Electrophoresis of a spherical particle normal to an air-water interface

Electrophoresis of a spherical particle normal to an air-water interface is considered theoretically in this study. The presence of the air-water interface is found to reduce the particle mobility in general, especially when the double layer is very thick. This boundary effect diminishes as the double layer gets very thin. The higher the surface potential, the more significant the reduction of mobility due to the polarization effect from the double layer deformation when the particle is in motion. Local extrema are observed in the mobility profiles with varying double layer thickness as a result. Comparison with a solid planar boundary is made. It is found that the particle mobility near an air-water interface is smaller than that near a solid one when the double layer is thick, and vice versa when the double layer is thin, with a critical threshold value of double layer thickness corresponding roughly to the touch of the interface. The reason behind it is clearly explained as the buildup of electric potential at the air-water interface, which reduces the driving force as a result.     

Theory of colloid stability and particle nucleation kinetics in emulsion polymerization

The DLVO theory of colloid stability is applied to the uncatalyzed and catalyzed agglomeration of small primary particles formed in the earliest stages of emulsion polymerization in the manufacture of a carboxylic styrene/butadiene latex. The inverse 6th-power relationship between the stability ratio and the cation concentration revealed experimentally in an earlier work can be confirmed theoretically using variable Stern potentials. The Stern potential changes as parabolic function of log cation concentration. From the viewpoint of DLVO and Stern theory it is suggested that a spacer effect is crucial for the activity of the catalyst used.Presented at the 5th European and Interface Society Conference together with the 35th meeting of the Deutsche Kolloidgesellschaft on Trends in Colloid and Interface Science September 25–28, 1991, Maiz, FRG     

The electrophoresis of a spherical particle

The problem of predicting the electrophoretic velocity of a spherical charged particle in an infinite dielectric liquid containing impurities is re-examined. A model, somewhat different from those commonly used, is postulated, and the associated equations are formulated and are solved subject to certain approximations. The electrophoretic velocityU is found to be linear in the applied field and to vary algebraically in the parameterχ=ka.     

Electrophoresis of a charge-regulated particle at an arbitrary position in a spherical cavity

The boundary effect on the electrophoretic behavior of a particle is examined by considering a sphere at an arbitrary position in a spherical cavity for the case of low electrical potential and weak applied electric field. Here, a charge-regulated model is used to describe the charge conditions on the particle surface. This model finds practical applications where the behavior of biocolloids such as cells or microorganisms and entities covered by an artificial membrane need to be simulated. The two idealized models often used in relevant studies can be recovered as the limiting cases of the present model.     

Dependence of emulsion stability on particle size: Relative importance of drop concentration and destabilization rate on the half lifetimes of O/W nanoemulsions

This study reports the behavior of ionic dodecane-in-water nanoemulsions in distinct salt concentrations. Systems of smaller particle size (74–285 nm) were synthesized by a sudden dilution of an equilibrated mixture. Larger size systems (384–670 nm) were obtained from a set of formerly smaller nanoemulsions that evolved unperturbed for 2 weeks. Characteristic destabilization times for flocculation, coalescence, and Ostwald ripening were evaluated. In general, it was observed that stability increases with drop size. However, this size dependence is largely the consequence of the lower particle concentration of the coarser emulsions.     

Transient electrophoresis of a conducting spherical particle embedded in an electrolyte-saturated Brinkman medium

In this study, the time-dependent electrophoretic motion of a conducting spherical particle embedded in an arbitrary electrolyte solution saturated porous medium is investigated. The porous medium is uniformly charged and the embedded hard particle is charged with constant -potential or constant surface charge density. The unsteady modified Brinkman equation with an electric force term, which governs the fluid velocity field, is used to model the porous medium and is solved by Laplace's transform technique. An analytical expression for the electrophoretic velocity of the spherical particle is obtained in Laplace transform domain as a function of the relevant parameters, and its inversion is obtained through numerical techniques. Also, in this study, the steady-state electrophoretic velocity is obtained analytically as linear functions of -potential (or surface density charge) and the fixed charge density. The steady-state electrophoretic velocity is displayed graphically for various relevant parameters and compered with the available data in the literature. Also, the numerical values of the transient electrophoretic velocity are plotted versus the nondimensional elapsed time and discussed for different values of the Debye length parameter, density ratio, permeability of the porous medium, and for high and nonconducting particles.     

Sedimentation of a composite particle in a spherical cavity

The boundary effect on the sedimentation of a colloidal particle is investigated theoretically by considering a composite sphere, which comprises a rigid core and an ion-penetrable membrane layer, in a spherical cavity. A pseudo-spectral method is adopted to solve the governing electrokinetic equations, and the influences of the key parameters on the sedimentation behavior of a particle are discussed. We show that both the qualitative and quantitative behaviors of a particle are influenced significantly by the presence of the membrane layer. For example, if the membrane layer is either free of fixed charge or positively charged and the surface potential of the rigid core is sufficiently high, the sedimentation velocity has a local minimum and the sedimentation potential has a local maximum as the thickness of the double layer varies. These local extrema are not observed when the membrane layer is negatively charged. If the double layer is thin, the influence of the fixed charge in the membrane layer on the sedimentation potential is inappreciable.     

Diffusiophoresis of a moderately charged spherical colloidal particle

An analytic expression is obtained for the diffusiophoretic mobility of a charged spherical colloidal particle in a symmetrical electrolyte solution. The obtained expression, which is expressed in terms of exponential integrals, is correct to the third order of the particle zeta potential so that it is applicable for colloidal particles with low and moderate zeta potentials at arbitrary values of the electrical double-layer thickness. This is an improvement of the mobility formula derived by Keh and Wei, which is correct to the second order of the particle zeta potential. This correction, which is related to the electrophoresis component of diffusiophoresis, becomes more significant as the difference between the ionic drag coefficients of electrolyte cations and anions becomes larger and vanishes in the limit of thin or thick double layer. A simpler approximate mobility expression is further obtained that does not involve exponential integrals.     

Heat transfer to a single particle exposed to a thermal plasma

This paper is concerned with an analytical study of the heat and mass transfer process of a single particle exposed to a thermal plasma, with emphasis on the effects which evaporation imposes on heat transfer from the plasma to the particle. The results refer mainly to an atmospheric-pressure argon plasma and, for comparison purposes, an argon-hydrogen mixture and a nitrogen plasma are also considered in a temperature range from 3000 to 16,000 K. Interactions with water droplets, alumina, tungsten, and graphite particles are considered in a range of small Reynolds numbers typical for plasma processing of fine powders. Comparisons between exact solutions of the governing equations and approximate solutions indicate the parameter range for which approximate solutions are valid. The time required for complete evaporation of a given particle can be determined from calculated values of the vaporization constant. This constant is mainly determined by the boiling (or sublimation) temperature of the particles and the density of the condensed phase. Evaporation severely reduces heat transfer to a particle and, in general, this effect is more pronounced for materials with low latent heat of evaporation.     

Donnan potential and surface potential of a spherical soft particle in an electrolyte solution

A simple numerical method, which does not involve numerical integration of the Poisson-Boltzmann equations, is presented for obtaining the relationship between the Donnan potential and surface potential of a spherical soft particle (i.e., a polyelectrolyte-coated particle) in a symmetrical electrolyte solution. We assume that a soft particle consists of the particle core of radius a covered with an ion-penetrable surface layer of polyelectrolytes of thickness d and that ionized groups of valence Z are distributed at a uniform density of N in the polyelectrolyte layer and the relative permittivity takes the same value in the regions outside and inside the polyelectrolyte layer. The Donnan potential and surface potential are determined by the values of a, d, Z, N, and the Debye-Hückel parameter kappa of the electrolyte solution. Numerical results obtained by the present method are in excellent agreement with exact results obtained by solving the nonlinear spherical Poisson-Boltzmann equations for the both regions inside and outside the polyelectrolyte layer.     

Electrophoretic mobility of a charged spherical colloidal particle covered with an uncharged polymer layer

A general expression is derived for the electrophoretic mobility of a spherical charged colloidal particle covered with an uncharged polymer layer in an electrolyte solution in an applied electric field for the case where the particle zeta potential is low. It is assumed that electrolyte ions as well as water molecules can penetrate the polymer layer. Approximate analytic expressions for the electrophoretic mobility of particles carrying low zeta potentials are derived for the two extreme cases in which the particle radius is very large or very small.     

From stability to permeability of adhesive emulsion bilayers

Water drops dispersed in chloroform and stabilized with phospholipids become adhesive if a bad solvent for lipids, such as silicone oil, is added to the continuous phase. In this way, two sticking drops are separated by a bilayer of phospholipids. By using microfluidic technologies, we probe the stability and properties of such membranes likewise encountered in foams or vesicles. We first establish the stability diagram of adhering drop pairs as a function of the continuous phase composition. We found two regimes of destabilization of the bilayer. The first one concerns a competition between the dynamics of adhesion and the transport of surfactants toward the interfaces that leads to a dilute surfactant coverage. The second one corresponds to a dense surface coverage where the lifetime distribution of the bilayer exponentially decreases as a signature of a nucleation process. In the stable regime, we observe the propagation of adhesion among a concentrated collection of drops. This is another remarkable illustration of the suction consequence when two close deformable objects are pulled apart. Moreover, the present experimental strategy offers a novel way to study the phase diagrams of bilayers from a single phospholipid to a mixture of phospholipids. Indeed, we detect phase transitions at a liquid-liquid interface that are ruled by the amount of bad solvent. Finally, we probe the transport of water molecules through the bilayer and show that its permeability is linked to the adhesion energy that reflects its fluidity.     

Electrophoretic motion of a soft spherical particle in a nanopore

Many biocolloids, biological cells and micro-organisms are soft particles, consisted with a rigid inner core covered by an ion-permeable porous membrane layer. The electrophoretic motion of a soft spherical nanoparticle in a nanopore filled with an electrolyte solution has been investigated using a continuum mathematical model. The model includes the Poisson-Nernst-Planck (PNP) equations for the ionic mass transport and the modified Stokes and Brinkman equations for the hydrodynamic fields outside and inside the porous membrane layer, respectively. The effects of the “softness” of the nanoparticle on its electrophoretic velocity along the axis of a nanopore are examined with changes in the ratio of the radius of the rigid core to the double layer thickness, the ratio of the thickness of the porous membrane layer to the radius of the rigid core, the friction coefficient of the porous membrane layer, the fixed charge inside the porous membrane layer of the particle and the ratio of the radius of the nanopore to that of the rigid core. The presence of the soft membrane layer significantly affects the particle electrophoretic mobility.     

Electrophoretic motion of a spherical particle in a converging-diverging nanotube

A charged spherical particle is concentrically positioned in a converging-diverging nanotube filled with an electrolyte solution, resulting in an electric double layer (EDL) forming around the particle's surface. In the presence of an axially applied electric field, the particle electrophoretically migrates along the axis of the nanotube due to the electrostatic and hydrodynamic forces acting on the particle. In contrast to a cylindrical nanotube with a constant cross-sectional area in which the electric field is almost uniform, the presence of a converging-diverging section in a nanotube alters the electric field, perturbs the charge distribution, and induces a pressure gradient and a recirculating flow that affect the electrostatic and hydrodynamic forces acting on both the particle and the fluid. Depending on the magnitude of the surface charge density along the nanotube's wall, the particle's electrophoretic motion may be significantly accelerated as the particle transverses the converging-diverging section. A continuum model consisting of the Nernst-Planck, Poisson, and Navier-Stokes equations for the ionic concentrations, electric potential, and flow field is implemented to compute the particle's velocity as a function of the particle's size, the nanotube's geometry, surface charges, electric field intensity, bulk electrolyte concentration, and the particle's location. When the particle is negatively charged and the wall of the nanotube is uncharged, the particle migrates in the direction opposite to that of the applied electric field and the presence of the converging-diverging section significantly accelerates the particle's motion. This, however, is not always true when the nanotube's wall is charged with the same sign as that of the particle. Once the ratio of the surface charge density of the nanotube's wall to that of the particle exceeds a certain value, the negatively charged particle will not translocate through the tube toward the anode and does not attain the maximum velocity at the throat of the converging-diverging section. One can envision such a device to be a nanofilter that allows molecules with surface charge densities much higher than that of the wall to go through the nanofilter, while preventing molecules with surface charge densities lower than that of the wall from passing through the nanofilter. The induced recirculating flow may be used to enhance mixing and to stretch, fold, and trap molecules in nanofluidic detectors and reactors.     

Kinetics of colloidal templating using emulsion drop consolidation

The emulsion templating of ordered colloidal microsphere assemblies by Manoharan et al. involves a consolidation process where dispersed phase fluid is transported from droplets into a continuous phase. Consolidation can be approximated as a diffusion process with moving boundaries. The kinetics of consolidation are investigated here by following droplet shrinkage with time as a prelude to understanding rate effects on assembly structure. Consolidation kinetics are influenced by liquid diffusivity, the number of colloidal particles in a droplet, and the surfactant concentration. While surfactant exhibits little effect well below its critical micelle concentration (CMC) value, it significantly slows consolidation above the CMC. For a specific continuous phase (i.e., silicone oil and fluorinated silicone oil), with proper scalings, the droplet size shrinks with time following a power law independent of droplet diameter, surfactant concentrations, and particle number concentration. The power law exponent varies from 1/2 to 2/3 with different continuous oil phases as a result of concentration and interfacial effects. This study leads to an improved understanding of colloidal microstructure development at interfaces that can be applied in novel materials synthesis and drug delivery areas.     

Monitoring the stability of an emulsion by high-frequency spectroscopy.

High-frequency spectroscopy has been applied to monitoring the stability of oil-in-water emulsions. It was found that stable emulsions showed absorption peaks at around 550 MHz; further, they shifted from lower to higher frequencies with time. The rate of increase of the frequencies was dependent on the amount of emulsifier added. These results show that the stability of emulsions can be monitored by the amount of the frequency shift.     

Electric forces induced by a charged colloid particle attached to the water-nonpolar fluid interface

Here, we solve the problem about the electric field of a charged dielectric particle, which is adsorbed at the water-nonpolar fluid (oil, air) boundary. The solution of this problem is a necessary step for the theoretical prediction of the electrodipping force acting on such particle, as well as of the electrostatic repulsion and capillary attraction between two adsorbed particles. In accordance with the experimental observations, we consider the important case when the surface charges are located at the particle-nonpolar fluid boundary. To solve the electrostatic problem, the Mehler-Fock integral transform is applied. In the special case when the dielectric constants of the particle and the nonpolar fluid are equal, the solution is obtained in a closed analytical form. In the general case of different dielectric constants, the problem is reduced to the numerical solution of an integral equation, which is carried out by iterations. The long-range asymptotics of the solution indicates that two similar particles repel each other as dipoles, whose dipole moments are related to the particle radius, contact angle, dielectric constant and surface charge density. The investigated short-range asymptotics ensures accurate calculation of the electrodipping force. For a fast and convenient application of the obtained results, the derived physical dependencies are tabulated as functions of the contact angle and the dielectric constants.     

Deformations of lipid vesicles induced by attached spherical particles

Wrapping of a spherical colloidal particle, located inside and outside a lipid vesicle, by the membrane which forms the wall of the vesicle is investigated. The process is studied for vesicles of different geometries: prolate, oblate, stomatocytes. We focus on the bending energy change and shape transformations induced by binding the membrane to the spherical particles. The ground-state shapes of vesicles are calculated within the framework of a Helfrich curvature energy functional.