Sedimentation velocity and potential in a concentrated suspension of charged liquid drops

The sedimentation behavior of a concentrated suspension of charged liquid drops is analyzed theoretically at arbitrary surface potential and arbitrary double-layer thickness; that is, the effects of double-layer polarization and double-layer overlapping are taken into account. Kuwabara's unit cell model is employed to model the suspension system, and a pseudospectral method based on the Chebyshev polynomial is adopted to solve the governing electrokinetic equations numerically. Several interesting phenomena, which are of significant influence if the internal flow inside a liquid drop is taken into account, are observed. Key factors are examined such as the thickness of the electric double layer, the magnitude of the surface potential, the volume fraction of liquid drops, and the viscosity of the internal fluid. The results presented here add another dimension to the previous studies, which include concentrated suspensions of rigid particles and mercury drops under low zeta potential, with the consideration of the internal flow of liquid drops and double-layer polarization, characterized by its viscosity and the zeta potential respectively. It is found, among other things, that the smaller the viscosity of the internal fluid is, the higher the sedimentation velocity of liquid drops. The higher the zeta potential is, the larger the decrease in sedimentation velocity. In particular, the sedimentation velocity of an inviscid drop (gas bubble) is about three times higher than that of a rigid one. The decrease in sedimentation velocity resulting from the effect of double-layer polarization achieves about 50% if the zeta potential is sufficiently high.     

Electrophoresis of a concentrated dispersion of spherical particles covered by an ion-penetrable membrane layer

The electrophoretic behavior of a concentrated dispersion of soft spherical particles is investigated theoretically, taking the effects of double-layer overlapping and double-layer polarization into account. Here, a particle comprises a rigid core and an ion-penetrable layer containing fixed charge, which mimics biocolloids and particles covered by artificial membrane layers. A cell model is adopted to simulate the system under consideration, and a pseudo-spectral method based on Chebyshev polynomials is chosen for the resolution of the governing electrokinetic equations. The influence of the key parameters, including the thickness of the double layer, the concentration of particles, the surface potential of the rigid core of a particle, and the thickness, the amount of fixed charge, and the friction coefficient of the membrane layer of a particle on the electrophoretic behavior of the system under consideration is discussed. We show that while the result for the case of a dispersion containing rigid particles can be recovered as the limiting case of a dispersion containing soft particles, qualitative behaviors that are not present in the former are observed in the latter.     

Direct Observation of Foam Film Rupture by Several Types of Antifoams Using a Scanning Laser Microscope

It is well known that the stability of a pseudoemulsion film, a thin liquid film formed between an antifoam particle and air, can be important during defoaming action. We have compared the bursting behavior of a two-dimensional thin liquid film from an aqueous surfactant solution on a glass plate, in which six types of antifoam particles have been dispersed, using laser microscopic techniques. The used antifoams were a silicone oil, a mixed-type antifoam (mixture of silicone oil and hydrophobic solid particles), a hydrophobic silica, and a silicone-based solid antifoam (prepared by interfacial polymerization with oil and water). The antifoaming performance of these six types of antifoams, measured by the glass cylinder shaking test, was in the order: the mixed-type antifoam >== the silicone-based solid antifoam > the hydrophobic silica >== the silicone oil. Pseudoemulsion film rupture was observed at the film thickness less than 0.1 μm for both the silocone oil and the hydrophobic silica. In the case of particles with rough edges (the silicone-based antifoam), pseudoemulsion film on the top of the particles can be easily ruptured at a convex part of the solid surface. Furthermore, solid particles existing on the surface of an oil droplet in the mixed-type antifoams form marked projections and these projections give rise to distortion of the thinning film. As soon as the distortion of the thinning film took place on the top of the antifoam droplet, the pseudoemulsion film can be instantaneously ruptured. Referring to the antifoaming mechanisms for mixed-type antifoams, both steps from the pseudoemulsion film formation to the lens formation and from the counter pseudoemulsion film formation to the bridge formation would be very fast and cause a very high antifoaming efficiency. Copyright 1999 Academic Press.     

Sedimentation of a concentrated dispersion of composite colloidal particles

The sedimentation of a concentrated spherical dispersion of composite particles, where a particle comprises a rigid core and a membrane layer containing fixed charge, is investigated theoretically. The dispersion is simulated by a unit cell model, and a pseudo-spectral method based on Chebyshev polynomials is adopted to solve the problem numerically. The influences of the thickness of double layer, the concentration of particles, the surface potential of the rigid core of a particle, and the amount of fixed charge in the membrane layer on both the sedimentation potential and the sedimentation velocity are discussed. Several interesting results are observed; for example, depending upon the charged conditions on the rigid core and in the membrane layer of a particle, the sedimentation potential might have both a local maximum and a local minimum and the sedimentation velocity can have a local minimum as the thickness of double layer varies. Also, the sedimentation velocity can have a local maximum as the surface potential varies. We show that the sedimentation potential increases with the concentration of particles. The relation between the sedimentation velocity and the concentration of particles, however, depends upon the thickness of double layer.     

Electrophoresis of a particle at an arbitrary surface potential and double layer thickness: importance of nonuniformly charged conditions

Recent advances in material science and technology yield not only various kinds of nano- and sub-micro-scaled particles but also particles of various charged conditions such as Janus particles. The characterization of these particles can be challenging because conventional electrophoresis theory is usually based on drastic assumptions that are unable to realistically describe the actual situation. In this study, the influence of the nonuniform charged conditions on the surface of a particle at an arbitrary level of surface potential and double layer thickness on its electrophoretic behavior is investigated for the first time in the literature taking account of the effect of double-layer polarization. Several important results are observed. For instance, for the same averaged surface potential, the mobility of a nonuniformly charged particle is generally smaller than that of a uniformly charged particle, and the difference between the two depends upon the thickness of double layer. This implies that using the conventional electrophoresis theory may result in appreciable deviation, which can be on the order of ca. 20%. In addition, the nonuniform surface charge can yield double vortex in the vicinity of a particle by breaking the symmetric of the flow field, which has potential applications in mixing and/or regulating the medium confined in a submicrometer-sized space, where conventional mixing devices are inapplicable.     

Impedance Response of a Thin Film on an Electrode: Deciphering the Influence of the Double Layer Capacitance

The different contributions of the interfacial capacitance are identified in the case of passive materials or thin protective coatings deposited on the electrode surface. The method is based on a graphical analysis of the EIS results to determine both the passive-film capacitance in the high-frequency domain and the double-layer capacitance in the low-frequency domain. The proposed analysis is shown to be independent of the physicochemical origins of the frequency dispersion of the interfacial capacitances which results, from an analysis point of view of the experimental results, in the use of a constant-phase element However, for a correct evaluation of the thin-film properties such as its thickness, the high-frequency data must be corrected for the double-layer contribution. In particular, it is shown that if the double-layer capacitance gives a frequency-dispersed response, it is necessary to correct the high-frequency part for the double-layer constant-phase elements. This is first demonstrated on synthetic data and then used for the determination of the thickness of thin oxide film formed on Al in neutral pH solution.     

Deposition of particles under external forces in laminar flow through parallel-plate and cylindrical channels

A theoretical analysis of particle deposition kinetics onto walls of parallel-plate and cylindrical channels is presented. Rigorous transport equations are formulated by taking into account specific surface forces as well as external forces, e.g., gravity. By solving the transport equations numerically, the dimensionless mass transfer Sherwood number is determined as a function of various dimensionless parameters introduced such as Pe, Gr, Ad, and Dl, accounting for convection and diffusion, and for gravity, dispersion, and electrical double-layer interactions, respectively. The influence of attractive surface forces and gravity on the deposition kinetics is graphically presented and discussed. For large particles, i.e., about 1-μm diameter (Pe > 1), and for short distances from the point where deposition starts, a considerable increase in particle flux (up to an order of magnitude) is predicted over previous analytical values when strong attractive double-layer forces are present. For particles smaller than 0.1-μm diameter (Pe < 10^-4) our numerical results show that particle deposition rates may be successfully predicted by an analytical formula derived for particles of negligible size even in the presence of double-layer attractions (provided external forces are absent). Experimental results reported in the literature obtained under conditions of negligible gravity force are reinterpreted in terms of the present theory. A somewhat closer agreement with experimental data as compared to the analytical formula mentioned above is found in cases of strong double-layer attractions.     

Stabilization of magnetorheological suspensions by polyacrylic acid polymers

This work is devoted to the synthesis and stabilization of magnetorheological suspensions constituted by monodisperse micrometer-sized magnetite spheres in aqueous media. The electrical double-layer characteristics of the solid/liquid interface were studied in the absence and presence of adsorbed layers of high molecular weight polyacrylic acids (PAA; Carbopol). Since the Carbopol-covered particles can be thought of as "soft" colloids, Ohshima's theory was used to gain information of the surface potential and the charge density of the polymer layer. The effect of the pH of the solution on the double-layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The stability of the suspensions was experimentally studied for different pH and polymer concentrations, and in the absence or presence of a weak magnetic field applied. The stability of the suspensions was explained using the classical DLVO theory of colloidal stability extended to account for hydration, steric, and magnetic interactions between particles. Diagrams of potential energy vs interparticle distance show the predominant effect of steric, hydrophilic/hydrophobic, and magnetic interactions on the whole stability of the system. The best conditions to obtain stable suspensions were found when strong steric and hydrophilic repulsions hinder the coagulation between polymer-covered particles, simultaneously avoiding sedimentation by the thickening effect of the polymer solution. When a not too high molecular weight PAA was employed in a low concentration, the task of a long-time antisettling effect compatible with the desired magnetic response of the fluid was achieved.     

An algorithm for estimating colloidal heterointeractions based on decoupling the Poisson-Boltzmann equation

An algorithm is presented for calculating the colloidal heterointeraction double-layer energy between spheres whose surface potentials may be very high. In most systems of industrial and biological importance, heterointeractions between particles with high surface potentials are often encountered, and the energy of interacting particles is needed in estimating the stability of such suspensions. The electrical double-layer energy of interaction is computed from the electrical potential distribution between and around the interacting particles and necessitates the solution of the non-linear Poisson-Boltzmann equation. In this study, the double-layer potential between two plates is assumed to be the sum of the potentials of two overlapping double-layers. This approach reproduces the exact double-layer potential distribution accurately. Although it makes use of empiricism, it offers advantages in obtaining the double-layer potential distribution more efficiently.     

Diffusiophoresis of concentrated suspensions of spherical particles with identical ionic diffusion velocities

Diffusiophoresis of concentrated suspensions of spherical particles subject to a small electrolyte gradient is analyzed theoretically at arbitrary levels of zeta potential and double-layer thickness. The Kuwabara unit cell model is adopted to describe the system under consideration. The effect of double-layer polarization is taken into account. It is found that the diffusiophoretic mobility exhibits a local maximum as well as a local minimum with varying zeta potential or double-layer thickness, similar to the corresponding dilute dispersion. The direction of the particle movement may even change back and forth. The previous low-zeta-potential approach is found to significantly overestimate the diffusiophoretic mobility as the zeta potential goes high. The deviation may be several fold sometimes. The effect of the volume fraction ratio of colloids is also examined. The higher the ratio, the lower the mobility.     

Electrophoresis of a membrane-coated sphere in a spherical cavity

The boundary effect on the electrophoresis of particles covered by a membrane layer is discussed by considering a spherical particle in a spherical cavity under the conditions where the effect of double-layer polarization can be significant. The influence of the key parameters of the system under consideration on the electrophoretic mobility of a particle is investigated. These include the surface potential; the thickness of the double layer; the relative size of the cavity; and the thickness, the fixed charge density, and the friction coefficient of the membrane layer. The fixed charge in the membrane layer of a particle is found to have a significant influence on its electrophoretic behavior. For instance, depending upon the amount of fixed charge in the membrane layer, the mobility of a particle may exhibit a local minimum as the thickness of the double layer varies.     

Electrokinetics of concentrated suspensions of spherical colloidal particles with surface conductance, arbitrary zeta potential, and double-layer thickness in static electric fields

In this paper the electrophoretic mobility and the electrical conductivity of concentrated suspensions of spherical colloidal particles have been numerically studied under arbitrary conditions including zeta potential, particle volume fraction, double-layer thickness (overlapping of double layers is allowed), surface conductance by a dynamic Stern layer model (DSL), and ionic properties of the solution. We present an extensive set of numerical data of both the electrophoretic mobility and the electrical conductivity versus zeta potential and particle volume fraction, for different electrolyte concentrations. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. Other theoretical approaches have also been considered for comparison. Furthermore, the study includes the possibility of adsorption and lateral motion of ions in the inner region of the double layers (DSL model), according to the theory developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans.86, 2859 (1990)). The results show that the correct limiting cases of low zeta potentials and thin double layers for dilute suspensions are fulfilled by our conductivity formula. Moreover, the presence of a DSL causes very important changes, even dramatic, on the values of both the electrophoretic mobility and the electrical conductivity for a great range of volume fractions and zeta potentials, specially when double layers of adjacent cells overlap, in comparison with the standard case (no Stern layer present). It can be concluded that in general the presence of a dynamic Stern layer causes the electrophoretic mobility to decrease and the electrical conductivity to increase in comparison with the standard case for every volume fraction, zeta potential, and double-layer thickness.     

Stability of dispersions of colloidal alumina particles in aqueous suspensions

The colloidal stability of suspensions of alumina particles has been investigated by measuring particle size distribution, sedimentation, viscosity, and zeta potential. Alumina particles were found to be optimally dispersed at pH around 3 to 7.8 without dispersant and at pH 8.5 and beyond with dispersant. The above results corroborate zeta potential and viscosity measurement data well. The surface charge of alumina powder changed significantly with anionic polyelectrolyte (ammonium polycarboxylate, APC) and the iep shifted toward more acidic range under different dispersant conditions. It was found that the essential role played by pH and dispersant (APC) on the charge generation and shift in the isoelectric point of alumina manifests two features: (i) the stability decreases on approaching the isoelectric point from either side of pH, and (ii) the maximum instability was found at pH 9.1 for alumina only and at pH 6.8 for alumina/APC, which is close to the isoelectric points for both the system, respectively. Using the model based on the electrical double-layer theory of surfactant adsorption through shift in isoelectric points, the authors could estimate the specific free energy of interaction (7.501 kcal/mol) between particles and dispersant. The interaction energy, zeta potential, sedimentation, and viscosity results, were used to explain the colloidal stability of the suspension.     

Electrokinetics of soft particles

Theories of electrokinetics of soft particles, which are particles covered with an ion-penetrable surface layer of polyelectrolytes, are reviewed. Approximate analytic expressions are given, which describe various electrokinetics of soft particles both in dilute and concentrated suspensions, that is, electrophoretic mobility, electrical conductivity, sedimentation velocity and potential, dynamic electrophoretic mobility, colloid vibration potential, and electrophoretic mobility under salt-free condition.     

Well-Characterized Monodisperse Latexes as Model Colloids

Monodisperse polystyrene latexes prepared with persulfate-ion initiator can be ion exchanged to remove the adsorbed emulsifier and solute electrolyte. Rigorous purification of the ion-exchange'resins is necessary to avoid contamination with leached polyelectrolytes. These ion-exchanged latexes are stabilized with the residual sulfate end-groups of the polymer molecules, the number of which is determined by conductoroetric titration. The result is a dispersion of monodisperse spheres with-a constant and known surface charge due to chemically-bound strong-acid groups. These latexes are ideal models for colloidal studies. Preliminary experiments of stability, adsorption, sedimentation, viscosity, interference colors, and conductance give consistent results, e.g., the particle double-layer interactions determined by viscosity are in accord -with the particle spacings estimated from interference colors, the double-layer parameters estimated from conductometric titration and conductance measurements account for the measured decrease in sedimentation rate due to double-layer interactions, and the molecular area of sodium dodecyl sulfate measured by adsorption in latex is in agreement with literature values.     

Mechanism of hydrodynamic separation of biological objects in microchannel devices

In this study, the separation mechanism employed in hydrodynamic chromatography in microchannel devices is analyzed. The main purpose of this work is to provide a methodology to develop a predictive model for hydrodynamic chromatography for biological macromolecules in microchannels and to assess the importance of various phenomenological coefficients. A theoretical model for the hydrodynamic chromatography of particles in a microchannel is investigated herein. A fully developed concentration profile for non-reactive particles in a microchannel was obtained to elucidate the hydrodynamic chromatography of these particles. The external forces acting on the particles considered in this model include the van der Waals attractive force, double-layer force as well as the gravitational force. The surface forces, such as van der Waals attractive force as well as the double-layer repulsive force, can either enhance or hinder the average velocity of the macromolecular particles. The average velocity of the particles decreases with the molecular radius because the van der Waals attractive force increases the concentration of the particles near the channel surface, which is the low-velocity region. The transport velocity of the particles is dominated by the gravity and the higher density enlarges the effect caused by gravity.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

Effect of stress-jump condition on electrophoretic behavior of a spherical dispersion of soft particles

The electrophoresis of a concentrated dispersion of soft particles, where a particle comprises a rigid core and an ion-penetrable membrane layer, is modeled theoretically, taking the effect of double-layer polarization into account. In particular, the influence of a stress-jump condition of the flow field at the membrane layer-liquid interface on the electrophoretic mobility of a particle is investigated. The type of particles considered mimic biocolloids, such as cells and microorganisms, and inorganic colloids covered by an artificial polymer layer such as surfactant molecules. A unit cell model is adopted to simulate the present spherical dispersion, and the governing equations and the associated boundary conditions are solved by a pseudo-spectral method based on Chebyshev polynomials. We show that while the stress-jump condition, characterized by a stress-jump coefficient, can have a significant influence on the mobility of a particle, the associated flow field is not influenced appreciably. Also, the influence of the stress-jump condition on the mobility of a particle depends largely on the nature of the membrane layer, characterized by its friction coefficient.     

Surface chemistry and rheology of polysulfobetaine-coated silica

We have measured the viscosity of suspensions of colloidal silica particles (d = 300 nm) and the properties of silica surfaces in solutions of a polymer consisting of zwitterionic monomer groups, poly(sulfobetaine methacrylate), polySBMA. This polymer has potential use in modifying surface properties because the polymer is net uncharged and therefore does not generate double-layer forces. The solubility of the polymer can be controlled and varies from poor to good by the addition of sodium chloride salt. Ellipsometry was used to demonstrate that polySBMA adsorbs to silica and exhibits an increase in surface excess at lower salt concentration, which is consistent with a smaller area per molecule at low salt concentration. Neutron reflectivity measurements show that the adsorbed polymer has a thickness of about 3.7 nm and is highly hydrated. The polymer can be used to exercise considerable control over suspension rheology. When silica particles are not completely covered in polymer, the suspension produces a highly viscous gel. Atomic force microscopy was used to show this is caused by bridging of polymer between the particles. At higher surface coverage, the polymer can produce either a high or very low viscosity slurry depending on the sodium chloride concentration. At high salt concentration, the suspension is stable, and the viscosity is lower. This is probably because the entrainment of many small ions renders the polymer film highly hydrophilic, producing repulsive surface forces and lubricating the flow of particles. At low salt concentrations, the polymer is barely soluble and more densely adsorbed. This produces less stable and more viscous solutions, which we attribute to attractive interactions between the adsorbed polymer layers.     

Dynamic Mobility of Particles with Thick Double Layers in a Nondilute Suspension

The dynamic mobility of a nondilute suspension of spherical particles is investigated in the case where the thickness of the electrical double layer around each particle is comparable to the particle radius. A formula is obtained for the O(φ) correction in a random suspension of particles with volume fraction φ, involving an integral over the dynamic mobility of a pair of spheres. This formula is then evaluated using both analytical approximations and numerical results previously obtained for the pair mobilities and valid for low surface potentials. The effect of double-layer thickness on the O(φ) coefficient is most pronounced at low frequencies, and lessens once the hydrodynamic penetration depth is smaller than the particle radius. Various approximations are considered that use the O(φ) result to predict the dynamic mobility in concentrated suspensions, and at high frequencies these approximations are shown to give results qualitatively different from those of recent cell models. Copyright 2000 Academic Press.