Free energy of colloidal particles at the surface of sessile drops

Particle-Bubble Interactions: an Investigation of the Three-Phase Contact Line by Atomic Force Microscopy

The dynamics of the three-phase contact line during particle-bubble interactions determine the stability of particle-bubble aggregates in flotation. The interaction of particles and sessile gas bubbles can be studied by colloidal probe atomic force microscopy (CP-AFM). This paper demonstrates a method to obtain the contact angle, the position of the three-phase contact line on the particle, and the bubble profile by utilizing the full information contained in AFM force-distance curves, i.e., force and CP-position information as well as the work done to move the three-phase contact line on the CP-particle. The proposed method does not require any assumption of a constant contact angle or a constant opening angle. This is achieved by the combined solution of the particle force balance and an expression for the work required to move the three-phase contact line over the colloid probe. The applicability to AFM force-distance measurements was demonstrated for the interaction of a hydrophobic SiO2 or a hydrophobic Al2O3 colloidal probe particle with sessile gas bubbles having radii between 45 and 80 μm.

Capillary Assembly of Anisotropic Particles at Cylindrical Fluid-Fluid Interfaces

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

Pickering Emulsion Transitions in 2,6-Lutidine Plus Water Critical Liquid Mixtures

Silica particle (S) stabilized oil-in-water Pickering emulsions are observed in the two-phase region of the critical liquid mixture 2,6-lutidine (L) plus water (W). De-emulsification is found at temperatures below a particle wetting transition temperature T_w(R) where T_w(R) decreases toward the lower critical temperature T_c for smaller particle radii R. The presence of a Pickering emulsion transition and its dependence upon particle radius can be explained by a competition between destabilizing gravitational forces and stabilizing forces originating from the critical interfacial tension. As a corollary to these observations, the line tension τ at the three-phase SLW contact line is determined as a function of temperature.

Capillarity-driven migration of small objects: A critical review

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

Bubble-bubble interactions in a 2d foam, close to the wet limit

Following the general approach of Morse and Witten for the deformation of a bubble in contact with neighbouring bubbles, we develop a model for contacting bubbles in two dimensions which can be solved analytically. The force-displacement relations are derived by elementary methods; unlike the case of 3d, no logarithmic factors arise in two dimensions. We also discuss the case of a uniform compression of a symmetric foam structure; the (osmotic) compressibility depends on the number of contacts, as was shown in earlier work by Lacasse et al. Our model, which is based on first principles, without any free parameters, may be extended to simulate 2d foams.

Buckling in armored droplets

The buckling mechanism in droplets stabilized by solid particles (armored droplets) is tackled at a mesoscopic level using dissipative particle dynamics simulations. We consider one spherical water droplet in a decane solvent coated with nanoparticle monolayers of two different types: Janus (particles whose surface shows two regions with different wetting properties) and homogeneous. The chosen particles yield comparable initial three-phase contact angles, selected to maximize the adsorption energy at the interface. We study the interplay between the evolution of droplet shape, layering of the particles, and their distribution at the interface when the volume of the droplets is reduced. We show that Janus particles affect strongly the shape of the droplet with the formation of a crater-like depression. This evolution is actively controlled by a close-packed particle monolayer at the curved interface. In contrast, homogeneous particles follow passively the volume reduction of the droplet, whose shape does not deviate too much from spherical, even when a nanoparticle monolayer/bilayer transition is detected at the interface. We discuss how these buckled armored droplets might be of relevance in various applications including potential drug delivery systems and biomimetic design of functional surfaces.

Detachment Force of Particles with Pinning of Contact Line from Fluid Bubbles/Droplets

Deformation of a spherical droplet or bubble containing a pair of particles on its surface is considered when equal but opposite forces are applied to the particles. The particles are placed opposite each other, thus providing a symmetric problem that is more amenable to analytical treatment. We extend our previous calculations concerning such arrangements with constant contact angles to situations where it is the contact line now that is pinned on the surface of the particles. The force-displacement curves are calculated as the particles are pulled apart and are found to be linear for small displacements. However, it is also found that the "Hookean constant" for the pinned contact line problem is different from the one derived for systems with a constant contact angle, the constant being larger if the pinned line is at the equator of the particles.

An Analysis of Bubble Deformation by a Sphere Relevant to the Measurements of Bubble-Particle Contact Interaction and Detachment Forces

Atomic force microscopy makes it possible to measure the interacting forces between individual colloidal particles and air bubbles, which can provide a measure of the particle hydrophobicity. To indicate the level of hydrophobicity of the particle, the contact angle can be calculated, assuming that no interfacial deformation occurs with the bubble retaining a spherical profile. Our experimental results obtained using a modified sphere tensiometry apparatus to detach submillimeter spherical particles show that deformation of the bubble interface does occur during particle detachment. We also develop a theoretical model to describe the equilibrium shape of the bubble meniscus at any given particle position, based on the minimization of the free energy of the system. The developed model allows us to analyze high-speed video captured during detachment. In the system model deformation of the bubble profile is accounted for by the incorporation of a Lagrange multiplier into both the Young-Laplace equation and the force balance. The solution of the bubble profile matched to the high-speed video allows us to accurately calculate the contact angle and determine the total force balance as a function of the contact point of the bubble on the particle surface.

Detachment force of particles from fluid droplets

We calculate the deformation of a spherical droplet, resulting from the application of a pair of opposite forces to particles located diametrically opposite at the two ends of the droplet. The free-energy analysis is used to calculate the force-distance curves for the generated restoring forces, arising from the displacement of the particles relative to each other. While the logarithmic dependence of the "de Gennes-Hooke" constant on the particle to droplet size ratio, ν, is rather well known in the limit of very small ν, we find that for more realistic particle to droplet size ratios, i.e. ν = 0.001 to 0.01, the additional constant terms of O(1) constitute a significant correction to previously reported results. We derive the restoring force constant to be 2πγ[0.5 - ln (ν/2)](-1), in perfect agreement with the exact semi-numerical analysis of the same problem. The deviation from the linear force-displacement behaviour, occurring close to the point of detachment, is also investigated. A study of the energy dissipated shows it to be an increasingly dominant component of the work done during the detachment of the particles, as ν decreases. This indicates the existence of a significantly higher energy barrier to desorption of very small particles, compared to the one suggested by their adsorption energy alone. The influence of the line tension on the detachment force is also considered. It is shown that where line tension is important, the contact angle is no longer a constant but instead alters with the displacement of the particles from their equilibrium positions.

Evaporation of a capillary bridge between a particle and a surface

The liquid bridge that forms between a particle and a flat surface, and the dynamics of its evaporation are pertinent to a range of physical processes including paint and ink deposition, spray drying, evaporative lithography and the flow and processing of powders. Here, using time-lapse photography, we investigate the evaporative dynamics of a sessile liquid bridge between a particle and a planar substrate. Different wetting characteristics of the particle and substrate are explored, as well as the effects of contact line pinning and stick-slip boundary conditions. A theoretical framework is developed to quantify and analyse the experimental observations. For the size range of particles and drops used in this study, gravity is by far the smallest force in the system when compared to the surface tension and capillary interactions that are present, but in certain circumstances it dictates the key evolution stages of the geometry of the particle-drop-substrate systems. Analysis of evaporation dynamics and capillary forces indicate that at low Bond numbers, surface tension forces dominate and provide unique opportunities for the control of particles on surfaces.

Capillary interactions in Pickering emulsions

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

An axisymmetric meniscus converges particles for microscopy

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