Force balance of particles trapped at fluid interfaces

Interactions and pattern formation in a macroscopic magnetocapillary SALR system of mermaid cereal

When particles are deposited at a fluid interface they tend to aggregate by capillary attraction to minimize the overall potential energy of the system. In this work, we embed floating millimetric disks with permanent magnets to introduce a competing repulsion effect and study their pattern formation in equilibrium. The pairwise energy landscape of two disks is described by a short-range attraction and long-range repulsion (SALR) interaction potential, previously documented in a number of microscopic condensed matter systems. Such competing interactions enable a variety of pairwise equilibrium states, including the possibility of a local minimum energy corresponding to a finite disk spacing. Two-dimensional (2D) experiments and simulations in confined geometries demonstrate that as the areal packing fraction is increased, the dilute repulsion-dominated lattice state becomes unstable to the spontaneous formation of localized clusters, which eventually merge into a system-spanning striped pattern. Finally, we demonstrate that the equilibrium pattern can be externally manipulated by the application of a supplemental vertical magnetic force that remotely enhances the effective capillary attraction.

Capillary Assembly of Anisotropic Particles at Cylindrical Fluid-Fluid Interfaces

The unique behavior of colloids at liquid interfaces provides exciting opportunities for engineering the assembly of colloidal particles into functional materials. The deformable nature of fluid-fluid interfaces means that we can use the interfacial curvature, in addition to particle properties, to direct self-assembly. To this end, we use a finite element method (Surface Evolver) to study the self-assembly of rod-shaped particles adsorbed at a simple curved fluid-fluid interface formed by a sessile liquid drop with cylindrical geometry. Specifically, we study the self-assembly of single and multiple rods as a function of drop curvature and particle properties such as shape (ellipsoid, cylinder, and spherocylinder), contact angle, aspect ratio, and chemical heterogeneity (homogeneous and triblock patchy). We find that the curved interface allows us to effectively control the orientation of the rods, allowing us to achieve parallel, perpendicular, or novel obliquely orientations with respect to the cylindrical drop. In addition, by tuning particle properties to achieve parallel alignment of the rods, we show that the cylindrical drop geometry favors tip-to-tip assembly of the rods, not just for cylinders, but also for ellipsoids and triblock patchy rods. Finally, for triblock patchy rods with larger contact line undulations, we can achieve strong spatial confinement of the rods transverse to the cylindrical drop due to the capillary repulsion between the contact line undulations of the particle and the pinned contact lines of the sessile drop. Our capillary assembly method allows us to manipulate the configuration of single and multiple rod-like particles and therefore offers a facile strategy for organizing such particles into useful functional materials.

Curvature-Mediated Forces on Elastic Inclusions in Fluid Interfaces

Heterogeneous fluid interfaces often include two-dimensional solid domains that mechanically respond to changes in interfacial curvature. While this response is well-characterized for rigid inclusions, the influence of solid-like elasticity remains essentially unexplored. Here, we show that an initially flat, elastic inclusion embedded in a curved, fluid interface will exhibit qualitatively distinct behavior depending on its size and stiffness. Small, stiff inclusions are limited by bending and experience forces directed up gradients of Gaussian curvature, in keeping with prior findings for rigid discoids. By contrast, larger and softer inclusions are driven down gradients of squared Gaussian curvature in order to minimize the elastic penalty for stretching. Our calculations of the force on a solid inclusion are shown to collapse onto a universal curve spanning the bending- and stretching-limited regimes. From these results, we make predictions for the curvature-directed motion of deformable solids embedded within a model interface of variable Gaussian curvature.

Spatiotemporal evaporating droplet dynamics on fomites enhances long term bacterial pathogenesis

Naturally drying bacterial droplets on inanimate surfaces representing fomites are the most consequential mode for transmitting infection through oro-fecal route. We provide a multiscale holistic approach to understand flow dynamics induced bacterial pattern formation on fomites leading to pathogenesis. The most virulent gut pathogen, Salmonella Typhimurium (STM), typically found in contaminated food and water, is used as model system in the current study. Evaporation-induced flow in sessile droplets facilitates the transport of STM, forming spatio-temporally varying bacterial deposition patterns based on droplet medium's nutrient scale. Mechanical and low moisture stress in the drying process reduced bacterial viability but interestingly induced hyper-proliferation of STM in macrophages, thereby augmenting virulence in fomites. In vivo studies of fomites in mice confirm that STM maintains enhanced virulence. This work demonstrates that stressed bacterial deposit morphologies formed over small timescale (minutes) on organic and inorganic surfaces, plays a significant role in enhancing fomite's pathogenesis over hours and days.

Capillary force on an 'inert' colloid: a physical analogy to dielectrophoresis

"Inert" colloids are μm-scale particles that create no distortion when trapped at a planar fluid-fluid interface. When placed in a curved interface, however, such colloids can create interfacial distortions of quadrupolar symmetry - so-called "induced capillary quadrupoles." The present work explores the analogy between capillary quadrupoles and electric dipoles, and the forces exerted on them by a symmetry-breaking gradient. In doing so, we weigh in on an outstanding debate as to whether a curvature gradient can induce a capillary force on an inert colloid. We argue that this force exists, for the opposite would imply that all dielectrophoretic forces vanish in two dimensions (2D). We justify our claim by solving 2D Laplace problems of electrostatics and capillary statics involving a single particle placed within a large circular shell with an imposed gradient. We show that the static boundary condition on the outer shell must be considered when applying the principle of virtual work to compute the force on the particle, as verified by a direct calculation of this force through integration of the particle stresses. Our investigation highlights some of the subtleties that emerge in virtual work calculations of capillary statics and electrostatics, thereby clarifying and extending previous results in the field. The broader implication of our results is that inert particles - including particles with planar, pinned contact lines and equilibrium contact angles - interact through interparticle capillary forces that scale quadratically with the deviatoric curvature of the host interface, contrary to recent claims made in the literature.

Self-assembly of charged colloidal cubes

In this work, we show how and why the interactions between charged cubic colloids range from radially isotropic to strongly directionally anisotropic, depending on tuneable factors. Using molecular dynamics simulations, we illustrate the effects of typical solvents to complement experimental investigations of cube assembly. We find that in low-salinity water solutions, where cube self-assembly is observed, the colloidal shape anisotropy leads to the strongest attraction along the corner-to-corner line, followed by edge-to-edge, with a face-to-face configuration of the cubes only becoming energetically favorable after the colloids have collapsed into the van der Waals attraction minimum. Analysing the potential of mean force between colloids with varied cubicity, we identify the origin of the asymmetric microstructures seen in experiment.

Direct Measurement of Capillary Attraction between Floating Disks

Two bodies resting at a fluid interface may interact laterally due to the surface deformations they induce. Here we use an applied magnetic force to perform direct measurements of the capillary attraction force between centimetric disks floating at an air-water interface. We compare our measurements to numerical simulations that take into account the disk's vertical displacement and spontaneous tilt, showing that both effects are necessary to describe the attraction force for short distances. We characterize the dependence of the attraction force on the disk mass, diameter, and relative spacing, and develop a scaling law that captures the observed dependence of the capillary force on the experimental parameters.

Capillarity-driven migration of small objects: A critical review

The phenomena on the capillarity-driven migration of small objects are full of interest for both scientific and engineering communities, and a critical review is thereby presented. The small objects mentioned here deal with the non-deformable objects, such as particles, rods, disks and metal sheets; and besides them, the soft objects are considered, such as droplets and bubbles. Two types of interfaces are analyzed, i.e., the solid-fluid interface and the fluid-fluid interface. Due to the easily deformable properties of the soft objects and distorted interfacial shapes induced by small objects, a more convenient way to obtain the driving force is through the potential energy of the system. The asymmetric factors causing the object migration include the asymmetric configuration of the interface, and the difference between the interfacial tensions. Finally, a simple outlook on the potential applications of small object migration is made. These behaviors may cast new light on the design of microfluidics and new devices, environment cleaning, oil and gas displacement and mineral industries.

Transport and trapping of nanosheets via hydrodynamic forces and curvature-induced capillary quadrupolar interactions

HYPOTHESIS

The manipulation of nanosheets on a fluid-fluid interface remains a significant challenge. At this interface, hydrodynamic forces can be used for long-range transport (>1× capillary length) but are difficult to utilize for accurate and repeatable positioning. While capillary multipole interactions have been used for particle trapping, how these interactions manifest on large but thin objects, i.e., nanosheets, remains an open question. Hence, we posit hydrodynamic forces in conjunction with capillary multipole interactions can be used for nanosheet transport and trapping.

EXPERIMENTS

We designed and characterized a fluidic device for transporting and trapping nanosheets on the water-air interface. Analytical models were compared against optical measurements of the nanosheet behavior to investigate capillary multipole interactions. Energy-based modeling and dimensional analysis were used to study trapping stability.

FINDINGS

Hydrodynamic forces and capillary interactions successfully transported and trapped nanosheets at a designated trapping location with a repeatability of 10% of the nanosheet's length and 12% of its width (length = 1500 µm, width = 1000 µm) and an accuracy of 20% of their length and width. Additionally, this is the first report that surface tension forces acting upon nanoscale-thick objects manifest as capillary quadrupolar interactions and can be used for precision manipulation of nanosheets.

Nano- and microparticles at fluid and biological interfaces

Systems with interfaces are abundant in both technological applications and biology. While a fluid interface separates two fluids, membranes separate the inside of vesicles from the outside, the interior of biological cells from the environment, and compartmentalize cells into organelles. The physical properties of interfaces are characterized by interface tension, those of membranes are characterized by bending and stretching elasticity. Amphiphilic molecules like surfactants that are added to a system with two immiscible fluids decrease the interface tension and induce a bending rigidity. Lipid bilayer membranes of vesicles can be stretched or compressed by osmotic pressure; in biological cells, also the presence of a cytoskeleton can induce membrane tension. If the thickness of the interface or the membrane is small compared with its lateral extension, both can be described using two-dimensional mathematical surfaces embedded in three-dimensional space. We review recent work on the interaction of particles with interfaces and membranes. This can be micrometer-sized particles at interfaces that stabilise emulsions or form colloidosomes, as well as typically nanometer-sized particles at membranes, such as viruses, parasites, and engineered drug delivery systems. In both cases, we first discuss the interaction of single particles with interfaces and membranes, e.g. particles in external fields, non-spherical particles, and particles at curved interfaces, followed by interface-mediated interaction between two particles, many-particle interactions, interface and membrane curvature-induced phenomena, and applications.

Compound Copper Chalcogenide Nanocrystals

This review captures the synthesis, assembly, properties, and applications of copper chalcogenide NCs, which have achieved significant research interest in the last decade due to their compositional and structural versatility. The outstanding functional properties of these materials stems from the relationship between their band structure and defect concentration, including charge carrier concentration and electronic conductivity character, which consequently affects their optoelectronic, optical, and plasmonic properties. This, combined with several metastable crystal phases and stoichiometries and the low energy of formation of defects, makes the reproducible synthesis of these materials, with tunable parameters, remarkable. Further to this, the review captures the progress of the hierarchical assembly of these NCs, which bridges the link between their discrete and collective properties. Their ubiquitous application set has cross-cut energy conversion (photovoltaics, photocatalysis, thermoelectrics), energy storage (lithium-ion batteries, hydrogen generation), emissive materials (plasmonics, LEDs, biolabelling), sensors (electrochemical, biochemical), biomedical devices (magnetic resonance imaging, X-ray computer tomography), and medical therapies (photochemothermal therapies, immunotherapy, radiotherapy, and drug delivery). The confluence of advances in the synthesis, assembly, and application of these NCs in the past decade has the potential to significantly impact society, both economically and environmentally.

Sinking a Granular Raft

We report experiments that yield new insights on the behavior of granular rafts at an oil-water interface. We show that these particle aggregates can float or sink depending on dimensionless parameters taking into account the particle densities and size and the densities of the two fluids. We characterize the raft shape and stability and propose a model to predict its shape and maximum length to remain afloat. Finally we find that wrinkles and folds appear along the raft due to compression by its own weight, which can trigger destabilization. These features are characteristics of an elastic instability, which we discuss, including the limitations of our model.

Collective dynamics of chemically active particles trapped at a fluid interface

Chemically active colloids generate changes in the chemical composition of their surrounding solution and thereby induce flows in the ambient fluid which affect their dynamical evolution. Here we study the many-body dynamics of a monolayer of spherically symmetric active particles trapped at a fluid-fluid interface. To this end we consider a model for the large-scale spatial distribution of particles which incorporates the direct pair interaction (including also the capillary interaction which is caused specifically by the interfacial trapping) as well as the effect of hydrodynamic interactions (including the Marangoni flow induced by the response of the interface to the chemical activity). The values of the relevant physical parameters for typical experimental realizations of such systems are estimated and various scenarios, which are predicted by our approach for the dynamics of the monolayer, are discussed. In particular, we show that the chemically-induced Marangoni flow can prevent the clustering instability driven by the capillary attraction.

Tuning the Structure and Rheology of Polystyrene Particles at the Air-Water Interface by Varying the pH

We form films of carboxylated polystyrene particles (C-PS) at the air-water interface and investigate the effect of subphase pH on their structure and rheology by using a suite of complementary experimental techniques. Our results suggest that electrostatic interactions drive the stability and the structural order of the films. In particular, we show that by increasing the pH of the subphase from 9 up to 13, the films exhibit a gradual transition from solid to liquidlike, which is accompanied by a loss of the long-range order (that characterizes them at lower values of pH). Direct optical visualization of the layers, scanning electron microscopy, and surface pressure isotherms indicate that the particles deposited at the interface form three-dimensional structures involving clusters, with the latter being suppressed and a quasi-2D particle configuration eventually reached at the highest pH values. Evidently, the properties of colloidal films can be tailored significantly by altering the pH of the subphase.

Hard and soft colloids at fluid interfaces: Adsorption, interactions, assembly & rheology

Soft microgel particles inherently possess qualities of both polymers as well as particles. We review the similarities and differences between soft microgel particles and stiff colloids at fluid-fluid interfaces. We compare two fundamental aspects of particle-laden interfaces namely the adsorption kinetics and the interactions between adsorbed particles. Although it is well established that the transport of both hard particles and microgels to the interface is driven by diffusion, the analysis of the adsorption kinetics needs reconsideration and a proper equation of state relating the surface pressure to the adsorbed mass should be used. We review the theoretical and experimental investigations into the interactions of particles at the interface. The rheology of the interfacial layers is intimately related to the interactions, and the differences between hard particles and microgels become pronounced. The assembly of particles into the layer is another distinguishing factor that separates hard particles from soft microgel particles. Microgels deform substantially upon adsorption and the stability of a microgel-stabilized emulsion depends on the conformational changes triggered by external stimuli.

Trapping and assembly of living colloids at water-water interfaces

We study the assembly of inert and living colloids in a two-phase water-water system that provides an environment that can sustain bacteria, providing a new structure with rich potential to confine and structure microbial communities. The water-water system, formed via phase separation of a casein and xanthan mixture, forms a 3-D structure of coexisting casein-rich and xanthan-rich phases. Fluorescent labelling and confocal microscopy reveal the attachment of these living colloids, including Escherichia coli and Pseudomonas aeruginosa, at the interface between the two phases. Inert colloids also become trapped at the interfaces, suggesting that the observed attachment can be attributed to capillarity. Over time, these structures coarsen and eventually degrade, illustrating the dynamic nature of these systems. This system lays the foundation for future studies of the interplay of physicochemical properties of the fluid interfaces and bulk phases and microbial responses they provoke to induce complex spatial organization, to study species which occupy distinct niches, and to optimize efficient microbial cross-feeding or protection from competitors.

Capillary migration of microdisks on curved interfaces

The capillary energy landscape for particles on curved fluid interfaces is strongly influenced by the particle wetting conditions. Contact line pinning has now been widely reported for colloidal particles, but its implications in capillary interactions have not been addressed. Here, we present experiment and analysis for disks with pinned contact lines on curved fluid interfaces. In experiment, we study microdisk migration on a host interface with zero mean curvature; the microdisks have contact lines pinned at their sharp edges and are sufficiently small that gravitational effects are negligible. The disks migrate away from planar regions toward regions of steep curvature with capillary energies inferred from the dissipation along particle trajectories which are linear in the deviatoric curvature. We derive the curvature capillary energy for an interface with arbitrary curvature, and discuss each contribution to the expression. By adsorbing to a curved interface, a particle eliminates a patch of fluid interface and perturbs the surrounding interface shape. Analysis predicts that perfectly smooth, circular disks do not migrate, and that nanometric deviations from a planar circular, contact line, like those around a weakly roughened planar disk, will drive migration with linear dependence on deviatoric curvature, in agreement with experiment.

Capillary attraction induced collapse of colloidal monolayers at fluid interfaces

We investigate the evolution of a system of colloidal particles, trapped at a fluid interface and interacting via capillary attraction, as a function of the range of capillary interactions and temperature. We address the collapse of an initially homogeneous particle distribution and of a radially symmetric (disk-shaped) distribution of finite size, both theoretically by using a perturbative approach inspired by cosmological models and numerically by means of Brownian dynamics (BD) and dynamical density functional theory (DDFT). The results are summarized in a "dynamical phase diagram", describing a smooth crossover from a collective (gravitational-like) collapse to local (spinodal-like) clustering. In this crossover region, the evolution exhibits a peculiar shock wave behavior at the outer rim of the contracting, disk-shaped distribution.

Capillary force acting on a colloidal particle floating on a deformed interface

We analytically determine the lateral capillary force acting on a spherical colloid trapped at an interface of arbitrary shape. Our calculations, which are valid for colloids that are small with respect to the capillary length, take into account surface tension, pressure and gravity. We relate the force acting on the colloid to the shape of the liquid interface prior to colloid deposition. Our approach is a generalization of a previous study of ours [Ch. Blanc et al., Phys. Rev. Lett., 2013, 111, 058302] to the case in which gravity is present. Our findings are in agreement with the so-called Nicolson superposition approximation [D. Y. C. Chan, J. D. J. Henry and L. R. White, J. Colloid Interface Sci., 1981, 79, 410] and with the curvature-dependent capillary force predicted by Würger [A. Würger, Phys. Rev. E, 2006, 74, 041402], and extend these results by including higher-order terms in the ratio between the size of the colloid and the capillary length. We thoroughly validate our theoretical expressions by means of an exact nonlinear numerical calculation.

Size limit for particle-stabilized emulsion droplets under gravity

We demonstrate that emulsion droplets stabilized by interfacial particles become unstable beyond a size threshold set by gravity. This holds not only for colloids but also for supracolloidal glass beads, using which we directly observe the ejection of particles near the droplet base. The number of particles acting together in these ejection events decreases with time until a stable acornlike configuration is reached. Stability occurs when the weight of all remaining particles is less than the interfacial binding force of one particle. We also show the importance of the curvature of the droplet surface in promoting particle ejection.

Field-induced breakup of emulsion droplets stabilized by colloidal particles

We simulate the response of a particle-stabilized emulsion droplet in an external force field, such as gravity, acting equally on all N particles. We show that the field strength required for breakup (at fixed initial area fraction) decreases markedly with droplet size, because the forces act cumulatively, not individually, to detach the interfacial particles. The breakup mode involves the collective destabilization of a solidified particle raft occupying the lower part of the droplet, leading to a critical force per particle that scales approximately as N(-1/2).

Curvature-driven capillary migration and assembly of rod-like particles

Capillarity can be used to direct anisotropic colloidal particles to precise locations and to orient them by using interface curvature as an applied field. We show this in experiments in which the shape of the interface is molded by pinning to vertical pillars of different cross-sections. These interfaces present well-defined curvature fields that orient and steer particles along complex trajectories. Trajectories and orientations are predicted by a theoretical model in which capillary forces and torques are related to Gaussian curvature gradients and angular deviations from principal directions of curvature. Interface curvature diverges near sharp boundaries, similar to an electric field near a pointed conductor. We exploit this feature to induce migration and assembly at preferred locations, and to create complex structures. We also report a repulsive interaction, in which microparticles move away from planar bounding walls along curvature gradient contours. These phenomena should be widely useful in the directed assembly of micro- and nanoparticles with potential application in the fabrication of materials with tunable mechanical or electronic properties, in emulsion production, and in encapsulation.

Collective dynamics of colloids at fluid interfaces

The evolution of an initially prepared distribution of micron-sized colloidal particles, trapped at a fluid interface and under the action of their mutual capillary attraction, is analyzed by using Brownian dynamics simulations. At a separation λ given by the capillary length of typically 1mm, the distance dependence of this attraction exhibits a crossover from a logarithmic decay, formally analogous to two-dimensional gravity, to an exponential decay. We discuss in detail the adaptation of a particle-mesh algorithm, as used in cosmological simulations to study structure formation due to gravitational collapse, to the present colloidal problem. These simulations confirm the predictions, as far as available, of a mean-field theory developed previously for this problem. The evolution is monitored by quantitative characteristics which are particularly sensitive to the formation of highly inhomogeneous structures. Upon increasing λ the dynamics shows a smooth transition from the spinodal decomposition expected for a simple fluid with short-ranged attraction to the self-gravitational collapse scenario.

Capillary interactions in Pickering emulsions

The effective capillary interaction potentials for small colloidal particles trapped at the surface of liquid droplets are calculated analytically. Pair potentials between capillary monopoles and dipoles, corresponding to particles floating on a droplet with a fixed center of mass and subjected to external forces and torques, respectively, exhibit a repulsion at large angular separations and an attraction at smaller separations, with the latter resembling the typical behavior for flat interfaces. This change of character is not observed for quadrupoles, corresponding to free particles on a mechanically isolated droplet. The analytical results are compared with the numerical minimization of the surface free energy of the droplet in the presence of spherical or ellipsoidal particles.

An axisymmetric meniscus converges particles for microscopy

Capillary rise on a tapered cylindrical rod creates a static axisymmetric meniscus that quantitatively attracts buoyant particles into a single microscopic field of view, providing a new method for small particle microscopy. This approach simplifies the visualization of micrometre-sized particles, such as pollen and parasite eggs, and has potential utility in remote location monitoring and clinical diagnosis.

How do mosquito eggs self-assemble on the water surface?

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.

Wetting behavior of spherical nanoparticles at a vapor-liquid interface: a density functional theory study

The wetting behavior of spherical nanoparticles at a vapor-liquid interface is investigated by using density functional theory, and the line tension calculation method is modified by analyzing the total energy of the vapor-liquid-particle equilibrium. Compared with the direct measurement data from simulation, the results reveal that the thermodynamically consistent Young's equation for planar interfaces is still applicable for high curvature surfaces in predicting a wide range of contact angles. The effect of the line tension on the contact angle is further explored, showing that the contact angles given by the original and modified Young's equations are nearly the same within the region of 60° < θ < 120°. Whereas the effect is considerable when the contact angle deviates from the region. The wetting property of nanoparticles in terms of the fluid-particle interaction strength, particle size, and temperature is also discussed. It is found that, for a certain particle, a moderate fluid-particle interaction strength would keep the particle stable at the interface in a wide temperature range.

Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals π/2 , a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free-energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.

Macroscopic ordering of polystyrene carboxylate-modified nanospheres self-assembled at the water-air interface

We present results from an experimental study of ordering characteristics in monolayers of polystyrene nanospheres self-assembled at a water-air interface. We demonstrate that the interaction of spheres, governed by the dissemination of surface charge, leads to the formation of macroscopic close-packed ordered areas or "domains" with a well-defined orientation of the lattice axes over areas of 25 mm(2). It was found that by changing the surface chemistry of the spheres it is possible to modify the balance between the attractive and repulsive forces and thus to control the ordering characteristics. We implemented a model that simulates the process of self-assembly and examines the ordering characteristics for layers with different ratio between attractive and repulsive forces. A good qualitative agreement was found between the simulations and experiment. These studies are technologically relevant as a method of producing nanosphere templates for large area patterned materials.

Dynamics of colloidal particles with capillary interactions

We investigate the dynamics of colloids at a fluid interface driven by attractive capillary interactions. At submillimeter length scales, the capillary attraction is formally analogous to two-dimensional gravity. In particular it is a nonintegrable interaction and it can be actually relevant for collective phenomena in spite of its weakness at the level of the pair potential. We introduce a mean-field model for the dynamical evolution of the particle number density at the interface. For generic values of the physical parameters the homogeneous distribution is found to be unstable against large-scale clustering driven by the capillary attraction. We also show that for the instability to be observable, the appropriate values for the relevant parameters (colloid radius, surface charge, external electric field, etc.) are experimentally well accessible. Our analysis contributes to current studies of the structure and dynamics of systems governed by long-ranged interactions and points toward their experimental realizations via colloidal suspensions.

Capillary forces between particles at a liquid interface: general theoretical approach and interactions between capillary multipoles

The liquid interface around an adsorbed colloidal particle can be undulated because of roughness or heterogeneity of the particle surface, or due to the fact that the particle has non-spherical (e.g. ellipsoidal or polyhedral) shape. In such case, the meniscus around the particle can be expanded in Fourier series, which is equivalent to a superposition of capillary multipoles, viz. capillary charges, dipoles, quadrupoles, etc. The capillary multipoles attract a growing interest because their interactions have been found to influence the self-assembly of particles at liquid interfaces, as well as the interfacial rheology and the properties of particle-stabilized emulsions and foams. As a rule, the interfacial deformation in the middle between two adsorbed colloidal particles is small. This fact is utilized for derivation of accurate asymptotic expressions for calculating the capillary forces by integration in the midplane, where the Young-Laplace equation can be linearized and the superposition approximation can be applied. Thus, we derived a general integral expression for the capillary force, which was further applied to obtain convenient asymptotic formulas for the force and energy of interaction between capillary multipoles of arbitrary orders. The new analytical expressions have a wider range of validity in comparison with the previously published ones. They are applicable not only for interparticle distances that are much smaller than the capillary length, but also for distances that are comparable or greater than the capillary length.

Effective interactions of colloids on nematic films

The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations d. The elastic interaction is repulsive and of quadrupolar type, varying as d⁻⁵. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to d⁻⁵ as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importance for the recently observed pattern formation of colloidal droplets on nematic films.

Rotation and alignment of anisotropic particles on nonplanar interfaces

We study the alignment of micron-scale particles at air-water interfaces with unequal principle radii of curvature by optical microscopy. The fluid interface bends to satisfy the wetting conditions at the three phase contact line where the interface intersects the particle, creating deflections that increase the area of the interface. These deflections decay far from the particle. The far field interface shape has differing principle radii of curvature over length scales large compared to the particle. The deflections create excess area which depends on the angle of the particle with respect to the principle axes of the interface. We show that when particles create surface deflections with quadrupolar modes, the particles rotate to preferred orientations to minimize the free energy. In experiment, we focus on uniform surface energy particles, for which quadrupolar modes are forced by the particle shape. Analytical expressions for the torque and stable states are derived in agreement with experiment and confirmed computationally.