The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

The electrophoresis in a monodisperse suspension of dielectric spheres with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations, which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell, are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of the colloidal sphere in closed form correct to O(zeta) are obtained. Based on the solution of the electrokinetic equations in a cell, a closed-form formula for the electric conductivity of the suspension up to O(zeta(2)) is derived from the average electric current density. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made for both the electrophoretic mobility and the electric conductivity. Copyright 2001 Academic Press.     

Zeta Potential of Highly Charged Thin Double-Layer Systems

Electrophoretic measurements under d.c. conditions involve a fundamental ambiguity for particles with a high zeta potential; two very different values of zeta potential can be ascribed to the same mobility. In the case of a polystyrene sulfate latex studied previously, selecting the higher (absolute) value gave a more consistent picture of the interface and also removed an anomaly in the electrokinetic behavior as a function of indifferent electrolyte concentration. Confirmation that the higher value is the correct one, however, was still needed. The ambiguity is resolved unequivocally here by the use of high-frequency mobility measurements using electroacoustics, since the mobility spectra for the high and low zeta potentials are very different. The interpretation is supported by the dielectric relaxation spectra of this material in the megahertz region. Copyright 2001 Academic Press.     

Electrophoresis and Sedimentation of Charged Fibers

The electrophoretic translational and rotational velocities of a fiber are determined in the limitsL/d≥≥ 1 and λ/d≥≥ 1, where λ is the double layer thickness andLanddare the fiber length and diameter, respectively. The fiber translates due to the imposed electric field at a rate that increases with increasing double layer thickness. A nonuniformly charged fiber with a net charge dipole rotates until it becomes aligned with the electric field. The results for the translational and rotational velocities are obtained in a semianalytic form. The effect of the deformation of the ion cloud surrounding a charged sedimenting fiber on the fiber's translational and rotational velocities is also determined. The ion cloud retards the sedimentation velocity relative to that of an uncharged fiber with the same orientation. If the fiber possesses both a net charge and a charge dipole, it will rotate into a vertical alignment in which the end with the larger absolute charge is on top.     

Analysis of the Isoelectric Point in Moderately Concentrated Alumina Suspensions Using Electroacoustic and Streaming Potential Methods

ABSTRACT

Alumina suspended in aqueous electrolytic solution was used as a model ceramic suspension to investigate the measurement precision and influencing factors for the determination of the isoelectric point (IEP) in moderately concentrated systems. Techniques used in this study include colloid vibration current (CVI), electrokinetic sonic amplitude (ESA), and particle charge detection (PCD). A number of important factors were examined, focusing on those related to sample preparation, measurement methodology and instrumentation. A total of 145 acid-base titrations were included in the analysis. Although sample preparation factors influence the magnitude of the measured signal, primarily due to agglomeration effects, these factors do not significantly impact the determination of the IEP for alumina. The primary factor affecting IEP precision and accuracy is the level of sample agitation during titration. Poor mixing gives rise to hysteresis phenomena that introduce large systematic errors. Colloid vibration current, ESA, and PCD produce comparable electrokinetic data over the solids volume fraction range between 1% and 10%, although some systematic differences are apparent. Further refinements in methodology and greater fundamental understanding are necessary to improve measurement agreement between different techniques and to reduce variability in IEP results.     

Electrophoretic Mobility of Soft Particles in Concentrated Suspensions

A general theory is developed for the electrophoretic mobility of spherical soft particles (i.e., spherical hard colloidal particles of radius a coated with a layer of polyelectrolytes of thickness d) in concentrated suspensions in an electrolyte solution as a function of the particle volume fraction φ on the basis of Kuwabara's cell model. In the limit d-->0, the mobility expression obtained tends to that for spherical hard particles in concentrated suspensions, whereas in the limit a-->0, it becomes that for spherical polyelectrolytes (charged porous spheres with no particle core). Simple approximate analytic mobility expressions are derived for the case where relaxation effect is negligible. It is found that in practical cases, the φ dependence of the mobility is negligible for da, the mobility strongly decreases with increasing φ. Copyright 2000 Academic Press.     

Yield Stress of Concentrated Zirconia Suspensions: Correlation with Particle Interactions

The presence of a sufficient concentration of solid particles in a solution gives rise to a large increase in its viscosity and, more importantly, to significant deviations with respect to its original Newtonian behavior. Different rheological techniques are available to characterize such deviations, but the simplest one, obtention of steady-state rheograms, is already extremely useful with that purpose. In this work, this technique is applied to suspensions of zirconia particles, both synthesized with spherical geometry and commercial. The sigma(shear stress)-gamma;(shear rate) curves show that the suspensions are nonideal plastic, thus exhibiting a finite yield stress, sigma(0), and a shear-thinning flow. It is through sigma(0) that a connection can be established between steady-state rheological behavior and interaction energy between particles, since sigma(0) can be estimated as the maximum attractive force between particles multiplied by the number of bonds per unit area between a given particle and its neighbors. Having an experimental determination of sigma(0), the verification of its relation with the attractive forces requires estimation of the potential energy of interaction between any pair of particles. Two approaches will be considered: one is the classical DLVO model, in which the potential energy, V, is the sum of the van der Waals (V(LW)) and electrostatic (V(EL)) contributions. The second approach is the so-called extended DLVO theory, in which the acid-base interaction V(AB) (related to the hydrophilic repulsion or hydrophobic attraction between the particles) is considered in addition to V(LW) and V(EL). The three contributions can be calculated as a function of the interparticle distance if the particle-solution interface is characterized from both the electric and the thermodynamic points of view. The former is carried out by means of electrophoretic mobility measurements and the latter by contact angle determinations for three probe liquids on zirconia powder layers. Comparison between measured and calculated sigma(0) values was carried out for suspensions of spherical, monodisperse ZrO(2) particles, with volume fraction of solids, straight phi, ranging between 4.6 and 21.7%, in 10(-3) M NaCl solutions. In the case of commercial particles, the effects of both NaCl concentration (10(-5) to 10(-1) M) and volume fraction (3.5 to 21%) were investigated. It is found that the classical DLVO theory cannot be used to predict the yield stress when [NaCl]=10(-5) M, since the high zeta potentials and thick double layers never yield partial differential V/ partial differential R>0 (the interaction is repulsive for all distances) in such a case. A similar problem was encountered in 10(-1) M solutions, but now because V is always attractive, and no maximum force can be found. On the contrary, the extended DLVO model always yield physically reasonable sigma(0) values (coincident with those deduced from the classical approach when calculation is possible in the latter case). The comparison with experimental data shows that theory clearly underestimates sigma(0) by one order of magnitude or even more. The possible role of particle aggregation in this underestimation is discussed in terms of the scaling behavior of sigma(0) as a function of straight phi. Copyright 2000 Academic Press.     

Entropy Calculations for Charged Spheres and the Entropy of Molten Salts

Abstract

We derive an expression for the entropy S of a system of charged hard spheres within the Mean Spherical Approximation (MSA). We study the behaviour of the coulombic contribution as a function of both the charging process and the ionic radii ratio. We find that the latter gives an important ordering contribution to S, which is greatly exaggerated in the MSA. We have also calculated S using the data appropriate for the molten alkali halides. The results compare poorly with the experimental entropies and therefore cast doubts on the MSA as a suitable reference system for molten salts.     

Effect of a Dynamic Stern Layer on the Sedimentation Velocity and Potential in a Dilute Suspension of Colloidal Particles

In this paper the theory of the sedimentation velocity and potential (gradient) in a dilute suspension of charged spherical colloidal particles developed by Ohshima et al. (H. Ohshima, T. W. Healy, L. R. White, and R. W. O'Brien, J. Chem. Soc., Faraday Trans. 2, 80, 1299 (1984)) has been modified to include the presence of a dynamic Stern layer on the particle surfaces. The starting point has been the theory that Mangelsdorf and White (C. S. Mangelsdorf, and L. R. White, J. Chem. Soc., Faraday Trans. 86, 2859 (1990)) developed to calculate the electrophoretic mobility of a colloidal particle allowing for the lateral motion of ions in the inner region of the double layer (dynamic Stern layer). The effects of varying the different Stern layer parameters on the sedimentation velocity and potential are discussed and compared to the case when a Stern layer is absent. The influence of electrolyte concentration and zeta potential of the particles is also analyzed. The results show that regardless of the chosen set of Stern layer and solution parameters, the presence of a dynamic Stern layer causes the sedimentation velocity to increase and the sedimentation potential to decrease, in comparison with the standard case (no Stern layer present). These changes are almost negligible when sedimentation velocity is concerned, but they are very important when it comes to the sedimentation potential. A justification for this fact can be given in terms of an Onsager reciprocal relation, connecting the magnitudes of the sedimentation potential and the electrophoretic mobility. As previously reported, the presence of a dynamic Stern layer exerts a great influence on the electrophoretic mobility of a colloidal particle, and by means of the Onsager relation, the same is confirmed to occur when the sedimentation potential is concerned. Copyright 2000 Academic Press.     

Drag and Torque on Clusters of N Arbitrary Spheres at Low Reynolds Number

Hydrodynamics of particle clusters suspended in viscous fluids is a subject of considerable theoretical and practical importance. Using a multipole expansion of the flow velocity in a series of spherical harmonics, Lamb's fundamental solution of the Stokes flow outside a single sphere is generalized in this work to the case of N nonoverlapping spheres of arbitrary size with slip boundary conditions. The expansion coefficients are found by transforming the boundary conditions to the Lamb form and by transforming the spherical coordinates and solid spherical harmonics centered at different spheres. The problem is reduced to the solution of the linear system of equations for the expansion coefficients, which is carried out numerically. Based on the developed theory, the relation between the hydrodynamic and gyration radius of fractal-like aggregates with different structure is established. In another application, an asymptotic slip-regime dependence of the aggregate hydrodynamic radius on the Knudsen number and the number of particles is found by performing calculations of drag forces acting on the gas-borne fractal-like and straight chain aggregates. A good agreement is shown in comparing predictions of the described theory with available experimental and theoretical results on motion of various small sphere clusters in viscous fluid. Copyright 2000 Academic Press.     

Nucleation of Supramolecular Crystals in Suspensions of Monodispersed Spherical Silica Particles During Sedimentation

Growth of supramolecular crystals (SC) was studied during sedimentation in suspensions of monodisperse spherical silica particles (MSSP). The number of growth centers was found to decrease depending on the deionization of the dispersion. The process is accompanied by the corresponding enlargement of the crystals. The volume and surface components of the Gibbs energy of nucleation do not determine the probability of nucleation. The energy of electrostatic repulsion of ions covering structural units (SU), which exceeds the MSSP molecular gravitation, was the only parameter found to correlate with the number of crystallization centers.     

Supramolecular Crystallization of Monodispersed Silica Spherical Particles (MSSP) in Concentrated Suspensions

The supramolecular crystallization of MSSP concentrated suspensions in alcohol and ethyl ether with various ammonia concentrations is found to occur as a phase transition, with appearence of a pre-transitional state. The temperature dependence of the time, it takes for this state to be established, evidences for the presence of processes of nucleation and activation character.     

Electrical Conductivity and Dielectric Dispersion Phenomena of Concentrated TiO(2) Suspensions

The complex conductivity of concentrated TiO(2) suspensions (up to 50 vol%) was measured over a large frequency range (1 MHz-1.8 GHz), as a function of grain volume content. These measurements highlight relaxation phenomena in the intermediate frequency range, which are associated with the dispersed powder. These phenomena were previously noted in O'Brien's theoretical developments. A quantitative data analysis was made, in terms of time constant distribution, using the CONTIN software, from Provencher. As a result, a complex process is highlighted, including two main mechanisms in different ranges of time constants. Particularly, we showed good agreement between the higher frequency mechanism and the O'Brien theory. From Dukhin's lambda ratios, which are ratios of grain surface to bulk electrolyte conductances, we calculated the electrolyte conductivity as a function of powder concentrations. At higher powder concentrations, these values are different from those measured with centrifuged liquids. Copyright 2000 Academic Press.     

Contribution of the Sedimentation and Coalescence Mechanisms to the Separation of Concentrated Water-in-Oil Emulsions

Crude oil is, in the vast majority of cases, produced together with formation water in the form of water/oil emulsions. Until recently oil/water separators were simply designed using Stokes' law. In order to improve the design of these separators the two main contributing mechanisms, sedimentation and coalescence, have to be better understood. This article presents a method that distinguishes the respective contributions of the sedimentation and coalescence mechanisms. Two series of experiments have been carried out, the first with a system heavily charged in surfactant that only allows sedimentation of the emulsions droplets. The second with a much lower surfactant concentration allows both sedimentation and coalescence to take place. By comparing the separation velocities of the oil/emulsion interfaces of the two series of experiments, it seems possible to determine the contribution of the two mechanisms towards the separation.     

Effect of Side Chains and Sulfonic Groups on the Performance of Polycarboxylate-Type Superplasticizers in Concentrated Cement Suspensions

Polycarboxylate-type superplasticizers (PCs) containing different side chains and sulfonic groups have been synthesized, and the effect of side chains and sulfonic groups on their performance in cementitious systems has been intensively investigated by measuring zeta potential, thickness of absorption layer, paste fluidity, rheological properties as well as the setting time in this paper. Results show that the PC containing both short poly(ethylene oxide) (PEO) side chains and long PEO side chains with the molar ratio of 1:1 has a better dispersibility than the PC containing only short PEO side chains or only long PEO side chains in cement suspensions. The shorter the side chain of the PC, the longer the setting time of cement paste incorporating it. An appropriate increase of sulfonic group content is beneficial for the improvement of dispersibility for the PC and leads to no obvious change for the setting time. It also suggests that there is a geometrical balance between the PEO side chains and sulfonic groups for the performance of PC. This work is not only helpful for understanding the relationship of molecular structure of PCs and their performance, but also further designing optimum molecular structure of PC to meet the requirement in different concrete system.     

Characterization of the Electrical Conductivity of Concentrated Suspensions of Silica in Aqueous Solutions of Sulfuric Acid

The electrical conductivity of stable concentrated suspensions of SiO₂ in aqueous solutions of sulfuric acid was studied as influenced by the concentration and size of SiO₂ particles.     

Electrokinetic Potential of Particles in Suspensions and Donnan Equilibrium in a Thin Gel Film

The influence exerted by the thickness of a gel layer on the difference of the electric potentials of phases and on the distribution of the potential near the phase boundary are considered in terms of the classical theory of the Donnan equilibrium in a two-phase system constituted by a gel and an electrolyte solution. The results obtained make it possible to explain a number of experimental facts.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 2, 2005, pp. 224–228.Original Russian Text Copyright © 2005 by Bibik.     

Low-Frequency Dielectrophoresis and the Polarization Interaction of Uncharged Spherical Particles with an Induced Debye Atmosphere of Arbitrary Thickness

The electroosmotic component of the mutual dielectrophoresis is accounted for in the theory of the polarization interaction of uncharged particles. Previously, for the case when the polarization charge layer thickness is small as compared with the particle radius, it was shown that the electro-osmosis exerts significant effect on the motion of a particle in a nonuniform field (external or induced by a neighboring particle). The electro-osmosis in the induced Debye atmosphere of arbitrary thickness is considered in this paper. A class of systems characterized by the formation of transverse linear aggregates of particles is determined. The aggregates are weakly conducting media with nonconducting particles but more polar than the medium. The possibility of the occurrence of transverse electrocoagulation structures, which was originally obtained by us using the heuristic approach, is supported by results obtained in the solution of the electrohydrodynamic problem of the long-range interaction of polarized particles. The results obtained confirm high efficiency of the heuristic method used.     

Colloid Vibration Potential in a Concentrated Suspension of Spherical Colloidal Particles

A relation between the dynamic electrophoretic mobility of spherical colloidal particles in a concentrated suspension and the colloid vibration potential (CVP) generated in the suspension by a sound wave is obtained from the analogy with the corresponding Onsager relation between electrophoretic mobility and sedimentation potential in concentrated suspensions previously derived on the basis of Kuwabara's cell model. The obtained expression for CVP is applicable to the case where the particle zeta potential is low, the particle relative permittivity is very small, and the overlapping of the electrical double layers of adjacent particles is negligible. It is found that CVP shows much stronger dependence on the particle volume fraction φ than predicted from the φ dependence of the dynamic electrophoretic mobility. It is also suggested that the same relation holds between the electrokinetic sonic amplitude of a concentrated suspension of spherical colloidal particles and the dynamic electrophoretic mobility. Copyright 1999 Academic Press.     

Calculation of the Liquid and Gas Permeability of Hydrophobic Low-Porosity Membranes of an Arbitrary Thickness

A method for calculating the liquid and gas permeability of hydrophobic low-porosity membranes of an arbitrary thickness is described. The calculation is based on the solution of a problem on percolation—the procedure of finding the distribution of liquid and gas over the membrane thickness. The dependence of the permeability for liquid on the share of pores that are potentially accessible to being filled with liquid is obtained for both thin and thick membranes. This dependence is of a universal nature and can easily be recalculated into a dependence of permeability on the pressure drop for membranes with any distribution of pores by size. Numerical estimates of principal characteristics for a membrane that possesses pores of three types are performed. The characteristics in question include permeabilities for liquid and gas; fluxes of the liquid; critical pressures, at which the permeability for liquid turns other than zero; and the working range of pressures, in which the membrane is capable of working normally. All these data permit the optimization of the operation of similar membranes, in particular, gas-delivering membranes that are used in hydrogen–oxygen fuel cells with a solid polymer electrolyte.     

Electric Potential and Reaction Rates at Charged Surfaces in Asymmetric Electrolytes-An Analytic Approach

The electric potential and reaction rates of ions hitting the chemically active surfaces of microcrystals in an asymmetric electrolyte are computed analytically. Following ideas of Debye we start by solving the Poisson-Boltzmann equations and by determining the electric potential of the transport equations. We find distinct deviations when comparing our result with the Gouy-Chapman formula. In a simple model approximating a situation in which lead and hydrogen ions can react at goethite surfaces we compute analytically the currents of ions diffusing to the surfaces of microcrystals where they undergo a chemical reaction. We compute the reaction rates that can be controlled either by chemical reactions at the surface of the microcrystals or by diffusional transport. For realistic parameters of our model we find that the diffusional transport is the rate determining step. Copyright 2001 Academic Press.