Capillary forces between spherical particles floating at a liquid-liquid interface

Quorum Sensing in Emulsion Droplet Swarms Driven by a Surfactant Competition System

Quorum sensing enables unicellular organisms to probe their population density and perform behavior that exclusively occurs above a critical density. Quorum sensing is established in emulsion droplet swarms that float at a water surface and cluster above a critical density. The design involves competition between 1) a surface tension gradient that is generated upon release of a surfactant from the oil droplets, and thereby drives their mutual repulsion, and 2) the release of a surfactant precursor from the droplets, that forms a strong imine surfactant which suppresses the surface tension gradient and thereby causes droplet clustering upon capillary (Cheerios) attraction. The production of the imine-surfactant depends on the population density of the droplets releasing the precursor so that the clustering only occurs above a critical population density. The pH-dependence of the imine-surfactant formation is exploited to trigger quorum sensing upon a base stimulus: dynamic droplet swarms are generated that cluster and spread upon spatiotemporally varying acid and base conditions. Next, the clustering of two droplet subpopulations is coupled to a chemical reaction that generates a fluorescent signal. It is foreseen that quorum sensing enables control mechanisms in droplet-based systems that display collective responses in contexts of, e.g., sensing, optics, or dynamically controlled droplet-reactors.

Facile and Programmable Capillary-Induced Assembly of Prototissues via Hanging Drop Arrays

An important goal for bottom-up synthetic biology is to construct tissue-like structures from artificial cells. The key is the ability to control the assembly of the individual artificial cells. Unlike most methods resorting to external fields or sophisticated devices, inspired by the hanging drop method used for culturing spheroids of biological cells, we employ a capillary-driven approach to assemble giant unilamellar vesicles (GUVs)-based protocells into colonized prototissue arrays by means of a coverslip with patterned wettability. By spatially confining and controllably merging a mixed population of lipid-coated double-emulsion droplets that hang on a water/oil interface, an array of synthetic tissue-like constructs can be obtained. Each prototissue module in the array comprises multiple tightly packed droplet compartments where interfacial lipid bilayers are self-assembled at the interfaces both between two neighboring droplets and between the droplet and the external aqueous environment. The number, shape, and composition of the interconnected droplet compartments can be precisely controlled. Each prototissue module functions as a processer, in which fast signal transports of molecules via cell-cell and cell-environment communications have been demonstrated by molecular diffusions and cascade enzyme reactions, exhibiting the ability to be used as biochemical sensing and microreactor arrays. Our work provides a simple yet scalable and programmable method to form arrays of prototissues for synthetic biology, tissue engineering, and high-throughput assays.

Measuring lateral capillary forces on floating particles using the Moses effect

This study presents a novel and user-friendly technique for detecting the lateral capillary force on a floating spherical particle. The technique leverages the interplay between the capillary attracting forces, hydrostatic pressure forces, and magnetic repulsion forces. A magnetic field is applied to induce a surface curvature in the liquid, resulting in a non-uniform distribution of capillary and hydrostatic pressure forces across the particle's surface. This leads to a stable equilibrium position of the particle at a specific distance from the magnet. The study analyzes the equilibrium position and other relevant parameters in comparison with the developed theory. Classical mechanics and intermolecular forces are applied to establish the theoretical basis for the method, modeling the behavior of the particle in response to the magnetic field, surface curvature, and hydrostatic pressure. The equilibrium position of the particle is determined by numerically solving the balance of forces equation.

Investigation of the Orientation and Assembly of Functionalized Microcubes at the Oil-Water Interface

The dependence of the preferred orientation of polystyrene microcubes on surface hydrophobicity at the water/hexadecane interface is reported. Similar to the water/air interfaces, the microcubes were shown to reside at the water/hexadecane interface with three distinct orientations: face-up, edge-up, and vertex-up. Concomitantly, ordered aggregates with flat plate, tilted linear, and close-packed hexagonal structures were formed, driven by capillary force. With increasing the hydrophobicity of five sides of the cubes, the preferential microcube orientation at the water/hexadecane interface changed sequentially from face-up to edge-up, to vertex-up, then back to edge-up, and to face-up. This dependence of the preferential microcube orientation on surface hydrophobicity at the water/hexadecane interface differs from that observed at the water/air interface, where the preferential orientation changed only from face-up to edge-up, then to vertex-up, as surface hydrophobicity increased. In addition, preformed microcube assemblies at the water/air interface could be dynamically reconfigured by replacing the air phase with hexadecane under stirring.

Hydrodynamic interactions between charged and uncharged Brownian colloids at a fluid-fluid interface

HYPOTHESIS

The cluster formation and self-assembly of floating colloids at a fluid/fluid interface is a delicate force balance involving deterministic lateral interaction forces, viscous resistance to relative colloid motion along the surface and thermal (Brownian) fluctuations. As the colloid dimensions get smaller, thermal forces and associated drag forces become important and can affect the self assembly into ordered patterns and crystal structures that are the starting point for various materials applications.

NUMERICS

Langevin dynamic simulations for particle pairs straddling a liquid-liquid interface with a high viscosity contrast are presented to describe the lateral interfacial assembly of particles in Brownian and non-Brownian dominated regimes. These simulations incorporate capillary attraction, electrostatic repulsion, thermal fluctuations and hydrodynamic interactions (HI) between particles (including the effect of the particle immersion depth). Simulation results are presented for neutrally wetted particles which form a contact angle θ=90⁰ at the interface.

FINDINGS

The simulation results suggest that clustering, fractal growth and particle ordering become favorable outcomes at critically large values of the Pe numbers, while smaller Pe numbers exhibit higher probabilities of final configurations where particle motion remains uncorrelated in space and particle pairs are found to be more widely separated especially upon the introduction of HI.

Dielectrowetting Control of Capillary Force (Cheerios Effect) between Floating Objects and Wall for Dielectric Fluid

A capillary interaction between floating objects and adjacent walls, which is known as “Cheerios effect”, is a common phenomenon that generates capillary attraction or repulsion forces between them depending on their wettabilities, densities, geometries, and so on. This paper deals with controlling the capillary forces, specifically, acting on objects floating on a dielectric (non-conductive) fluid. A key control input parameter is the wettability (contact angle) of the sidewall adjacent to the floating object. By introducing dielectrowetting to the sidewall and actively changing the contact angle on the sidewall, the capillary force is controlled and easily reversed between attraction and repulsion. In this reversing process, the tilting angle of the sidewall is another critical parameter. A theoretical relation taking the titling angle into account is compared and in good agreement with experimental results obtained from the trajectory of the floating object. Finally, a continuous motion of the floating object is demonstrated using this control where an array of dielectrowetting electrode pads is sequentially activated.

Particle rotation speeds up capillary interactions

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

Janus Particles at Fluid Interfaces: Stability and Interfacial Rheology

The use of the Janus motif in colloidal particles, i.e., anisotropic surface properties on opposite faces, has gained significant attention in the bottom-up assembly of novel functional structures, design of active nanomotors, biological sensing and imaging, and polymer blend compatibilization. This review is focused on the behavior of Janus particles in interfacial systems, such as particle-stabilized (i.e., Pickering) emulsions and foams, where stabilization is achieved through the binding of particles to fluid interfaces. In many such applications, the interface could be subjected to deformations, producing compression and shear stresses. Besides the physicochemical properties of the particle, their behavior under flow will also impact the performance of the resulting system. This review article provides a synopsis of interfacial stability and rheology in particle-laden interfaces to highlight the role of the Janus motif, and how particle anisotropy affects interfacial mechanics.

Drag force on a particle straddling a fluid interface: Influence of interfacial deformations

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

Interactions between polystyrene particles with diameters of several tens to hundreds of micrometers at the oil-water interface

HYPOTHESIS

The charged spherical colloidal particles at the fluid-fluid interface experience considerably strong and long-ranged electrostatic and capillary interactions. The contribution of capillary force becomes more significant as the particle size increases beyond a certain limit. The relative strengths of the two competing interactions between the spherical polystyrene particles at the oil-water interface are quantified depending on their size.

EXPERIMENTS

The studied particles, obtained using the microfluidic method, have diameters of tens to hundreds of micrometers. The scaling behaviors of the commercially available colloidal particles with diameters of ~3 μm are also compared. An optical laser tweezer apparatus is used to directly or indirectly measure the interparticle force. Subsequently, the capillary force that can be attributed to the gravity-induced interface deformation and contact line undulation is calculated and compared with the measured interaction force.

FINDINGS

Regardless of the particle diameter (~3-330 μm), the measured force is observed to decay as r^-4, where r denotes the center-to-center separation, demonstrating that the dipolar electrostatic interaction is important and that the gravity-induced capillary interaction is negligible. Furthermore, numerical calculations with respect to the undulated meniscus confirm that the magnitude of capillary interaction is significantly smaller than that of the measured electrostatic interaction.

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.

The capillary interaction between pairs of granular rafts

When an object is placed at the surface of a liquid, its weight deforms the interface. For two identical spherical objects, such a deformation creates an attractive force, leading to the aggregation of the two-body system. Here, we experimentally investigate the interaction between two granular rafts, formed by the aggregation of dense millimeter-sized beads placed at an oil-water interface. The interfacial deformation created by such a two-dimensional object exceeds by at least an order of magnitude the deformation of a single bead. This leads to unusually high capillary forces which strongly depend on the number of particles. Likewise, because the raft grows in size as more particles are added, the viscous drag experienced increases along with the capillary attraction, leading to a non-trivial dependence of the balance of forces on the number of beads. By studying the relative motion of two granular rafts in relation with the interfacial deformation they generate, we derive a model for the observed speed profiles. With this work, we generalize how the capillary interaction between two non-identical complex structures evolves with their respective geometry.

Dynamic capillary assembly of colloids at interfaces with 10,000g accelerations

High-rate deformation of soft matter is an emerging area central to our understanding of far-from-equilibrium phenomena during shock, fracture, and phase change. Monolayers of colloidal particles are a convenient two-dimensional model system to visualise emergent behaviours in soft matter, but previous studies have been limited to slow deformations. Here we probe and visualise the evolution of a monolayer of colloids confined at a bubble surface during high-rate deformation driven by ultrasound. We observe the emergence of a transient network of strings, and use discrete particle simulations to show that it is caused by a delicate interplay of dynamic capillarity and hydrodynamic interactions between particles oscillating at high frequency. Remarkably for a colloidal system, we find evidence of inertial effects, caused by accelerations approaching 10,000g. These results also suggest that extreme deformation of soft matter offers new opportunities for pattern formation and dynamic self-assembly.

Experimental and Theoretical Validation of System Variables That Control the Position of Particles at the Interface of Immiscible Liquids

We construct a mathematical model describing the equilibrium flotation height of a spherical particle at the interface of immiscible liquids. The behavior of such a system depends on several experimentally measurable parameters, which include surface tensions, densities of all phases, and system scale. These parameters can be absorbed into three quantities that entirely determine the equilibrium position of the particle: the contact angle between the interface and particle, the Bond number, and the ratio of particle buoyant density to liquid phase densities-a new, dimensionless number that we introduce here. This experimentally convenient treatment allows us to make predictions that apply generally to the large parameter space of interesting systems. We find the model is in good agreement with experiments for particle size and interfacial tension spanning 3 orders of magnitude. We also consider the low interfacial tension case of aqueous two-phase systems (ATPSs) theoretically and experimentally. Such systems are more sensitive to changes in density than higher-tension aqueous/organic two-phase systems; we experimentally demonstrate that a millimeter-sized bead in an ATPS can be controllably positioned with between 5.9 and 95.1% of its surface area exposed to the bottom phase, whereas the same bead in an aqueous/organic system is limited to a range of 18.2-61.6%. Finally, we discuss the potential for wettability-based control for micron length-scale particles, which are not sensitive to changes in density. Our results can be used to simply define the experimentally controllable parameters that affect the equilibrium position and the length scales of a particle over which such parameters can be effectively tuned. A complete understanding of these properties is important for a number of applications including colloidal self-assembly and chemical patterning (e.g., formation of desymmetrized or Janus particles). By considering ATPSs, we broaden the potential uses to biological applications such as cell separation and interfacial tissue assembly.

Capillary interactions between dynamically forced particles adsorbed at a planar interface and on a bubble

We investigate the dynamic interfacial deformation induced by micrometric particles exerting a periodic force on a planar interface or on a bubble, and the resulting lateral capillary interactions. Assuming that the deformation of the interface is small, neglecting the effect of viscosity, and assuming point particles, we derive analytical formulas for the dynamic deformation of the interface. For the case of a planar interface the dynamic point force simply generates capillary waves, while for the case of a bubble it excites shape oscillations, with a dominat deformation mode that depends on the bubble radius for a given forcing frequency. We evaluate the lateral capillary force acting between two particles, by superimposing the deformations induced by two point forces. We find that the lateral capillary forces experienced by dynamically forced particles are non monotonic and can be repulsive. The results are applicable to micrometric particles driven by different dynamic forcing mechanisms such as magnetic, electric or acoustic fields.

The Translational and Rotational Dynamics of a Colloid Moving Along the Air-Liquid Interface of a Thin Film

This study examines the translation and rotation of a spherical colloid straddling the (upper) air/liquid interface of a thin, planar, liquid film bounded from below by either a solid or a gas/liquid interface. The goal is to obtain numerical solutions for the hydrodynamic flow in order to understand the influence of the film thickness and the lower interface boundary condition. When the colloid translates on a film above a solid, the viscous resistance increases significantly as the film thickness decreases due to the fluid-solid interaction, while on a free lamella, the drag decreases due to the proximity to the free (gas/liquid) surface. When the colloid rotates, the contact line of the interface moves relative to the colloid surface. If no-slip is assumed, the stress becomes infinite and prevents the rotation. Here finite slip is used to resolve the singularity, and for small values of the slip coefficient, the rotational viscous resistance is dominated by the contact line stress and is surprisingly less dependent on the film thickness and the lower interface boundary condition. For a colloid rotating on a semi-infinite liquid layer, the rotational resistance is largest when the colloid just breaches the interface from the liquid side.

2D Stokesian Approach to Modeling Flow Induced Deformation of Particle Laden Interfaces

A Stokesian dynamics simulation of the effect of surface Couette flow on the microstructure of particles irreversibly adsorbed to an interface is presented. Rather than modeling both bulk phases, the interface, and particles in a full 3D simulation, known interfacial interactions between adsorbed particles are used to create a 2D model from a top down perspective. This novel methodology is easy to implement and computationally inexpensive, which makes it favorable to simulate behavior of particles under applied flow at fluid-fluid interfaces. The methodology is used to examine microstructure deformation of monodisperse, rigid spherical colloids with repulsive interactions when a surface Couette flow is imposed. Simulation results compare favorably to experimental results taken from literature, showing that interparticle forces must be 1 order of magnitude greater than viscous drag for microstructure to transition from aligned particle strings to rotation of local hexagonal domains. Additionally, it is demonstrated that hydrodynamic interactions between particles play a significant role in the magnitude of these microstructure deformations.

Self-Assembly of Mesoscale Artificial Clathrin Mimics

Fluidic control and sampling in complex environments is an important process in biotechnology, materials synthesis, and microfluidics. An elegant solution to this problem has evolved in nature through cellular endocytosis, where the dynamic recruitment, self-assembly, and spherical budding of clathrin proteins allows cells to sample their external environment. Yet despite the importance and utility of endocytosis, artificial systems which can replicate this dynamic behavior have not been developed. Guided by clathrin's unusual structure, we created simplified metallic microparticles that capture the three-legged shape, particle curvature, and interfacial attachment characteristics of clathrin. These artificial clathrin mimics successfully recreate biomimetic analogues of clathrin's recruitment, assembly, and budding, ultimately forming extended networks at fluid interfaces and invaginating immiscible phases into spheres under external fields. Particle curvature was discovered to be a critical structural motif, greatly limiting irreversible aggregation and inducing the legs' selective tip-to-tip attraction. This architecture provides a template for a class of active self-assembly units to drive structural and dimensional transformations of liquid-liquid interfaces and microscale fluidic sampling.

Electrokinetic motion of a spherical micro particle at an oil-water interface in microchannel

The electrokinetic motion of a negatively charged spherical particle at an oil-water interface in a microchannel is numerically investigated and analyzed in this paper. A three-dimensional (3D) transient numerical model is developed to simulate the particle electrokinetic motion. The channel wall, the surface of the particle and the oil-water interface are all considered negatively charged. The effects of the direct current (DC) electric field, the zeta potentials of the particle-water interface and the oil-water interface, and the dynamic viscosity ratio of oil to water on the velocity of the particle are studied in this paper. In addition, the influences of the particle size are also discussed. The simulation results show that the micro-particle with a small value of negative zeta potential moves in the same direction of the external electric field. However, if the zeta potential value of the particle-water interface is large enough, the moving direction of the particle is opposite to that of the electric field. The velocity of the particle at the interface increases with the increase in the electric field strength and the particle size, but decreases with the increase in the dynamic viscosity ratio of oil to water, and the absolute value of the negative zeta potentials of both the particle-water interface and the oil-water interface. This work is the first numerical study of the electrokinetic motion of a charged particle at an oil-water interface in a microchannel.

Measuring the Coefficient of Friction of a Small Floating Liquid Marble

This paper investigates the friction coefficient of a moving liquid marble, a small liquid droplet coated with hydrophobic powder and floating on another liquid surface. A floating marble can easily move across water surface due to the low friction, allowing for the transport of aqueous solutions with minimal energy input. However, the motion of a floating marble has yet to be systematically characterised due to the lack of insight into key parameters such as the coefficient of friction between the floating marble and the carrier liquid. We measured the coefficient of friction of a small floating marble using a novel experimental setup that exploits the non-wetting properties of a liquid marble. A floating liquid marble pair containing a minute amount magnetite particles were immobilised and then released in a controlled manner using permanent magnets. The capillarity-driven motion was analysed to determine the coefficient of friction of the liquid marbles. The "capillary charge" model was used to fit the experimental results. We varied the marble content and carrier liquid to establish a relationship between the friction correction factor and the meniscus angle.

Hydrodynamics of Particles at an Oil-Water Interface

This study is a theoretical and experimental investigation of the hydrodynamics of the mutual approach of two floating spherical particles moving along an oil-water interface. An analytical expression is obtained for the (inertialess) Stokes drag for an isolated particle translating on a flat interface as a function of the immersion depth into the water phase for the case in which the viscosity of the oil is much larger than that of the water. An approximation for the viscous drag due to the mutual approach of identical spheres is formulated as the product of the isolated drag multiplied by the resistance of approaching spheres in an infinite medium. Experiments are undertaken on the capillary attraction of large, millimeter-sized Teflon spheres floating at the interface between a very viscous oil and water. With the use of image visualization and particle tracking, the separation distance as a function of time [[Formula: see text](t)] is measured along with the immersion depth and predicted by setting the capillary attraction force equal to the viscous drag resistance. The excellent agreement validates the approximating formula.

Cheerios Effect Controlled by Electrowetting

The Cheerios effect is a common phenomenon in which small floating objects are either attracted or repelled by the sidewall due to capillary interaction. This attractive or repulsive behavior is highly dependent on the slope angles (angles of the interface on the wall or floating object with respect to a horizontal line) that can be mainly controlled by the wettability of the wall and floating object and the density of the object. In this paper, electrowetting on dielectric (EWOD) is implemented to the wall or floating object in order to actively control the wettability and thus capillary interaction. As such, the capillary force on buoyant and dense floating objects can be easily switched between repulsion and attraction by simply applying an electrical input. In addition, the theoretical prediction for the capillary force is verified experimentally by measuring the motion of floating particle and the critical contact angle on the wall at which the capillary force changes from attraction to repulsion. This successive verification is enabled by the merit of EWOD that allows for continuous change in the contact angle. Finally, the control method is extended to continuously move a floating object along a linear path and to continuously rotate a dumbbell-like floating object in centimeter scales using arrays of EWOD electrodes. A continuous linear motion is also accomplished in a smaller scale where the channel width (3 mm) is comparable to the capillary length.

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.

Tunable capillary-induced attraction between vertical cylinders

Deformation of a fluid interface caused by the presence of objects at the interface can lead to large lateral forces between objects. We explore these fluid-mediated attractive force between partially submerged vertical cylinders. Forces are experimentally measured by slowly separating cylinder pairs and cylinder triplets after capillary rise is initially established for cylinders in contact. For cylinder pairs, numerical computations and a theoretical model are found to be in good agreement with measurements. The model provides insight into the relative importance of the contributions to the total force. For small separations, the lateral force is dominated by the fluid pressure acting over the wetted cylinder surfaces. At large separations, the surface tension acting along the contact line dominates the lateral force. A crossover between the two regimes occurs at a separation of around half of a capillary length. The experimentally measured forces between cylinder triplets are also in good agreement with numerical computations, and we show that pairwise contributions account for nearly all of the attractive force between triplets. For cylinders with an equilibrium capillary rise height greater than the height of the cylinder, we find that the attractive force depends on the height of the cylinders above the submersion level, which provides a means to create precisely controlled tunable cohesive forces between objects deforming a fluid interface.

Capillary-bridge-derived particles with negative Gaussian curvature

We report the preparation of millimeter-scale particles by thermal polymerization of liquid monomer capillary bridges to form catenoid-shaped particles that exhibit negative Gaussian curvature. The shape of the capillary bridges and resulting particles can be finely tuned using several addressable parameters: (i) the shape, size, and orientation of lithographic pinning features on the spanned surfaces; (ii) the distance between opposing support surfaces; and (iii) the lateral displacement (shear) of opposing features. The catenoid-shaped particles exhibit controllable optical properties as a result of their concave menisci, the shape of which can be easily manipulated. The particles self assemble in the presence of a condensing liquid (water) to form reversible neck-to-neck pairs and less reversible end-to-end aggregates. We argue that this approach could be scaled down to micrometer dimensions by fabricating an array of micrometer-scale particles. We also argue, with a discussion of dynamic wetting, that these particles will exhibit interesting anisotropic adhesive properties.

Analysis of menisci formed on cones for single field of view parasite egg microscopy

Parasite ova caused to accumulate in a single microscopic field simplifies monitoring soil-transmitted helminthiasis by optical microscopy. Here we demonstrate new egg-accumulating geometries based on annular menisci formed on the surface of a wetted cone. Fluidic features extracted from profile images of the system provided mathematical representations of the meniscus gradient that were compared quantitatively to numerical solutions of an axisymmetric Young-Laplace equation. Our results show that the governing dynamics of these systems is dominated by the surface tension of the fluid. These image analysis and mathematical tools provide simple quantitative methods for system analysis and optimization.

From antinode clusters to node clusters: the concentration-dependent transition of floaters on a standing Faraday wave

A hydrophilic floating sphere that is denser than water drifts to an amplitude maximum (antinode) of a surface standing wave. A few identical floaters therefore organize into antinode clusters. However, beyond a transitional value of the floater concentration ϕ, we observe that the same spheres spontaneously accumulate at the nodal lines, completely inverting the self-organized particle pattern on the wave. From a potential energy estimate we show (i) that at low ϕ antinode clusters are energetically favorable over nodal ones and (ii) how this situation reverses at high ϕ, in agreement with the experiment.

Elastocapillary interaction of particles on the surfaces of ultrasoft gels: a novel route to study self-assembly and soft lubrication

We study the interaction of small hydrophobic particles on the surface of an ultrasoft elastic gel, in which a small amount of elasticity of the medium balances the weights of the particles. The excess energy of the surface of the deformed gel causes them to attract as is the case with the generic capillary interactions of particles on a liquid surface. The variation of the gravitational potential energies of the particles resulting from their descents in the gel coupled with the superposition principle of Nicolson allow a fair estimation of the distance dependent attractive energy of the particles. This energy follows a modified Bessel function of the second kind with a characteristic elastocapillary decay length that decreases with the elasticity of the medium. An interesting finding of this study is that the particles on the gel move toward each other as if the system possesses a negative diffusivity that is inversely proportional to friction. This study illustrates how the capillary interaction of particles is modified by the elasticity of the medium, which is expected to have important implications in the surface force driven self-assembly of particles. In particular, this study points out that the range and the strength of the capillary interaction can be tuned in by appropriate choices of the elasticity of the support and the interfacial tension of the surrounding medium. Manipulation of the particle interactions is exemplified in such fascinating mimicry of the biological processes as the tubulation and phagocytic engulfment and in the assembly of particles that can be used to study nucleation and clustering phenomena in well-controlled settings.

Equilibrium orientation of nonspherical Janus particles at fluid-fluid interfaces

We study the equilibrium orientation of nonspherical Janus particles at an oil-water interface. Two types of nonspherical Janus particles are considered: Janus ellipsoids and Janus dumbbells. To find their equilibrium orientation, we calculate and minimize the attachment energy of each Janus particle as a function of its orientation angle with respect to the oil-water interface. We find that the equilibrium orientation of the interface trapped Janus particles strongly depends on the particle characteristics, such as their size, aspect ratio, and surface properties. In general, nonspherical Janus particles adopt the upright orientation (i.e., the long axis of ellipsoids or dumbbells is perpendicular to the interface) if the difference in the wettability of the two sides is large or if the particle aspect ratio is close to 1. In contrast, Janus particles with a large aspect ratio or a small difference in the wettability of the two regions tend to have a tilted orientation at equilibrium. Moreover, we find that Janus ellipsoids, under appropriate conditions, can be kinetically trapped in a metastable state due to the presence of a secondary energy minimum. In contrast, Janus dumbbells possess only a primary energy minimum, indicating that these particles prefer to be in a single orientation. The absence of a secondary minimum is potentially advantageous for obtaining particle layers at fluid-fluid interfaces with uniform orientation. Our calculation provides a detailed guidance for synthesizing nonspherical Janus particles that can be used as effective solid surfactants for the stabilization of multiphasic fluid mixtures and the modification of the rheological properties of fluid interfaces.

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.

Aggregation of frictional particles due to capillary attraction

Capillary attraction between identical millimeter-sized spheres floating at a liquid-air interface and the resulting aggregation are investigated at low Reynolds number. We show that the measured capillary forces between two spheres as a function of distance can be described by expressions obtained using the Nicolson approximation at low Bond numbers for far greater particle sizes than previously assumed. We find that viscous hydrodynamic interactions between the spheres needs to be included to describe the dynamics close to contact. We then consider the aggregates formed when a third sphere is added after the initial two spheres are already in contact. In this case, we find that linear superposition of capillary forces describes the observed approach qualitatively but not quantitatively. Further, we observe an angular dependence of the structure due to a rapid decrease of capillary force with distance of separation, which has a tendency to align the particles before contact. When the three particles come into contact, they may preserve their shape or rearrange to form an equilateral triangle cluster-the lowest-energy state-depending on the competition between attraction between particles and friction. Using these observations, we demonstrate that a linear particle chain can be built from frictional particles with capillary attraction.

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.

Optical trapping forces for colloids at the oil-water interface

We calculate the optical trapping forces exerted by a single laser beam strongly focused on a dielectric sphere located at a two-dimensional (2D) oil-water interface. The calculated lateral trapping forces, based on the geometrical optics approximation (GOA), agree with experimental measurements of the trapping force. Importantly, the calculations verify that the radiation force exerted on particles perpendicular to the interface is not sufficient to induce capillary interactions between particle pairs, which could be mistaken for particle-particle interactions. Finally, we find that the trapping forces depend on the three-phase contact angle of the particle at the interface.

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.

Direct measurements of the effects of salt and surfactant on interaction forces between colloidal particles at water-oil interfaces

The forces between colloidal particles at a decane-water interface, in the presence of low concentrations of a monovalent salt (NaCl) and the surfactant sodium dodecyl sulfate (SDS) in the aqueous subphase, have been studied using laser tweezers. In the absence of electrolyte and surfactant, particle interactions exhibit a long-range repulsion, yet the variation of the interaction for different particle pairs is found to be considerable. Averaging over several particle pairs was hence found to be necessary to obtain a reliable assessment of the effects of salt and surfactant. It has previously been suggested that the repulsion is consistent with electrostatic interactions between a small number of dissociated charges in the oil phase, leading to a decay with distance to the power -4 and an absence of any effect of electrolyte concentration. However, the present work demonstrates that increasing the electrolyte concentration does yield, on average, a reduction of the magnitude of the interaction force with electrolyte concentration. This implies that charges on the water side also contribute significantly to the electrostatic interactions. An increase in the concentration of SDS leads to a similar decrease of the interaction force. Moreover, the repulsion at fixed SDS concentrations decreases over longer times. Finally, measurements of three-body interactions provide insight into the anisotropic nature of the interactions. The unique time-dependent and anisotropic interactions between particles at the oil-water interface allow tailoring of the aggregation kinetics and structure of the suspension structure.

Meniscus-climbing behavior and its minimum free-energy mechanism

Some insects can climb up the top of the meniscus surface generated by a hydrophilic wall by fixing their posture without moving their appendages [Baudoin, R. Bull. Biol. Fr. Belg. 1955, 89, 16. Hu, D. L.; Bush, J. W. M. Nature 2005, 437, 733]. To better understand this interesting phenomenon, we did meniscus-climbing experiments of bent copper sheets. It was found that the sheets do not always climb up the top of the meniscus surface but may stop and stably stay at various positions on the meniscus surface, depending upon their curvatures and masses, and that bent copper sheets can self-assemble into an oriented array (or an anisotropic form) through self-rotating on the water surface. The minimum energy mechanism of meniscus-climbing and self-rotating was then numerically studied. It was further shown that the meniscus-climbing and the rotating behavior is not only a general phenomenon for floating objects with hydrophilic surfaces, even those with fairly large sizes and weights (e.g., a metal bottle cap), but is also conditionally realizable for floating objects with hydrophobic surfaces.

Fragmentation and erosion of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates containing glass particles trapped at a water/oil or water/air interface. Two modes for aggregate break-up are observed: break-up by fragmentation into a few parts and break-up by erosion of single particles. We have studied the critical shear rate for these modes as a function of the aggregate size. Two different particle sizes were used. The smaller particles, with a radius of 65 microm, form aggregates that break up predominantly by erosion at a shear rate between 0.5 and 0.7 s(-1). This value hardly depends on the size of the aggregates. The larger particles, with a radius of 115 microm, form aggregates that break by erosion or by fragmentation. In both modes, the critical shear rate again depends only weakly on the size of the aggregates and ranges between 1.6 and 2.2 s(-1). Also the structural changes inside the aggregate before break-up were studied. The aggregate behavior at the water/air and water/oil interfaces is quite similar. The critical shear rate for break up was also modeled. The model shows in both modes a weak dependence of the critical shear rate on the aggregate size, which is consistent with the experimental observations. The kinetics of the erosion process was also modeled and compared with the experimentally obtained time dependence of the aggregate size. The differences in the large and small particle systems can be attributed to the occurrence of friction forces between the particles, which one expects to be much larger for the large particle system, due to the stronger two-particle interaction.

Restructuring and break-up of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates, containing glass particles, placed at a water/air interface. We have investigated the critical shear rate for break-up of aggregates with different sizes in a simple shear flow. All aggregates break-up nearly at the same shear rate (1.8 +/- 0.2 s(-)(1)) independent of their size. The evolution of the aggregate structure before break-up was also investigated. With increasing shear rate, the aggregates adopt a more circular shape, and the particles order in a more dense, hexagonal structure. A simple theoretical model was developed to explain the experimentally observed break-up. In the model, the aggregate is considered as a solid circular disk that will break near its diameter. The capillary and drag force on the two parts of the aggregate were calculated, and from this force balance, the critical shear rate was found. The model shows a weak size dependence of the critical shear rate for the considered aggregates. This is consistent with the experimental observations.

Control over colloidal aggregation in monolayers of latex particles at the oil-water interface

The controlled generation of 2D aggregate networks is studied experimentally using micrometer-sized polystyrene latex particles attached to the oil-water interface. Starting from an initially crystalline monolayer, appropriate combinations of carefully added electrolyte and surfactant enable control over both the fractal dimension and the kinetics of aggregation. Remarkably, the colloidal crystals formed upon first spreading remain stable, even for days, when substantial amounts of electrolyte are added to the aqueous phase. Pressure-area isotherms reveal a slow time evolution of the electrostatic dipole-dipole interaction. When the electrostatic interaction has been sufficiently weakened, aggregation proceeds in well-defined, reproducible manner. The aggregation process is analyzed using quantitative video microscopy. The evolution of the cluster size distribution and its moments is characterized, and static and dynamic scaling exponents are derived to identify the nature of the aggregation process. In the range of concentrations studied here, the kinetics all agree with a "fast", diffusion-limited cluster type of aggregation. However, the fractal dimension strongly depends on the composition of the aqueous subphase. Rather dense structures are found when only electrolyte is used, whereas more open structures are obtained when even small amounts of surfactant are added. It is suggested that this structural dependency is related to the effect of surfactant on the contact angle and its consequences for the anisotropic nature of the capillary interactions.