Capillary assembly of microscale ellipsoidal, cuboidal, and spherical particles at interfaces

The Paradoxical Behavior of Rough Colloids at Fluid Interfaces

Colloidal particles adsorb and remain trapped at immiscible fluid interfaces due to strong interfacial adsorption energy with a contact angle defined by the chemistry of the particle and fluid phases. An undulated contact line may appear due to either particle surface roughness or shape anisotropy, which results in a quadrupolar interfacial deformation and strong long-range capillary interaction between neighboring particles. While each effect has been observed separately, here we report the paradoxical impact of surface roughness on spherical and anisotropic ellipsoidal polymer colloids. Using a seeded emulsion polymerization technique, we synthesize spherical and ellipsoidal particles with controlled roughness magnitudes and topography (convex/concave). Via in situ measurement of the interfacial deformation around colloids at an air-water interface, we find that while surface roughness strengthens the quadrupolar deformation in spheres as expected by theory, in stark contrast, it weakens the same in ellipsoids. As roughness increases, particles of both shapes become more hydrophilic, and their apparent contact angle decreases. Using numerical predictions, we show that this partially explains the decreased interfacial deformation and capillary interactions between the ellipsoids. Therefore, particle surface engineering has the potential to decrease the capillary deformation by asymmetric particles via changing their capillary pinning, as well as wetting behavior at fluid interfaces.

The Roles of Oil-Water Interfaces in Forming Ultrasmall CaSO4 Nanoparticles

In natural and engineered environmental systems, calcium sulfate (CaSO4) nucleation commonly occurs at dynamic liquid-liquid interfaces. Although CaSO4 is one of the most common minerals in oil spills and oil-water separation, the mechanisms driving its nucleation at these liquid-liquid interfaces remain poorly understood. In this study, using in situ small-angle X-ray scattering (SAXS), we examined CaSO4 nucleation at oil-water interfaces and found that within 60 minutes of reaction, short rod-shaped nanoparticles (with a radius of gyration (Rg) of 17.2 ± 2.7 nm and a length of 38.2 ± 5.8 nm) had formed preferentially at the interfaces. Wide-angle X-ray scattering (WAXS) analysis identified these nanoparticles as gypsum (CaSO4·2H2O). In addition, spherial nanoparticles measuring 4.1 nm in diameter were observed at oil-water interfaces, where surface-enhanced Raman spectroscopy (SERS) revealed an elevated pH compared to the bulk solution. The negatively charged oil-water interfaces preferentially adsorb calcium ions, collectively promoting CaSO4 formation there. CaSO4 particle formation at the oil-water interface follows a nonclassical nucleation (N-CNT) pathway by forming ultrasmall amorphous spherical particles which then aggregate to form intermediate nanoparticles, subsequently growing into nanorod-shaped gypsum. These findings of this study provide insights into mineral scaling during membrane separation and can inform more efficient oil transport in energy recovery systems.

Nanoscale Porosity in Microellipsoids Cloaks Interparticle Capillary Attraction at Fluid Interfaces

Anisotropic particles pinned at fluid interfaces tend toward disordered multiparticle configurations due to large, orientationally dependent, capillary forces, which is a significant barrier to exploiting these particles to create functional self-assembled materials. Therefore, current interfacial assembly methods typically focus on isotropic spheres, which have minimal capillary attraction and no dependence on orientation in the plane of the interface. In order to create long-range ordered structures with complex configurations via interfacially trapped anisotropic particles, control over the interparticle interaction energy via external fields and/or particle engineering is necessary. Here, we synthesize colloidal ellipsoids with nanoscale porosity and show that their interparticle capillary attraction at a water-air interface is reduced by an order of magnitude compared to their smooth counterparts. This is accomplished by comparing the behavior of smooth, rough, and porous ellipsoids at a water-air interface. By monitoring the dynamics of two particles approaching one another, we show that the porous particles exhibit a much shorter-range capillary interaction potential, with scaling intriguingly different than theory describing the behavior of smooth ellipsoids. Further, interferometry measurements of the fluid deformation surrounding a single particle shows that the interface around porous ellipsoids does not possess the characteristic quadrupolar symmetry of smooth ellipsoids, and quantitatively confirms the decrease in capillary interaction energy. By engineering nanostructured surface features in this fashion, the interfacial capillary interactions between particles may be controlled, informing an approach for the self-assembly of complex two-dimensional microstructures composed of anisotropic particles.

Using adsorption kinetics to assemble vertically aligned nanorods at liquid interfaces for metamaterial applications

Vertically aligned monolayers of metallic nanorods have a wide range of applications as metamaterials or in surface enhanced Raman spectroscopy. However the fabrication of such structures using current top-down methods or through assembly on solid substrates is either difficult to scale up or have limited possibilities for further modification after assembly. The aim of this paper is to use the adsorption kinetics of cylindrical nanorods at a liquid interface as a novel route for assembling vertically aligned nanorod arrays that overcomes these problems. Specifically, we model the adsorption kinetics of the particle using Langevin dynamics coupled to a finite element model, accurately capturing the deformation of the liquid meniscus and particle friction coefficients during adsorption. We find that the final orientation of the cylindrical nanorod is determined by their initial attack angle when they contact the liquid interface, and that the range of attack angles leading to the end-on state is maximised when nanorods approach the liquid interface from the bulk phase that is more energetically favorable. In the absence of an external field, only a fraction of adsorbing nanorods end up in the end-on state (≲40% even for nanorods approaching from the energetically favourable phase). However, by pre-aligning the metallic nanorods with experimentally achievable electric fields, this fraction can be effectively increased to 100%. Using nanophotonic calculations, we also demonstrate that the resultant vertically aligned structures can be used as epsilon-near-zero and hyperbolic metamaterials. Our kinetic assembly method is applicable to nanorods with a range of diameters, aspect ratios and materials and therefore represents a versatile, low-cost and powerful platform for fabricating vertically aligned nanorods for metamaterial applications.

Chains of cubic colloids at fluid-fluid interfaces

Inspired by recent experimental observations of spontaneous chain formation of cubic particles adsorbed at a fluid-fluid interface, we theoretically investigate whether capillary interactions can be responsible for this self-assembly process. We calculate adsorption energies, equilibrium particle orientations, and interfacial deformations, not only for a variety of contact angles but also for single cubes as well as an infinite 2D lattice of cubes at the interface. This allows us to construct a ground-state phase diagram as a function of areal density for several contact angles, and upon combining the capillary energy of a 2D lattice with a simple expression for the entropy of a 2D fluid we also construct temperature-density or size-density phase diagrams that exhibit large two-phase regions and triple points. We identify several regimes with stable chainlike structures, in line with the experimental observations.

Solvent-Mediated Forces between Ellipsoidal Nanoparticles Adsorbed at Liquid-Vapor Interfaces

Classical capillary theory predicts that a non-neutrally wetting ellipsoidal particle adsorbed at a liquid-vapor interface will deform the interface. The deformation gives rise to anisotropic capillary forces of a quadrupolar nature that induce strong directionality in the particle interactions. Here, we investigate the interactions between nanoparticles with characteristic lengths of 1-5 nm. We show that the near-field interactions are dominated by solvent-mediated forces, which arise from the fluid packing between the nanoparticles and direct nanoparticle-nanoparticle interactions. The solvent-mediated forces are two orders of magnitude larger than the estimated capillary force. We find that interacting ellipsoidal nanoparticles adsorbed at the liquid-vapor interface have a larger repulsion in the depletion region than the nanoparticles submerged in a dense bulk phase and argue that this is because of a negative line tension associated with the three-phase line.

Interfacial viscoelasticity and jamming of colloidal particles at fluid-fluid interfaces: a review

Colloidal particles can be adsorbed at fluid-fluid interfaces, a phenomenon frequently observed in particle-stabilized foams, Pickering emulsions, and bijels. Particles adsorbed at interfaces exhibit unique physical and chemical behaviors, which affect the mechanical properties of the interface. Therefore, interfacial colloidal particles are of interest in terms of both fundamental and applied research. In this paper, we review studies on the adsorption of colloidal particles at fluid-fluid interfaces, from both thermodynamic and mechanical points of view, and discuss the differences as compared with surfactants and polymers. The unique particle interactions induced by the interfaces as well as the particle dynamics including lateral diffusion and contact line relaxation will be presented. We focus on the rearrangement of the particles and the resultant interfacial viscoelasticity. Particular emphasis will be given to the effects of particle shape, size, and surface hydrophobicity on the interfacial particle assembly and the mechanical properties of the obtained particle layer. We will also summarize recent advances in interfacial jamming behavior caused by adsorption of particles at interfaces. The buckling and cracking behavior of particle layers will be discussed from a mechanical perspective. Finally, we suggest several potential directions for future research in this area.

Single Droplet Assembly for Two-Dimensional Nanosheet Tiling

Recent advances in two-dimensional (2D) materials offer an opportunity for atomic layer engineering of functional thin films and superlattices. For future applications of 2D materials, there is an urgent need to develop convenient deposition processes that enable precise control of thin-film architectures while reducing the time, cost, and energy/sample consumption. Here, we demonstrate a strategy for nanosheet assembly using a simple drop casting with a pipet and a hot plate. By controlled thermal convection of a single droplet on a hot plate, a range of 2D nanosheets, such as Ti_0.87O₂^0.52-, Ca₂Nb₃O₁₀^-, Ru_0.95O₂^0.2-, and graphene oxide, can be neatly tiled to form an ideal monolayer on various substrates in ∼30 s over a wide area (i.e., a 50 mmϕ substrate). The mechanism and control strategies are discussed. We also demonstrate the production of various functional coatings such as conducting, semiconducting, insulating, magnetic, and photochromic coatings in multilayer, superlattice, and submicrometer-thick forms, offering the potential for a convenient way to produce high-quality 2D nanosheet films.

Static and dynamic behavior of magnetic particles at fluid interfaces

This perspective work reviews the current status of research on magnetic particles at fluid interfaces. The article gives both a unified overview of recent experimental advances and theoretical studies centered on very different phenomena that share a common characteristic: they involve adsorbed magnetic particles that range in size from a few nanometers to several millimeters. Because of their capability of being remotely piloted through controllable external fields, magnetic particles have proven essential as building blocks in the design of new techniques, smart materials and micromachines, with new tunable properties and prospective applications in engineering and biotechnology. Once adsorbed at a fluid-fluid interfase, in a process that can be facilitated via the application of magnetic field gradients, these particles often result sorely confined to two dimensions (2D). In this configuration, inter-particle forces directed along the perpendicular to the interface are typically very small compared to the surface forces. Hence, the confinement and symmetry breaking introduced by the presence of the surface play an important role on the response of the system to the application of an external field. In monolayers of particles where the magnetic is predominant interaction, the states reached are strongly determined by the mode and orientation of the applied field, which promote different patterns and processes. Furthermore, they can reproduce some of the dynamic assemblies displayed in bulk or form new ones, that take advantage of the interfacial phenomena or of the symmetry breaking introduce by the confining boundary. Magnetic colloids are also widely used for unraveling the guiding principles of 2D dynamic self-assembly, in designs devised for producing interface transport, as tiny probes for assessing interfacial rheological properties, neglecting the bulk and inertia contributions, as well as actuated stabilizing agents in foams and emulsions.

An Implicit-Solvent Model for the Interfacial Configuration of Colloidal Nanoparticles and Application to the Self-Assembly of Truncated Cubes

This study outlines the development of an implicit-solvent model that reproduces the behavior of colloidal nanoparticles at a fluid-fluid interface. The center point of this formulation is the generalized quaternion-based orientational constraint (QOCO) method. The model captures three major energetic characteristics that define the nanoparticle configuration-position (orthogonal to the interfacial plane), orientation, and inter-nanoparticle interaction. The framework encodes physically relevant parameters that provide an intuitive means to simulate a broad spectrum of interfacial conditions. Results show that for a wide range of shapes, our model is able to replicate the behavior of an isolated nanoparticle at an explicit fluid-fluid interface, both qualitatively and often nearly quantitatively. Furthermore, the family of truncated cubes is used as a test bed to analyze the effect of changes in the degree of truncation on the potential-of-mean-force landscape. Finally, our results for the self-assembly of an array of cuboctahedra provide corroboration to the experimentally observed honeycomb and square lattices.

Biophysical methods to quantify bacterial behaviors at oil-water interfaces

Motivated by the need for improved understanding of physical processes involved in bacterial biodegradation of catastrophic oil spills, we review biophysical methods to probe bacterial motility and adhesion at oil-water interfaces. This review summarizes methods that probe bulk, average behaviors as well as local, microscopic behaviors, and highlights opportunities for future work to bridge the gap between biodegradation and biophysics.

Detachment work of prolate spheroidal particles from fluid droplets: role of viscous dissipation

The force-displacement curve for removal of an elongated solid particle from the surface of liquid droplets or gas bubbles is calculated and compared to our previous reported results for spherical particles. The surface adsorption energy for prolate particles is known to be larger than that for spheres. We show that in fact the minimum possible work done upon removal of an elongated particle from surface can be less than that for a sphere. This result is obtained when the dissipation of interfacial energy, stored in the fluid film, attaching the particles to the surface during their displacement, is properly accounted for. This dissipation is unavoidable, even if the particles are removed infinitely slowly. Once the particle actually leaves the surface, the formed liquid bridge relaxes thus dissipating any stored interfacial energy as the surface returns to its original undistorted state. The difference between the work of removal of a particle from surface and its adsorption energy is seen to become increasingly larger with smaller particle to droplet size ratios. For example, for a size ratio of 1 : 100, the work of removal is 1.93 times greater than the adsorption energy. However, we also find that for any given size ratio, there is a value of particle aspect ratio for which the work of removal of particles (combined dissipated and adsorbed energy) attains its minimum value.

Vorticity-Aligned Droplet Bands in Sheared Immiscible Polymer Blends Induced by Solid Particles

The spatiotemporal organization of complex fluids under flow can be strongly affected by incorporating solid particles. Here, we report that a monolayer of interfacially active microspheres preferentially wetted by the matrix phase can bridge droplets into vorticity-aligned bands in immiscible polymer blends at intermediate particle concentrations and low shear rates. Strong particle bridging ability and the formation of rigid anisotropic droplet bands with a negligible inertia effect in the Newtonian matrix are suggested to be responsible for the vorticity orientation of droplet bands during slow shear flow, which could be understood based on Jeffery orbit theory in the framework of fluid mechanics and strong confinement effect acted by shear walls and adjacent bands. However, increasing the aspect ratio of particles could restrain the formation of anisotropic bands because of reduced particle coverage and promoted droplet coalescence induced by sharp particle corners, increased and uneven distribution of particle aggregates in the matrix phase, and weakened particle bridging ability.

Super-resolution microscopy on single particles at fluid interfaces reveals their wetting properties and interfacial deformations

Solid particles adsorbed at fluid interfaces are crucial for the mechanical stability of Pickering emulsions. The key parameter which determines the kinetic and thermodynamic properties of these colloids is the particle contact angle, θ. Several methods have recently been developed to measure the contact angle of individual particles adsorbed at liquid-liquid interfaces, as morphological and chemical heterogeneities at the particle surface can significantly affect θ. However, none of these techniques enables the simultaneous visualization of the nanoparticles and the reconstruction of the fluid interface to which they are adsorbed, in situ. To tackle this challenge, we utilize a newly developed super-resolution microscopy method, called iPAINT, which exploits non-covalent and continuous labelling of interfaces with photo-activatable fluorescent probes. Herewith, we resolve with nanometer accuracy both the position of individual nanoparticles at a water-octanol interface and the location of the interface itself. First, we determine single particle contact angles for both hydrophobic and hydrophilic spherical colloids. These experiments reveal a non-negligible dependence of θ on particle size, from which we infer an effective line tension, τ. Next, we image elliptical particles at a water-decane interface, showing that the corresponding interfacial deformations can be clearly captured by iPAINT microscopy.

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.

Shape-Anisotropic Colloids at Interfaces

Research in the 1980s demonstrated the formation of monolayers of particles achieved by interfacial particle trapping as a model system for investigating colloids in two dimensions. Since then, microscopy visualization of two-dimensional particle monolayers and quantification of the microstructure have led to significant fundamental understanding of a number of phenomena such as crystallization, freezing and melting transitions, dislocation dynamics, aggregation kinetics, and others. On the application front, particles at curved interfaces, as often the case in particle-stabilized emulsions and foams, have received considerable attention in the last few decades. The growing interest in the search for novel particles and new strategies to effect emulsion stabilization stems from their application in several disciplines. Moreover, particle-stabilized Pickering emulsions and foams can also be used to derive a number of advanced functional materials. Compared to several accounts of research on spherical colloids at fluid-fluid interfaces, investigations of the behavior of shape-anisotropic particles at interfaces, albeit receiving considerable attention in recent years, are still in a nascent stage. The objective of this feature article is to highlight our recent work in this area. In particular, the adsorption of shape-anisotropic particles to interfaces, wetting behavior, interfacial self-assembly, the response of nonspherical-particle-coated interfaces to compression and shear, and their ability to stabilize emulsions are discussed.

Capillary Interaction and Self-Assembly of Tilted Magnetic Ellipsoidal Particles at Liquid Interfaces

Magnetic ellipsoidal particles adsorbed at a liquid interface provide exciting opportunities for creating switchable functional materials, where self-assembly can be switched on and off using an external field [Davies et al., Adv. Mater., 2014, 26, 6715]. In order to gain a deeper understanding of this novel system in the presence of an external field, we study the capillary interaction and self-assembly of tilted ellipsoids using analytical theory and finite element simulations. We derive an analytical expression for the dipolar capillary interaction between tilted ellipsoids in elliptical polar coordinates, which exhibits a 1/r ² power law dependence in the far field (i.e., large particle separations r) and correctly captures the orientational dependence of the capillary interactions in the near field. Using this dipole potential and finite element simulations, we further analyze the energy landscape of particle clusters consisting of up to eight tilted ellipsoids in contact. For clusters of two particles, we find that the side-to-side configuration is stable, whereas the tip-to-tip configuration is unstable. However, for clusters of more than three particles, we find that circular loops of side-to-side particles become globally stable, whereas linear chains of side-to-side particles become metastable. Furthermore, the energy barrier for the linear-to-loop transition decreases with increasing particle number. Our results explain both thermodynamically and kinetically why tilted ellipsoids assemble side-to-side locally but have a strong tendency to form loops on larger length scales.

Adhesion of Marinobacter hydrocarbonoclasticus to Surfactant-Decorated Dodecane Droplets

We investigate the effect of interfacial properties on the adhesion of bacteria at oil/water interfaces using confocal microscopy. Surfactant-decorated dodecane droplets of diameter 20-60 μm are generated using a coflow microfluidic device, introduced into an aqueous saline suspension of Marinobacter hydrocarbonoclasticus bacteria, and imaged in 3-D over time. Using image analysis algorithms, we determine the number of bacteria adhering at oil/water interfaces over time in the presence of dioctyl sodium succinate (DOSS), a component of the dispersant used in oil-spill recovery. The adsorption of bacteria at the oil/water interface follows Langmuir first-order kinetics for all droplet sizes, with the greatest areal number density of bacteria adhered to the smallest droplets. We vary the surfactant type [DOSS, dicyclohexyl sodium sulfosuccinate, dibutyl sodium sulfosuccinate, cetyltrimethylammonium bromide, and Tween 20] and concentration and examine the effects on long-time adhesion of bacteria. For a fixed droplet size, the areal density of bacteria at the interface decreases with increasing surfactant concentration because of a reduction in oil/water interfacial tension that increases the free energy of adhesion of the bacterium.

Aggregation of nanoparticles regulated by mechanical properties of nanoparticle-membrane system

The aggregation of nanoparticles (NPs) on the cell membrane is crucial for the cellular uptake process and has important biological implications in protein-membrane interactions. In this paper, we systematically investigate how the aggregation is regulated by the mechanical properties of the NP-membrane system, including the membrane tension, and the size and shape of the NPs. Results show that when NPs aggregate parallel to the cell membrane, increasing the membrane tension will modulate the membrane-mediated interaction between the NPs from attractive to attractive-repulsive and finally to purely repulsive. In contrast, the membrane-mediated interaction is attractive and independent of the membrane tension when the NPs aggregate to a tubular configuration. For the aggregation of NPs of different sizes, the large-size NP is wrapped to a greater extent than the small-size NP. For the aggregation of nonspherical NPs, low aspect ratio and weak NP-membrane adhesion strength lead to the side-to-side configuration, whereas a system with a high aspect ratio and strong NP-membrane adhesion strength prefers the tip-to-tip configuration. Importantly, NPs of different sizes and anisotropic shapes are found to facilitate the aggregation process by reducing the energy barrier that should be overcome during the aggregation. The results reveal the mechanism of the aggregation of NPs on the cell membrane and provide guidelines to the design of NP-based drug delivery systems.

Seeded Emulsion Polymerization of Styrene in the Presence of Water-Swollen Hydrogel Microspheres

In a previous study, we have ascertained that the charge distribution in hydrogel microspheres (microgels) plays a crucial role in controlling the nanocomposite structure of the polystyrene obtained from the seeded emulsion polymerization (SEP) of styrene in the presence of microgels. However, all these polymerizations were conducted at high temperature, where most of these microgels were dehydrated and deswollen. In the present study, we initially verified that the nanocomposite microgels can be synthesized even when the seed microgels are swollen and hydrated during the SEP of styrene. These highly swollen microgels were used as the nucleation sites for the polystyrene, and subsequently the propagation of the hydrophobic polystyrenes proceeded within water-swollen microgels.

A review on suppression and utilization of the coffee-ring effect

Evaporation of sessile droplets containing non-volatile solutes dispersed in a volatile solvent leaves behind ring-like solid stains. As the volatile species evaporates, pinning of the contact line gives rise to capillary flows that transport non-volatile solutes to the contact line. This phenomenon, called the coffee-ring effect, compromises the overall performance of industrially relevant manufacturing processes involving evaporation such as printing, biochemical analysis, manufacturing of nano-structured materials through colloidal and macromolecular patterning. Various approaches have been developed to suppress this phenomenon, which is otherwise difficult to avoid. The coffee-ring effect has also been leveraged to prepare new materials through convection induced assembly. This review underlines not only the strategies developed to suppress the coffee-ring effect but also sheds light on approaches to arrive at novel processes and materials. Working principles and applicability of these strategies are discussed together with a critical comparison.

Conformations and membrane-driven self-organization of rodlike fd virus particles on freestanding lipid membranes

Membrane-mediated interactions and aggregation of colloidal particles adsorbed to responsive elastic membranes are challenging problems relevant for understanding the microscopic organization and dynamics of biological membranes. We experimentally study the behavior of rodlike semiflexible fd virus particles electrostatically adsorbed to freestanding cationic lipid membranes and find that their behavior can be controlled by tuning the membrane charge and ionic strength of the surrounding medium. Three distinct interaction regimes of rodlike virus particles with responsive elastic membranes can be observed. (i) A weakly charged freestanding cationic lipid bilayer in a low ionic strength medium represents a gentle quasi-2D substrate preserving the integrity, structure, and mechanical properties of the membrane-bound semiflexible fd virus, which under these conditions is characterized by a monomer length of 884 ± 4 nm and a persistence length of 2.5 ± 0.2 μm, in perfect agreement with its properties in bulk media. (ii) An increase in the membrane charge leads to the membrane-driven collapse of fd virus particles on freestanding lipid bilayers and lipid nanotubes into compact globules. (iii) When the membrane charge is low, and the mutual electrostatic repulsion of membrane-bound virus particles is screened to a considerable degree, membrane-driven self-organization of membrane-bound fd virus particles into long linear tip-to-tip aggregates showing dynamic self-assembly/disassembly and quasi-semiflexible behavior takes place. These observations are in perfect agreement with the results of recent theoretical and simulation studies predicting that membrane-mediated interactions can control the behavior of colloidal particles adsorbed on responsive elastic membranes.

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.

Self-Assembly of Silver Nanowire Ring Structures Driven by the Compressive Force of a Liquid Droplet

In a nanowire dispersed in liquid droplets, the interplay between the surface tension of the liquid and the elasticity of the nanowire determines the final morphology of the bent or buckled nanowire. Here, we investigate the fabrication of a silver nanowire ring generated as the nanowire encapsulated inside of fine droplets. We used a hybrid aerodynamic and electrostatic atomization method to ensure the generation of droplets with scalable size in the necessary regime for ring formation. We analytically calculate the compressive force of the droplet driven by surface tension as the key mechanism for the self-assembly of ring structures. Thus, for potential large-scale manufacturing, the droplet size provides a convenient parameter to control the realization of ring structures from nanowires.

Shape-Induced Deformation, Capillary Bridging, and Self-Assembly of Cuboids at the Fluid-Fluid Interface

The controlled assembly of anisotropic particles through shape-induced interface deformations is shown to be a potential route for the fabrication of novel functional materials. In this article, the shape-induced interface deformation, capillary bridging, and directed self-assembly of cuboidal-shaped hematite particles at fluid-fluid interfaces are reported. The multipolar nature of the interface distortions is directly visualized using high-resolution scanning electron microscopy and 3D optical surface profiling. The nature of the interface deformations around cuboidal particles vary from monopolar to octupolar types depending on their orientation and position with respect to the interface. The deformations are of either hexapolar or octupolar type in the face-up orientation, quadrupolar or monopolar type in the edge-up orientation, and monopolar type in the vertex-up orientation. The particles adsorbed at the interface interact through the interface deformations, forming capillary bridges that lead to isolated assemblies of two or more particles. The arrangement of particles in any assembly is such that the condition for capillary attraction is satisfied, that is, in accordance with predictions based on the nature of interface deformations. At sufficient particle concentrations, these isolated structures interact to form a percolating network of cuboids. Furthermore, the difference in the nature of the assembly structures formed at the air-water interface and in the bulk water phase indicates that the interfacial assembly of these particles is controlled by the capillary interactions.

Direct numerical simulation of gas-solid-liquid flows with capillary effects: An application to liquid bridge forces between spherical particles

In this study, a numerical method is developed to perform the direct numerical simulation (DNS) of gas-solid-liquid flows involving capillary effects. The volume-of-fluid method employed to track the free surface and the immersed boundary method is adopted for the fluid-particle coupling in three-phase flows. This numerical method is able to fully resolve the hydrodynamic force and capillary force as well as the particle motions arising from complicated gas-solid-liquid interactions. We present its application to liquid bridges among spherical particles in this paper. By using the DNS method, we obtain the static bridge force as a function of the liquid volume, contact angle, and separation distance. The results from the DNS are compared with theoretical equations and other solutions to examine its validity and suitability for modeling capillary bridges. Particularly, the nontrivial liquid bridges formed in triangular and tetrahedral particle clusters are calculated and some preliminary results are reported. We also perform dynamic simulations of liquid bridge ruptures subject to axial stretching and particle motions driven by liquid bridge action, for which accurate predictions are obtained with respect to the critical rupture distance and the equilibrium particle position, respectively. As shown through the simulations, the strength of the present method is the ability to predict the liquid bridge problem under general conditions, from which models of liquid bridge actions may be constructed without limitations. Therefore, it is believed that this DNS method can be a useful tool to improve the understanding and modeling of liquid bridges formed in complex gas-solid-liquid flows.

Deposition of Colloidal Drops Containing Ellipsoidal Particles: Competition between Capillary and Hydrodynamic Forces

Ellipsoidal particles have previously been shown to suppress the coffee-ring effect in millimeter-sized colloidal droplets. Compared to their spherical counterparts, ellipsoidal particles experience stronger adsorption energy to the drop surface where the anisotropy-induced deformation of the liquid-air interface leads to much greater capillary attractions between particles. Using inkjet-printed colloidal drops of varying drop size, particle concentration, and particle aspect ratio, the present work demonstrates how the suppression of the coffee ring is not only a function of particle anisotropy but rather a competition between the propensity for particles to assemble at the drop surface via capillary interactions and the evaporation-driven particle motion to the contact line. For ellipsoidal particles on the drop surface, the capillary force (F_γ) increases with the particle concentration and aspect ratio, and the hydrodynamic force (F_μ) increases with the particle aspect ratio but decreases with drop size. When F_γ/F_μ > 1, the surface ellipsoids form a coherent network inhibiting their migration to the drop contact line, and the coffee-ring effect is suppressed, whereas when F_γ/F_μ < 1, the ellipsoids move to the contact line, resulting in coffee-ring deposition.

Interactions of rod-like particles on responsive elastic sheets

What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive-repulsive rod-rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.

Translational viscous drags of an ellipsoid straddling an interface between two fluids

We study the dynamics of individual polystyrene ellipsoids of different aspect ratios trapped at the air-water interface. Using particle tracking and in situ vertical scanning interferometry techniques we are able to measure translational drags and the protrusion in air of the ellipsoids. We report that translational drags on the ellipsoid are unexpectedly enhanced: despite the fact that a noticeable part of the ellipsoid is in air, drags are found larger than the bulk one in water.

Magnetic cylindrical colloids at liquid interfaces exhibit non-volatile switching of their orientation in an external field

We study the orientation of magnetic cylindrical particles adsorbed at a liquid interface in an external field using analytical theory and high resolution finite element simulations. Cylindrical particles are interesting since they possess multiple locally stable orientations at the liquid interface so that the orientational transitions induced by an external field will not disappear when the external field is removed, i.e., the switching effect is non-volatile. We show that, in the absence of an external field, as we reduce the aspect ratio α of the cylinders below a critical value (αc≈ 2) the particles undergo spontaneous symmetry breaking from a stable side-on state to one of two equivalent stable tilted states, similar to the spontaneous magnetisation of a ferromagnet going through the Curie point. By tuning both the aspect ratio and contact angle of the cylinders, we show that it is possible to engineer particles that have one, two, three or four locally stable orientations. We also find that the magnetic responses of cylinders with one or two stable states are similar to that of paramagnets and ferromagnets respectively, while the magnetic response of systems with three or four stable states are even more complex and have no analogs in simple magnetic systems. Magnetic cylinders at liquid interfaces therefore provide a facile method for creating switchable functional monolayers where we can use an external field to induce multiple non-volatile changes in particle orientation and self-assembled structure.

Near-post meniscus-induced migration and assembly of bubbles

Although the effect of interfacial tension of liquids is often negligible at the macroscale, it plays an essential role in areas such as superhydrophobicity on rough surfaces, water walking of aquatic creatures and self-assembly of small particles or droplets. In this study, we investigate the migration and assembly of bubbles near the meniscus produced by a slender post with various cross-sections. The results show that the bubble always migrates to the solid wall of the post, although the cross-section shape, material and tilt angle of the post are different. In particular, the final position of the bubble is not located at the singular point of the cross-section, which is beyond what we have imagined. We simulate the morphology of the triple contact line via Surface Evolver, and then address the mechanism of bubble's migration from the viewpoint of force analysis and energy calculation. The factors governing the final position of the bubble are analyzed according to the scaling law. These obtained results cast new light on modulating the assembly of bubbles and small droplets by varying the material, geometric shape and posture of the post in water. These findings also have important implications for oil collection and oil displacement in petroleum engineering, drug delivery, design of microfluidic devices and chemical sensors.

Capillary force and torque on spheroidal particles floating at a fluid interface beyond the superposition approximation

By means of a perturbative scheme, we determine analytically the capillary energy of a spheroidal colloid floating on a deformed fluid interface in terms of the local curvature tensor of the background deformation. We validate our results, that hold for small ellipticity of the particle and small deformations of the surface, by an exact numerical calculation. As an application of our perturbative approach, we determine the asymptotic interaction, for large separations d, between two different spheroidal particles. The dominant contribution is quadrupolar and proportional to d(-4). It coincides with the known superposition approximation and is zero if one of the two particles is spherical. The next to leading approximation, proportional to d(-8), is always attractive and independent of the orientation of the two colloids. It is the dominant contribution to the interaction between a spheroidal and a spherical colloid.

Tunable dipolar capillary deformations for magnetic Janus particles at fluid-fluid interfaces

Janus particles have attracted significant interest as building blocks for complex materials in recent years. Furthermore, capillary interactions have been identified as a promising tool for directed self-assembly of particles at fluid-fluid interfaces. In this paper, we develop theoretical models describing the behaviour of magnetic Janus particles adsorbed at fluid-fluid interfaces interacting with an external magnetic field. Using numerical simulations, we test the models predictions and show that the magnetic Janus particles deform the interface in a dipolar manner. We suggest how to utilise the resulting dipolar capillary interactions to assemble particles at a fluid-fluid interface, and further demonstrate that the strength of these interactions can be tuned by altering the external field strength, opening up the possibility to create novel, reconfigurable materials.

Entropic self-assembly of freely rotating polyhedral particles confined to a flat interface

The self-assembly of hard polyhedral particles confined to a flat interface is studied using Monte Carlo simulations. The particles are pinned to the interface by restricting their movement in the direction perpendicular to it while allowing their free rotations. The six different polyhedral shapes studied in this work are selected from a family of truncated cubes defined by a truncation parameter, s, which varies from cubes (s = 0) via cuboctahedra (s = 0.5) to octahedra (s = 1). Our results suggest that shapes with small values of s show square-like behavior whereas shapes with large values of s tend to show more disc-like behavior. At an intermediate value of s = 0.4, the phase behavior of the system shows both square-like and disc-like features. The results are also compared with the phase behavior of 3D bulk polyhedra and of 2D rounded hard squares. Both comparisons reveal key similarities in the number and sequence of mesophases and solid phases observed. These insights on 2D entropic self-assembly of polyhedral particles is a first step toward understanding the self-assembly of particles at fluid-fluid interfaces, which is driven by a complex interplay of entropic and enthalpic forces. A first-order analysis of the particle-surface energies associated with a fluid-fluid interface indicates that such enthalpic interactions will be particularly important in determining particle orientation behavior at low to intermediate concentrations.