Forces between a Rigid Probe Particle and a Liquid Interface

The effect of disjoining pressure between a rigid spherical probe particle (attached to an AFM cantilever) and a liquid interface (e.g., oil/water or air/water) is treated in an analytic manner to describe the total force F exerted on the probe as a function of the distance X of the probe from the rigid substrate (AFM stage) on which the liquid interface resides. Two cases (i) a flat interface under gravity and (ii) a drop whose size is sufficiently small that gravity can be neglected have been examined. A simple numerical algorithm is given for computing F(X) (the AFM observable) from a given form for the disjoining pressure. Numerical results are displayed for electrostatic probe/interface interactions which reveal the linear compliance regime experimentally observed in AFM experiments on these systems. The slope of the linear compliance regime is shown to be a function of the properties of the interface (capillary length, particle radius, drop size, contact angle of drop on rigid substrate etc.). Copyright 2001 Academic Press.     

Effect of the range of repulsions on the existence of a stable liquid phase

Experimental and theoretical results have established that the range of the attraction plays a critical role in determining whether a particle system exhibits a stable liquid phase. Changes to the range of the repulsions can similarly affect the existence of a stable liquid phase; however, these effects have not been clearly elucidated. We demonstrate that an increase in the range of repulsions can either enhance or decrease the stability of the liquid phase, depending on the form of the interaction potential. For either case, the critical variable that controls the stability of the liquid phase is the ratio of the representative energies of the liquid and solid phases.     

Time evolution of the drop size distribution for liquid–liquid dispersion in an agitated tank

Agitating two immiscible liquids or a solid–liquid suspension is an operation frequently performed in the chemical and metallurgical industries, for example, in suspension/emulsion polymerization, heterogeneous/phase-transfer catalytic chemical reactions, and hydrometallurgical solvent extraction. For emulsification, suspension polymerization, solid particle dispersion, and crystallization, it is essential to be able to predict the mean drop/particle size and the drop/particle size distribution. A simple model was proposed for predicting the time evolution of drop size distribution during drop breaking, and was successfully tested on data published by Ruiz and Padilla (Hydrometallurgy 72:245–258, 2004) and by Sathyagal et al. (Chem Eng Sci 51: 1377–1391, 1996) and on our own data. The time evolution of DSD was investigated in a baffled tank agitated by a Rushton turbine for a liquid–liquid dispersion. The tests were carried out on a silicone oil–water dispersion (oil in water) with a dispersed-phase fraction of 0.00047. The drop sizes were determined by image analysis.     

Numerical analysis of the shapes and energies of droplets on micropatterned substrates

The shapes and energies of drops on substrates patterned with either holes or posts are computed using Surface Evolver software. The holes and posts are cylindrical in shape and distributed in a 6-fold symmetric pattern. The wetting conditions are such that the liquid does not fill the holes and the interface between the drop and the substrate is composite, i.e., partly solid/liquid and partly liquid/vapor. The sequence of stable drop configurations with increasing volume is analyzed and provides, in part, an explanation for superhydrophobic drop spreading.     

Oil-in-water Pickering emulsion destabilisation at low particle concentrations

Droplet evolution in unstable, dilute oil-in-water Pickering emulsions was characterised using a combination of light scattering, confocal microscopy and rheology. Emulsions were formed at concentrations of silanised fumed silica particles that are not sufficient to prevent destabilisation. The key result is that destabilisation initially occurs via a combination of droplet flocculation and permeation. Close contact between the drops enhances oil transfer from smaller drops to the larger ones. The large drops swell over time until the attached particle density is insufficient to protect the drops against coalescence. Examination of the emulsion microstructure revealed the relationship between drop stability and the structural characteristics of the aggregates formed due to coagulation of the silica particles in the emulsions. The implications of these results for controlling Pickering emulsion stability are discussed.     

Detachment force of particles from air-liquid interfaces of films and bubbles

The detachment force required to pull a microparticle from an air-liquid interface is measured using atomic force microscopy (AFM) and the colloidal probe technique. Water, solutions of sodium dodecyl sulfate (SDS), and silicone oils are tested in order to study the effects of surface tension and viscosity. Two different liquid geometries are considered: the air-liquid interface of a bubble and a liquid film on a solid substrate. It was shown that detaching particles from liquid films is fundamentally different than from bubbles or drops due to the restricted flow of the liquid phase. Additional force is required to detach a particle from a film, and the maximum force during detachment is not necessarily at the position where the particle breaks away from the interface (as seen in bubble or drop systems). This is due to the dynamics of meniscus formation and viscous effects, which must be considered if the liquid is constrained in a film. The magnitude of these effects is related to the liquid viscosity, film thickness, and detachment speed.     

Gibbs free energy of liquid drops on conical fibers

Small drops can move spontaneously on conical fibers. As a drop moves along the cone, it must change shape to maintain a constant volume, and thus, it must change its surface energy. Simultaneously, the exposed surface area of the underlying cone must also change. The associated surface energies should balance each other, and the drop should stop moving when it reaches a location where the free energy is a minimum. In this paper, a minimum Gibbs free energy analysis has been performed to predict where a drop will stop on a conical fiber. To obtain the Gibbs free energies of a drop at different locations of a conical fiber, the theoretical expressions for the shape of a droplet on a conical fiber are derived by extending Carroll's equations for a drop on a cylindrical fiber. The predicted Gibbs free energy exhibits a minimum along the length of the cone. For a constant cone angle, as the contact angle between the liquid and the cone increases, the drop will move toward the apex of the cone. Likewise, for a constant contact angle, as the cone angle increases, the drop moves toward the apex. Experiments in which water and dodecane were placed on glass cones verify these dependencies. Thus, the final location of a drop on a conical fiber can be predicted on the basis of the geometry and surface energy of the cone, the surface tension and volume of the liquid, and the original location where the drop was deposited.     

Spreading of a fluid phase on a spherical surface

The adsorption between a liquid drop and a micro-particle in an air or an air bubble and a micro-particle in water is dominated by liquid-solid or air-solid interfacial tension and wetting area of the liquid or air on the particle surface. The wetting area is determined by the spreading of the liquid drop or the bubble on the micro-particle. To explore this spreading, a wetting model of a fluid phase on a spherical particle was built. According to the theoretical results, the contact angle is constant when a fluid phase spreads on a spherical solid surface; the micro-particle can not submerge under a fluid when only interfacial tensions are involved and the wetting is not a complete wetting. The corresponding experiments were performed to confirm the theoretical results.     

Bubble particle heterocoagulation under turbulent conditions

An analytical model that enables the calculation of the flotation rate constant of particles as a function of particle size with, as input parameters, measurable particle, bubble, and hydrodynamic quantities has been derived. This model includes the frequency of collisions between particles and bubbles as well as their efficiencies of collision, attachment, and stability. The generalized Sutherland equation collision model and the modified Dobby-Finch attachment model developed previously for potential flow conditions were used to calculate the efficiencies of particle-bubble collision and attachment, respectively. The bubble-particle stability efficiency model includes the various forces acting between the bubble and the attached particle, and we demonstrate that it depends mainly on the relative magnitude of particle contact angle and turbulent dissipation energy. The flotation rate constants calculated with these models produced the characteristic shape of the flotation rate constant versus particle size curve, with a maximum appearing at intermediate particle size. The low flotation rate constants of fine and coarse particles result from their low efficiency of collision and low efficiencies of attachment and stability with gas bubbles, respectively. The flotation rate constants calculated with these models were compared with the experimental flotation rate constants of methylated quartz particles with diameters between 8 and 80 micro m interacting with gas bubbles under turbulent conditions in a Rushton flotation cell. Agreement between theory and experiment is satisfactory.     

Dynamic Photocontrol of the Coffee‐Ring Effect with Optically Tunable Particle Stickiness

When a colloidal drop dries on a surface, most of the particles accumulate at the drop periphery, yielding a characteristic ring‐shaped pattern. This so‐called coffee‐ring effect (CRE) is observed in any pinned evaporating drop containing non‐volatile solutes. Here, the CRE is dynamically controlled for the first time by using light, and an unprecedented reconfigurability of the deposit profile is demonstrated. This is achieved through a new mechanism where particle stickiness is optically tuned on demand, thus offering reliable modulation of the deposition pattern. The system consists of anionic nanoparticles and photosensitive cationic surfactants dispersed in water. It is shown that light‐dependent modulation of surfactant–particle interactions dictates particle attraction and trapping at the liquid–gas interface, which allows us to direct particle deposition into a wide range of patterns from rings to homogeneous disks. Patterning from single drops is photoreversible upon changing the wavelength whereas spatial control in multiple drop arrays is achieved using a photomask.     

Concentrating particles on drop surfaces using external electric fields

We propose to use an externally applied uniform electric field to alter the distribution of particles on the surface of a drop immersed in another immiscible liquid. Specifically, we seek to generate well-defined concentrated regions at the drop surface while leaving the rest of the surface particle free. Experiments show that when the dielectric constant of the drop is greater than that of the ambient liquid the particles for which the Clausius-Mossotti factor is positive move along the drop surface to the two poles of the drop. Particles with a negative Clausius-Mossotti factor, on the other hand, move along the drop surface to form a ring near the drop equator. The opposite takes place when the dielectric constant of the drop is smaller than that of the ambient liquid, namely particles for which the Clausius-Mossotti factor is positive form a ring near the equator while those for which such a factor is negative move to the poles. This motion is due to the dielectrophoretic force that acts upon particles because the electric field on the surface of the drop is nonuniform, despite the uniformity of the applied electric field. Experiments also show that when small particles collect at the poles of a deformed drop the electric field needed to break the drop is smaller than without particles. These phenomena could be useful to concentrate particles at a drop surface within well-defined regions (poles and equator), separate two types of particles at the surface of a drop or increase the drop deformation to accelerate drop breakup.     

Molecular dynamics study of the influence of surfactant structure on surfactant-facilitated spreading of droplets on solid surfaces

The spreading of a partially wetting aqueous drop in air on a hydrophobic surface can be facilitated by the adsorption of surfactants from the drop phase onto the air/aqueous and aqueous/hydrophobic solid interfaces of the drop. At the contact line at which these interfaces meet, conventional surfactants with a linear alkyl hydrophobic chain attached to a polar group adsorb onto the surfaces, forming monolayers which remain distinct as they merge at the contact juncture. The adsorption causes a decrease in the interfacial tensions and reduction in the contact angle but the angle remains above zero so the drop is still nonwetting. Trisiloxane surfactants with a T-shaped geometry in which the hydrophobic group is composed of a trisiloxane oligomer with a polar group attached at the center of the chain can give rise to a zero contact angle at the contact line and complete wetting (superspreading). Experimental evidence suggests the adsorption of the T-shaped molecule, in addition to significantly decreasing the tensions of the interfaces (relative to the conventional surfactants), promotes the formation of a precursor film consisting of a surfactant bilayer at the contact line which facilitates the spreading. The aim of this study is to use molecular dynamics to examine if the T-shaped structure can promote spreading by the formation of a bilayer and to contrast this case with that of the linear chain surfactant where complex assembly does not occur. The simulation models the solvent as a monatomic liquid, the substrate as a particle lattice, and the surfactants as united atom structures, with all interactions given by Lennard-Jones potentials. We start with a base case in which the solvent partially wets a substrate comprised of a lattice of particles. We demonstrate that adsorbed T-shaped surfactant monolayers can, when the interaction between the solvent and the hydrophile particles is strong enough, assemble into a bilayer, allowing the drop to extend to a thin planar film. In the case of the flexible linear chain surfactant, there is no interaction between the monolayers on the two interfaces in the case of a strong hydrophile-solvent interaction and less coordination for a weaker interaction. In either case, the monolayers remain distinct, as the surfactant only marginally improves wetting.     

Quantification of the chiral recognition in electrochemically driven ion transfer across the interface water/chiral liquid

The electrochemically driven transfer of the chiral anions of d- and l-tryptophan across the interface water/chiral liquid (d- or l-menthol) is stereoselective, and it can be used to determine quantitatively the difference in Gibbs energies for the solvation of chiral ions in chiral liquids. The ion transfer can be achieved in a three-phase arrangement where a droplet of the chiral liquid containing decamethylferrocene as the electroactive redox probe is attached to a graphite electrode immersed in the aqueous solution containing the chiral ions.     

Synthesis and characterization of rigid‐chain liquid–crystalline polymers containing laterally attached side rods

A series of rigid‐chain polymers containing different concentrations of laterally attached side rods was synthesized. These polymers exhibited liquid crystallinity even up to a maximum side rod concentration of 20 mol %. The crystallinity of the polymers, however, decreased with an increase in the side‐rod concentration. These polymers had lower dielectric constants compared with their parent polymers, that is, similar polymers, but without laterally attached side rods. A dielectric constant of 2.6 can be achieved by incorporating 10 mol % of laterally attached side rods, which is 0.5 lower than that of its parent polymer. The reduction of dielectric constant may be attributed to low crystallinity as well as the less dense packing structure of the polymers induced by the incorporation of laterally attached side rods. This series of polymers also had good thermal stability. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1288–1294, 2001     

Microscopic treatment of a barrel drop on fibers and nanofibers

The microscopic approach of Berim and Ruckenstein (J. Phys. Chem. B 108 (2004) 19330, 19339) regarding the shape and stability of a liquid drop on a planar bare solid surface is extended to a liquid barrel drop on the bare surface of a solid cylinder (fiber) of arbitrary radius. Assuming the interaction potentials of the liquid molecules between themselves and with the molecules of the solid of the London-van der Waals form, the potential energy of a liquid molecule with an infinitely long fiber was calculated analytically. A differential equation for the drop profile was derived by the variational minimization of the total potential energy of the drop by taking into account the structuring of the liquid near the fiber. This equation was solved in quadrature and the shape and stability of the barrel drop were analyzed as functions of the radius of the fiber and the microscopic contact angle theta(0) which the drop profile makes with the surface of the fiber. The latter angle is dependent on the fiber radius and on the microscopic parameters of the model (strength of the intermolecular interactions, densities of the liquid and solid phases, hard core radii, etc.). Expressions for the evaluation of the microcontact angle from experimentally measurable characteristics of the drop profile (height, length, volume, location of inflection point) are obtained. All drop characteristics, such as stability, shape, are functions of theta(0) and a certain parameter a which depends on the model parameters. In particular, the range of drop stability consists of three domains in the plane theta(0)-a, separated by two critical curves a=a(c)(theta(0)) and a=a(c1)(theta(0)) [a(c)(theta(0))h(m1) cannot exist, whereas in the third domain (between those curves) the drop can have values of h(m) either smaller than h(m1) or larger than h(m2), where h(m2)>h(m1) is a second critical height. For sufficiently large fiber radii, R(f)1 >/= microm, the critical curves almost coincide and only two domains, the first and the second, remain. The smaller the radius, the larger is the difference between the critical curves and the larger is the second domain of drop stability. The shape of the drop depends on whether the point (theta(0),a) on the theta(0)-a plane is far from the critical curve or near it. In the first case the drop profile has generally a large circular part, while in the second case the shape is either almost planar or contains a long manchon that is similar to a film on the fiber.     

Liquid drops on vertical and inclined surfaces; I. An experimental study of drop geometry

Experiments have been conducted to investigate the geometric parameters necessary to describe the shapes of liquid drops on vertical and inclined plane surfaces. Two liquids and eight surfaces have been used to study contact angles, contact lines, profiles, and volumes of drops of different sizes for a range of surface conditions. The results show the contact-angle variation along the circumference of a drop to be best fit by a third-degree polynomial in the azimuthal angle. This contact-angle function is expressed in terms of the maximum and minimum contact angles of the drop, which are determined for various conditions. The maximum contact angle, thetamax, is approximately equal to the advancing contact angle, thetaA, of the liquid on the surface. As the Bond number, Bo, increases from 0 to a maximum, the minimum contact angle, thetamin, decreases almost linearly from the advancing to the receding angle. A general relation is found between thetamin/thetaA and Bo for different liquid-surface combinations. The drop contour can be described by an ellipse, with the aspect ratio increasing with Bo. These experimental results are valuable in modeling drop shape, as presented in Part II of this work.     

Liquid drop and optical model calculations of elastic,vibrationally inelastic and absorptive scattering of4He atoms from4He n -clusters

The scattering of He atoms from liquid He _n -clusters withn=10 to 1000 at energies between 0.01 and 5.0 meV has been investigated by calculating integral cross sections for elastic scattering, absorption scattering and vibrational excitation of the liquid drop vibrations using a hard core potential, a transparent core potential, a black core and an optical model potential. The implications for planned scattering experiments are discussed.     

Numerical simulation of rapid pressurization and depressurization of a zeolite column using nitrogen

The required durations of pressurization and depressurization steps of a rapid pressure swing adsorption process are primarily governed by adsorbent particle size, adsorption kinetics, column pressure drop, column length to diameter ratio, and the valve constant of the gas inlet and outlet control valve attached to the adsorbent column. A numerical model study of the influence of these variables for an adiabatic LiX zeolite column is presented using pure N₂ as an adsorbate gas. An adsorbent particle size range of 200–350 μm was found to minimize (<1 s) the times required for the pressurization and depressurization steps.     

Retention forces and contact angles for critical liquid drops on non-horizontal surfaces

Retention forces and drop parameters are investigated for drops on the verge of sliding on vertical and inclined surfaces. Using earlier observations of drop geometry, the retentive-force factor relating surface-tension forces to contact-angle hysteresis is reliably determined. The retention force for a drop is found to be insignificantly affected by the aspect ratio of its contour. The maximum size of a drop is predicted with good accuracy, based on the two-circle method for approximating shapes of drops. The Bond number of a critical drop is found to be constant for a given surface and liquid. A general relation is proposed between the characteristic advancing and receding contact angles. The relation is supported by a large set of contact-angle data. In the absence of theta R data, the relation allows estimating the receding contact angle and the critical drop size, using only the advancing angle.