Wetting and contact lines of micrometer-sized ellipsoids

Structures in the meniscus of smectic membranes: the role of dislocations?

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

Adsorption of Ellipsoidal Particles at Liquid-Liquid Interfaces

The adsorption of particles at liquid-liquid interfaces is of great scientific and technological importance. In particular, for nonspherical particles, the capillary forces that drive adsorption vary with position and orientation, and complex adsorption pathways have been predicted by simulations. On the basis of the latter, it has been suggested that the timescales of adsorption are determined by a balance between capillary and viscous forces. However, several recent experimental results point out the role of contact line pinning in the adsorption of particles to interfaces and even suggest that the adsorption dynamics and pathways are completely determined by the latter, with the timescales of adsorption being determined solely by particle characteristics. In the present work, the adsorption trajectories of model ellipsoidal particles are investigated experimentally using cryo-SEM and by monitoring the altitudinal orientation angle using high-speed confocal microscopy. By varying the viscosity and the viscosity jump across the interfaces, we specifically interrogate the role of viscous forces.

Discrete Element Model for Suppression of Coffee-Ring Effect

When a sessile droplet evaporates, coffee-ring effect drives the suspended particulate matters to the droplet edge, eventually forming a ring-shaped deposition. Because it causes a non-uniform distribution of solid contents, which is undesired in many applications, attempts have been made to eliminate the coffee-ring effect. Recent reports indicated that the coffee-ring effect can be suppressed by a mixture of spherical and non-spherical particles with enhanced particle-particle interaction at air-water interface. However, a model to comprehend the inter-particulate activities has been lacking. Here, we report a discrete element model (particle system) to investigate the phenomenon. The modeled dynamics included particle traveling following the capillary flow with Brownian motion, and its resultant 3D hexagonal close packing of particles along the contact line. For particles being adsorbed by air-water interface, we modeled cluster growth, cluster deformation, and cluster combination. We found that the suppression of coffee-ring effect does not require a circulatory flow driven by an inward Marangoni flow at air-water interface. Instead, the number of new cluster formation, which can be enhanced by increasing the ratio of non-spherical particles and the overall number of microspheres, is more dominant in the suppression process. Together, this model provides a useful platform elucidating insights for suppressing coffee-ring effect for practical applications in the future.

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.

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.

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.

Vorticity Deformation in Polymeric Emulsions Induced by Anisotropic Ellipsoids

We study the influence of particle shape on shear-induced droplet deformation in polymeric emulsions. During shearing, droplets become elongated and rotate periodically about their major axes while aligning along the vorticity direction in ellipsoid-filled emulsions, while similar behavior is not observed in the pristine, microsphere-filled or ellipsoid-filled inverse systems. Based on the Jeffery orbit theory, the formation of anisotropic droplets with extremely small Reynolds number due to arrested coalescence in Newtonian matrix and strong confinement effect are suggested to be responsible for the vorticity alignment of droplets during slow shearing.

Particle contact angles at fluid interfaces: pushing the boundary beyond hard uniform spherical colloids

Micro and nanoparticles at fluid interfaces have been attracting increasing interest in the last few decades as building blocks for materials, as mechanical and structural probes for complex interfaces and as models for two-dimensional systems. The three-phase contact angle enters practically all aspects of the particle behavior at the interface: its thermodynamics (binding energy to the interface), dynamics (motion and drag at the interface) and interactions with the interface (adsorption and wetting). Moreover, many interactions among particles at the interface also strongly depend on the contact angle. These concepts have been extensively discussed for non-deformable, homogeneous and mostly spherical particles, but recent progress in particle synthesis and fabrication has instead moved in the direction of producing more complex micro and nanoscale objects, which can be responsive, deformable, heterogenous and/or anisotropic in shape, surface chemistry and material properties. These new particles have a much greater potential for applications and new science, and the study of their behavior at interfaces has only very recently started. In this paper, we critically review the current state of the art of the experimental methods available to measure the contact angle of micro and nanoparticles at fluid interfaces, indicating their strengths and limitations. We then comment on new particle systems that are currently attracting increasing interest in relation to their adsorption and assembly at fluid interfaces and discuss if and which ones of the current techniques are suited to investigate their properties at interfaces. Based on this discussion, we will finally try to indicate a direction in which new experimental methods should develop in the future to tackle the new challenges posed by the novel types of particles that more and more often are used at interfaces.

Capillarity-induced directed self-assembly of patchy hexagram particles at the air-water interface

Directed self-assembly can produce ordered or organized superstructures from pre-existing building blocks through pre-programmed interactions. Encoding desired information into building blocks with specific directionality and strength, however, poses a significant challenge for the development of self-assembled superstructures. Here, we demonstrate that controlling the shape and patchiness of particles trapped at the air-water interface can represent a powerful approach for forming ordered macroscopic complex structures through capillary interactions. We designed hexagram particles using a micromolding method that allowed for precise control over the shape and, more importantly, the chemical patchiness of the particles. The assembly behaviors of these hexagram particles at the air-water interface were strongly affected by chemical patchiness. In particular, two-dimensional millimeter-scale ordered structures could be formed by varying the patchiness of the hexagram particles, and we attribute this effect to the delicate balance between the attractive and repulsive interactions among the patchy hexagram particles. Our results provide important clues for encoding information into patchy particles to achieve macroscopic assemblies via a simple molding technique and potentially pave a new pathway for the programmable assembly of particles at the air-water interface.

Optical trapping force and torque on spheroidal Rayleigh particles with arbitrary spatial orientations

We investigate the spatial orientation dependence of optical trapping forces and intrinsic torques exerted on spheroidal Rayleigh particles under irradiation of highly focused linearly and circularly polarized beams. It is revealed that the maximal trapping forces and torques strongly depend on the orientation of the spheroid, and the spheroidal particle is driven to be stably trapped at the beam focus with its major axis perpendicular to the optical axis. For a linearly polarized trapping beam, the optical torque is always perpendicular to the plane containing the major axis and the polarization direction of the incident beam. Therefore, the spheroid tends to rotate its major axis along with the polarization direction. However, for a circularly polarized trapping beam, the optical torque is always perpendicular to the plane containing the major axis and the optical axis. What is different from the linear polarization case is that the spheroid tends to have the major axis parallel to the projection of the major axis in the transverse plane. The optical torque in the circular polarization case is half of that in the linear polarization case. These optical trapping properties may be exploited in practical optical manipulation, especially for the nonspherical particle's trapping.

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.

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.

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.

Monolayers of charged particles in a Langmuir trough: Could particle aggregation increase the surface pressure?

The effect of aggregation on the surface pressure, Π, of monolayers from charged micrometer-sized colloidal particles on the air/water interface is investigated. Π is completely due to the long-range electrostatic repulsion between the particles mediated by their electrostatic field in the air. The most probable origin of particle aggregation is the attraction between capillary quadrupoles due to undulated contact lines on particle surfaces. Aggregates have higher charge and repel each other stronger than single particles. The data analysis by means of a theoretical model implies that Π linearly increases with n(1/2); n is the mean aggregation number, which can be determined from the experimental Π vs. area curves. The presence of electrolyte promotes aggregation, which tends to increase Π, but simultaneously reduces the surface charge that leads to lower Π. For our system, the first effect prevails and apparently paradoxical behavior is observed: the addition of salt in water enhances the electrostatic surface pressure. The data indicate limited aggregation: the rise of the electrostatic barrier prevents the further coalescence of aggregates if they have become sufficiently large. The results contribute for a better understanding of the factors that control the interactions in monolayers of charged particles at liquid interfaces.

Brownian diffusion of a partially wetted colloid

The dynamics of colloidal particles at interfaces between two fluids plays a central role in microrheology, encapsulation, emulsification, biofilm formation, water remediation and the interface-driven assembly of materials. Common intuition corroborated by hydrodynamic theories suggests that such dynamics is governed by a viscous force lower than that observed in the more viscous fluid. Here, we show experimentally that a particle straddling an air/water interface feels a large viscous drag that is unexpectedly larger than that measured in the bulk. We suggest that such a result arises from thermally activated fluctuations of the interface at the solid/air/liquid triple line and their coupling to the particle drag through the fluctuation-dissipation theorem. Our findings should inform approaches for improved control of the kinetically driven assembly of anisotropic particles with a large triple-line-length/particle-size ratio, and help to understand the formation and structure of such arrested materials.

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.

Interaction between colloidal particles on an oil-water interface in dilute and dense phases

The interaction between micron-sized charged colloidal particles at polar/non-polar liquid interfaces remains surprisingly poorly understood for a relatively simple physical chemistry system. By measuring the pair correlation function g(r) for different densities of polystyrene particles at the decane-water interface, and using a powerful predictor-corrector inversion scheme, effective pair-interaction potentials can be obtained up to fairly high densities, and these reproduce the experimental g(r) in forward simulations, so are self consistent. While at low densities these potentials agree with published dipole-dipole repulsion, measured by various methods, an apparent density dependence and long range attraction are obtained when the density is higher. This condition is thus explored in an alternative fashion, measuring the local mobility of colloids when confined by their neighbors. This method of extracting interaction potentials gives results that are consistent with dipolar repulsion throughout the concentration range, with the same magnitude as in the dilute limit. We are unable to rule out the density dependence based on the experimental accuracy of our data, but we show that incomplete equilibration of the experimental system, which would be possible despite long waiting times due to the very strong repulsions, is a possible cause of artefacts in the inverted potentials. We conclude that to within the precision of these measurements, the dilute pair potential remains valid at high density in this system.

Solid particles adsorbed on capillary-bridge-shaped fluid polystyrene surfaces

Particles adsorbed on microscopic polystyrene (PS) capillary bridge surfaces were observed to investigate their motion under capillary forces arising from a nonuniform shape. Capillary bridges were created by placing thin PS films, heated above the glass transition temperature (Tg), between two electrodes with an air gap between the surface of the PS and the upper electrode. Silica particles, 100 nm in diameter, were placed on the surface of the PS capillary bridges, and the sample was heated above the Tg of PS to enable particle motion. Samples were cooled to below Tg, and the locations of the particles were observed using scanning electron microscopy. The particles did not preferentially locate around the center of the capillary bridge, as predicted by others, but instead segregated to the edges. These results indicate that the forces driving particles to the three-phase contact line (air/PS/electrode surface) are greater than those locating particles around the center.

Influence of magnetic field on the orientation of anisotropic magnetic particles at liquid interfaces

We study theoretically the influence of an external magnetic field on the orientation of an ellipsoidal magnetic particle adsorbed at a liquid interface. Using the finite element program Surface Evolver, we calculate the equilibrium meniscus shape around the ellipsoidal particle and its equilibrium tilt angle with respect to the undeformed interface θt when a magnetic field B is applied perpendicular to the interface. We find that as we increase field strength, θt increases and at a critical magnetic field Bc1 and tilt angle θc1, the particle undergoes a discontinuous transition to the 'perpendicular' orientation (θt = 90°). Our results agree qualitatively with the simplified theory of Bresme and Faraudo [F. Bresme and J. Faraudo, J. Phys.: Condens. Matter, 2007, 19, 375110] which assumes that the liquid interface is flat, while they agree quantitatively with recent lattice-Boltzmann simulations of Davies et al. [G. Davies et al., Soft Matter, 2014, 10, 6742] which account for the deformation of the liquid meniscus. We also show for the first time that upon reducing the external magnetic field, at a critical magnetic field Bc2 < Bc1, the particle undergoes a second discontinuous transition from the perpendicular orientation to a finite tilt angle θc2 < θc1. In other words, for micron-sized particles where the thermal energy kBT is negligible compared to the interfacial energy, the tilt angle vs. magnetic field curve exhibits hysteresis behaviour. Due to the higher degree of accuracy of the Surface Evolver method, we are able to analyse the behaviour of the particles near these orientational transitions accurately and study how the critical quantities Bc1, Bc2, θc1 and θc2 vary with particle aspect ratio and contact angle.

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

Micron-sized anisotropic particles with homogeneous surface properties at a fluid interface can deform the interface due to their shape. The particles thereby create excess interfacial area and interact in order to minimize this area, which lowers the total interfacial energy. We present a systematic investigation of the interface deformations around single ellipsoidal particles and cuboidal particles with rounded edges in the near field for various contact angles and particle aspect ratios. The correlation of these deformations with capillary bond energies-the interaction energies of two particles at contact-quantifies the relation between the interactions and the near-field deformations. We characterize the interactions using effective power laws and investigate how anisotropic particles self-assemble by capillary forces. Interface deformations and particle interactions for cuboidal particles are weaker compared with those for ellipsoidal particles with the same aspect ratios. For both particle shapes, the bound state in side-by-side orientation is most stable, while the interaction in tip-to-side orientation is repulsive. Furthermore, we find capillary attraction between spherical and ellipsoidal particles. Our calculations therefore suggest cluster formation of spherical and ellipsoidal particles, which elucidates the role of spherical particles as stoppers for the growth of worm-like chains of ellipsoidal particles. The interaction between spherical and ellipsoidal particles might also explain the suppression of the "coffee-ring effect" that has been observed for evaporating droplets with mixtures of spherical and ellipsoidal particles. In general, our calculations of the near-field interactions complement previous calculations in the far field and help to predict colloidal assembly and rheological properties of particle-laden interfaces.

Ellipsoidal particles encapsulated in droplets

Using hydrodynamic focusing, we encapsulated polystyrene ellipsoidal particles in water droplets dispersed in an immiscible, continuous phase of light mineral oil. The axisymmetric shape of the drop partially encapsulating an elongated particle was computed as a function of the particle aspect ratio, droplet volume, and contact angle. When the droplet volume is within a certain range, pinned (partially engulfed) and fully engulfed equilibrium configurations coexist. Partial encapsulation may be preferred (has a lower free energy) even when the droplet's volume is sufficient to fully engulf the particle. The co-existence of multiple equilibrium states suggests possible hysteretic encapsulation behavior. We also estimate the axial capillary force exerted by the droplet on the particle as a function of volume and contact angle. The theoretical predictions are critically compared with experimental observations.

Contact angles of microellipsoids at fluid interfaces

The wetting of anisotropic colloidal particles is of great importance in several applications, including Pickering emulsions, filled foams, and membrane transduction by particles. However, the combined effect of shape and surface chemistry on the three-phase contact angle of anisotropic micrometer and submicrometer colloids has been poorly investigated to date, due to the lack of a suitable experimental technique to resolve individual particles. In the present work, we investigate the variation of the contact angle of prolate ellipsoidal colloids at a liquid-liquid interface as a function of surface chemistry and aspect ratio using freeze-fracture shadow-casting cryo-SEM. The method, initially demonstrated for spherical colloids, is extended here to the more general case of ellipsoids. The prolate ellipsoidal particles are prepared from polystyrene and poly(methyl methacrylate) spheres using a film stretching technique, in which cleaning steps are needed to remove all film material from the particle surface. The effects of the preparation protocol are reported, and wrinkling of the three-phase contact line is observed when the particle surface is insufficiently cleaned. For identically prepared ellipsoids, the cosine of the measured contact angle is, in a first approximation, a linearly decreasing function of the contact line length and thus a decreasing function of the aspect ratio. Such a trend violates Young-Laplace's equation and can be rationalized by adding a correction term to the ideal Young-Laplace contact angle that expresses the relative importance of line effects relative to surface effects. From this term the contribution of an effective line tension can be extracted. This contribution includes the effects that both surface chemical and topographical heterogeneities have on the contact line and which become increasingly more important for ellipsoids with higher aspect ratios, where the contact line length to contact area ratio increases.

The superiority of silver nanoellipsoids synthesized via a new approach in suppressing the coffee-ring effect during drying and film formation processes

Silver nanoellipsoids (Ag NEs) with about 40 nm diameter minor axis and 100 nm major axis were prepared by a typical polyol process in the presence of poly(vinyl pyrrolidone), using Cl(-) as etching agent at the early stage of synthesis and poly(ethylene glycol) at the later stage to control the size. A suspension of these kinds of Ag NEs can resist the coffee-ring effect and deposit uniform films after drying. By contrast, suspensions of spherical silver nanoparticles suffer the coffee-ring effect badly, always leaving a ring on the edge of patterns after evaporation is complete. The reasons behind these phenomena can be mainly attributed to the long-ranged interparticle attraction between Ag NEs that preserves them from being transported by Marangoni flows during the drying process. These Ag NEs will be very useful in the preparation of conductive inks. They can perform well in the solidification process of printed patterns, forming uniform and smooth films, greatly enhancing the printing efficiency.

Particle shape anisotropy in pickering emulsions: cubes and peanuts

We have investigated the effect of particle shape in Pickering emulsions by employing, for the first time, cubic and peanut-shaped particles. The interfacial packing and orientation of anisotropic microparticles are revealed at the single-particle level by direct microscopy observations. The uniform anisotropic hematite microparticles adsorb irreversibly at the oil-water interface in monolayers and form solid-stabilized o/w emulsions via the process of limited coalescence. Emulsions were stable against further coalescence for at least 1 year. We found that cubes assembled at the interface in monolayers with a packing intermediate between hexagonal and cubic and average packing densities of up to 90%. Local domains displayed densities even higher than theoretically achievable for spheres. Cubes exclusively orient parallel with one of their flat sides at the oil-water interface, whereas peanuts preferentially attach parallel with their long side. Those peanut-shaped microparticles assemble in locally ordered, interfacial particle stacks that may interlock. Indications for long-range capillary interactions were not found, and we hypothesize that this is related to the observed stable orientations of cubes and peanuts that marginalize deformations of the interface.

Effect of particle shape on capillary forces acting on particles at the air-water interface

The capillary forces exerted by moving air-water interfaces can dislodge particles from stationary surfaces. The magnitude of the capillary forces depends on particle shape, orientation, and surface properties, such as contact angle and roughness. The objective was to quantify, both experimentally and theoretically, capillary force variations as an air-water interface moves over the particles. We measured capillary forces as a function of position, i.e., force-position curves, on particles of different shape by using force tensiometry. The particles (5 mm nominal size) were made of polyacrylate and were fabricated using a 3D printer. Experimental measurements were compared with theoretical calculations. We found that force-position curves could be classified into in three categories according to particle shapes: (1) curves for particles with round cross sections, such as spheroidal particles, (2) curves for particles with fixed cross sections, such cylindrical or cubical particles, and (3) curves for particles with tapering cross sections, such as prismatic or tetrahedral particles. Spheroidal particles showed a continuously varying capillary force. Cylindrical or cubical particles showed pronounced pinning of the air-water interface line at edges. The pinning led to an increased capillary force, which was relaxed when the interface snapped off from the edges. Particles with tapering cross section did not show pinning and showed reduced capillary forces as the air-water interface line perimeter and displacement cross section continuously decrease when the air-water interface moved over the particles.

Effects of particle shape on growth dynamics at edges of evaporating drops of colloidal suspensions

We study the influence of particle shape on growth processes at the edges of evaporating drops. Aqueous suspensions of colloidal particles evaporate on glass slides, and convective flows during evaporation carry particles from drop center to drop edge, where they accumulate. The resulting particle deposits grow inhomogeneously from the edge in two dimensions, and the deposition front, or growth line, varies spatiotemporally. Measurements of the fluctuations of the deposition front during evaporation enable us to identify distinct growth processes that depend strongly on particle shape. Sphere deposition exhibits a classic Poisson-like growth process; deposition of slightly anisotropic particles, however, belongs to the Kardar-Parisi-Zhang universality class, and deposition of highly anisotropic ellipsoids appears to belong to a third universality class, characterized by Kardar-Parisi-Zhang fluctuations in the presence of quenched disorder.

Calculation of optical forces on an ellipsoid using vectorial ray tracing method

For a triaxial ellipsoid in an optical trap with spherical aberration, the optical forces, torque and stress are analyzed using vectorial ray tracing. The torque will automatically regulate ellipsoid's long axis parallel to optic axis. For a trapped ellipsoid with principal axes in the ratio 1:2:3, the high stress distribution appears in x-z plane. And the optical force at x-axis is weaker than at y-axis due to the shape size. While the ellipsoid departs laterally from trap center, the measurable maximum transverse forces will be weakened due to axial equilibrium and affected by inclined orientation. For an appropriate ring beam, the maximum optical forces are strong in three dimensions, thus, this optical trap is appropriate to trap cells for avoiding damage from laser.

Influence of particle shape on bending rigidity of colloidal monolayer membranes and particle deposition during droplet evaporation in confined geometries

We investigate the influence of particle shape on the bending rigidity of colloidal monolayer membranes (CMMs) and on evaporative processes associated with these membranes. Aqueous suspensions of colloidal particles are confined between glass plates and allowed to evaporate. Confinement creates ribbonlike air-water interfaces and facilitates measurement and characterization of CMM geometry during drying. Interestingly, interfacial buckling events occur during evaporation. Extension of the description of buckled elastic membranes to our quasi-2D geometry enables the determination of the ratio of CMM bending rigidity to its Young's modulus. Bending rigidity increases with increasing particle anisotropy, and particle deposition during evaporation is strongly affected by membrane elastic properties. During drying, spheres are deposited heterogeneously, but ellipsoids are not. Apparently, increased bending rigidity reduces contact line bending and pinning and induces uniform deposition of ellipsoids. Surprisingly, suspensions of spheres doped with a small number of ellipsoids are also deposited uniformly.

Stability and minimum size of colloidal clusters on a liquid-air interface

A vertical force applied to each of two colloids, trapped at a liquid-air interface, induces their logarithmic pairwise attraction. I recently showed [Phys. Rev. E 79, 011407 (2009)] that in clusters of size R much larger than the capillary length λ, the attraction changes to that of a power law and is much stronger due to a many-body effect, and I derived two equations that describe the equilibrium coarse-grained meniscus profile and colloid density in such clusters. In this paper, this theory is shown also to describe small clusters with R≪ λ provided the number N of colloids therein is sufficiently large. An analytical solution for a small circular cluster with an arbitrary short-range power-law pairwise repulsion is found. The energy of a cluster is obtained as a function of its radius R and colloid number N. As in large clusters, the attraction force and energy universally scale with the distance L between colloids as L(-3) and L(-2), respectively, for any repulsion forces. The states of an equilibrium cluster, predicted by the theory, are shown to be stable with respect to small perturbations of the meniscus profile and colloid density. The minimum number of colloids in a circular cluster, which sustains the thermal motion, is estimated. For standard parameters, it can be very modest, e.g., in the range 20-200, which is in line with experimental findings on reversible clusterization on a liquid-air interface.

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.

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

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

Undulation instabilities in the meniscus of smectic membranes

Using optical microscopy, phase shifting interferometry, and atomic force microscopy, we characterize the undulated structures which appear in the meniscus of freestanding ferroelectric smectic-C* films. We demonstrate that these periodic structures correspond to undulations of the smectic-air interface. The resulting striped pattern disappears in the untilted smectic-A phase. The modulation amplitude and wavelength of the instability both depend on meniscus thickness. We study the temperature evolution and propose a model that qualitatively accounts for the observations.

Orientation and self-assembly of cylindrical particles by anisotropic capillary interactions

In this research, we study cylindrical microparticles at fluid interfaces. Cylinders orient and assemble with high reliability to form end-to-end chains in dilute surfaces or dense rectangular lattices in crowded surfaces owing to capillary interactions. In isolation, a cylinder assumes one of two possible equilibrium states, the end-on state, in which the cylinder axis is perpendicular to the interface, or the side-on state, in which the cylinder axis is parallel to the interface. A phase diagram relating aspect ratio and contact angle is constructed to predict the preferred state and verified in experiment. Cylinders in the side-on state create distortions that result in capillary interactions. Overlapping deformations by neighboring particles drive oriented capillary assembly. Interferometry, electron microscopy, and numerical simulations are used to characterize the interface shape around isolated particles. Experiments and numerics show that "side-on" cylinders have concentrated excess area near the end faces, and that the interface distortion resembles an elliptical quadrupole a few radii away from the particle surface. To model the cylinder interactions for separations greater than a few radii, an anisotropic potential is derived based on elliptical quadrupoles. This potential predicts an attractive force and a torque, both of which depend strongly on aspect ratio, in keeping with experiment. Particle trajectories and angular orientations recorded by video microscopy agree with the predicted potential. In particular, the analysis predicts the rate of rotation, a feature lacking in prior analyses. To understand interactions near contact, the concentrated excess area near the cylinder ends is quantified and its role in creating stable end-to-end assemblies is discussed. When a pair of cylinders is near contact, these high excess area regions overlap to form a capillary bridge between the particles. This capillary bridge may stabilize the end-to-end chains. Finally, on densely packed surfaces, cylinder-covered colloidosomes form with particles arranged in regular, rectangular lattices in the interface; this densely packed structure differs significantly from assemblies reported for colloidosomes or particle-stabilized droplets in the literature.

Fabrication of unusual asymmetric colloids at an oil-water interface

We present a novel method for creating asymmetrical particles with unusual, flattened shapes from colloidal latex microspheres pinned at an oil-water interface. The shape and degree of asymmetry are controlled by incubating particles for minutes to tens of minutes at an elevated temperature. Estimates of the surface energy and work account for the shape-change mechanism in which heated particles deform as they spread at the oil-water interface to minimize the contact between these immiscible phases.

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.

Attraction between particles at a liquid interface due to the interplay of gravity- and electric-field-induced interfacial deformations

In a previous study, we established that the attraction between electrically charged particles attached to a water/tetradecane interface is stronger than predicted on the basis of the gravity-induced lateral capillary force. Here, our goal is to explain this effect. The investigated particles are hydrophobized glass spheres of radii between 240 and 320 microm. Their weight is large enough to deform the liquid interface. The interfacial deformation is considerably greater for charged particles because of the electrodipping force that pushes the particles toward the water phase. By independent experiments with particles placed between two electrodes, we confirmed the presence of electric charges at the particle/tetradecane interface. The theoretical analysis shows that if the distribution of these surface charges is isotropic, the meniscus produced by the particle electric field decays too fast with distance and cannot explain the experimental observations. However, if the surface-charge distribution is anisotropic, it induces a saddle-shaped deformation in the liquid interface around each particle. This deformation, which is equivalent to a capillary quadrupole, decays relatively slow. Its interference with the gravity-induced isotropic meniscus around the other particle gives rise to a long-range attractive capillary force, F approximately 1/L3 (L=interparticle distance). The obtained agreement between the experimental and theoretical curves, and the reasonable values of the parameters determined from the fits, indicate that the observed stronger attraction in the investigated system can be really explained as a hybrid interaction between gravity-induced "capillary charges" and electric-field-induced "capillary quadrupoles".

Self-assembly and rheology of ellipsoidal particles at interfaces

Colloidal particles confined at liquid interfaces have important applications, for example in the stabilization of emulsions and foams. Also the self-assembly of particles at interfaces offers potential for novel applications and structured particle films. As the colloidal interactions of colloidal particles at interfaces differ from those in bulk, colloidal microstructures can be achieved at an interface which cannot be produced in bulk. In the present work the particle shape, surface charge, and wetting properties are varied, and the resulting self-assembly of particles at a fluid interface is studied. Model monodisperse micrometer-sized ellipsoidal particles were prepared by a mechanical stretching method. These particles were chosen to be well-suited for investigation by optical microscopy. When deposited at an interface between two fluids, shape-induced capillary interactions compete with the electrostatic repulsion. Changing the surface charge and the position at the interface can be used to manipulate the experimentally observed self-assembly process. The initial microstructure of charged ellipsoids at a decane-water interface consists of individual ellipsoids coexisting with linear chains of ellipsoids, connected at their tips. The aggregation behavior in these monolayers was investigated by optical microscopy combined with quantitative image analysis and a dominant tip-tip aggregation was observed. Microstructural information was quantified by calculating the pair-distribution and orientation-distribution functions, as a function of time. Compared to particles at an oil-water interface, particles of the same surface chemistry and charge at an air-water interface seem to have weaker electrostatic interactions, and they also have a different equilibrium position at the interface. The latter leads to differences in the capillary forces. The subsequent change in the balance between electrostatic and capillary forces gave rise to very dense networks having as a typical building block ellipsoids connected at their tips in triangular or flower-like configuration. These networks were very stable and did not evolve in time. The resulting monolayers responded elastically and buckled under compression. Furthermore, the mechanical properties of these monolayers, as measured by surface shear rheology, showed that the monolayer of ellipsoids exhibit a substantial surface modulus even at low surface coverage and can be used to create more elastic monolayers compared to aggregate networks of spheres of the same size and surface properties.

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.

Force balance of particles trapped at fluid interfaces

We study the effective forces acting between colloidal particles trapped at a fluid interface which itself is exposed to a pressure field. To this end, we apply what we call the "force approach," which relies solely on the condition of mechanical equilibrium and turns to be in a certain sense less restrictive than the more frequently used "energy approach," which is based on the minimization of a free energy functional. The goals are (i) to elucidate the advantages and disadvantages of the force approach as compared to the energy approach, and (ii) to disentangle which features of the interfacial deformation and of the capillary-induced forces between the particles follow from the gross feature of mechanical equilibrium alone, as opposed to features which depend on the details of, e.g., the interaction of the interface with the particles or the boundaries of the system. First, we derive a general stress-tensor formulation of the forces at the interface. On that basis we work out a useful analogy with two-dimensional electrostatics in the particular case of small deformations of the interface relative to its flat configuration. We apply this analogy in order to compute the asymptotic decay of the effective force between particles trapped at a fluid interface, extending the validity of the previous results and revealing the advantages and limitations of the force approach compared to the energy approach. It follows the application of the force approach to the case of deformations of a nonflat interface. In this context, we first compute the deformation of a spherical droplet due to the electric field of a charged particle trapped at its surface and conclude that the interparticle capillary force is unlikely to explain certain recent experimental observations within such a configuration. We finally discuss the application of our approach to a generally curved interface and show as an illustrative example that a nonspherical particle deposited on an interface forming a minimal surface is pulled to regions of larger curvature.

Ellipsoidal particles at fluid interfaces

For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interface-mediated interactions of capillary and fluctuation-induced type are analyzed. For contact angles different from 90( degrees ) , static interface deformations arise which lead to anisotropic capillary forces that are substantial already for micrometer-sized particles. The capillary problem is solved using an efficient perturbative treatment which allows a fast determination of the capillary interaction for all distances between and orientations of two particles. Besides static capillary forces, fluctuation-induced forces caused by thermally excited capillary waves arise at fluid interfaces. For the specific choice of a spatially fixed three-phase contact line, the asymptotic behavior of the fluctuation-induced force is determined analytically for both the close-distance and the long-distance regime and compared to numerical solutions.