthorhombic unit cell is antiparallel to the dipoles at the corners. The predicted configuration agrees with neutron scattering data.