Primary electroviscous effect in a moderately concentrated suspension of charged spherical colloidal particles

On the basis of the standard theory of the primary electroviscous effect in a moderately concentrated suspension of charged spherical particles in an electrolyte solution presented by Ruiz-Reina et al. (Ruiz-Reina, E.; Carrique, F.; Rubio-Hernández, F. J.; Gómez-Merino, A. I.; García-Sánchez, P. J. Phys. Chem. B 2003, 107, 9528), which is applicable for the case where overlapping of the electrical double layers of adjacent particles can be neglected, the general expression for the effective viscosity or the primary electroviscous coefficient p of the suspension is derived. This expression is applicable for a suspension of spherical particles of radius a carrying arbitrary zeta potentials zeta at the particle volume fraction phi < or = 0.3 for the case of nonoverlapping double layers, that is, at kappaalpha > 10 (where kappa is the Debye-Hückel parameter). A simple approximate analytic expression for p applicable for particles with large kappaalpha and arbitrary zeta is presented. The obtained viscosity expression is a good approximation for moderately concentrated suspensions of the particle volume fraction phi < or = 0.3, where the relative error is negligible for kappaalpha > or =100 and even at kappaalpha = 50 the maximum error is approximately 20%. It is shown that a maximum of p, which appears when plotted as a function of the particle zeta potential, is due to the relaxation effect as in the case of the electrophoresis problem.     

Electrophoresis of a concentrated aqueous dispersion of non-Newtonian drops

The electrophoresis of a concentrated dispersion of non-Newtonian drops in an aqueous medium, which has not been investigated theoretically in the literature, is analyzed under conditions of low zeta potential and weak applied electric field. The results obtained provide a theoretical basis for the characterization of the nature of an emulsion and a microemulsion system. A Carreau fluid, which has wide applications in practice, is chosen for the non-Newtonian drops, and the unit cell model of Kuwabara is adopted to simulate a dispersion. The effects of the key parameters of a dispersion, including its concentration, the shear-thinning nature of the drop fluid, and the thickness of the double layer, on the electrophoretic behavior of a drop are discussed. In general, the more significant the shear-thinning nature of the drop fluid is, the larger the mobility is, and this effect is pronounced as the thickness of the double layer decreases. However, if the double layer is sufficiently thick, this effect becomes negligible. In general, the higher the concentration of drops is, the smaller the mobility is; however, if the double layer is either sufficiently thin or sufficiently thick, this effect becomes unimportant.     

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.     

Destabilization mechanisms in a triple emulsion with Janus drops

The destabilization mechanism was investigated of a triple Janus emulsion. The inner part of the emulsion consisted of Janus drops of a vegetable oil (VO) and a silicone oil (SO) in an aqueous (W) drop, (VO+SO)/W. This drop, in turn was dispersed in a VO drop forming a double emulsion (VO+SO)/W/VO. Finally, these complex drops generated a complex Janus (SO+VO)/W/VO/SO triple emulsion by being dispersed in a continuous SO phase. The observations were limited to the time dependence of the over-all creaming/sedimentation processes, to the separation of layers of the compounds and to optical microscopy of the drop configuration with time. In the destabilization process the rise of the complex drops, (SO+VO)/W/VO, caused crowding in the upper part of the emulsion, which in turn led to enhanced coalescence, inversion and separation of a dilute vegetable oil emulsion. As a consequence of the separation of VO in the process, the remaining drops contained a greater W fraction and greater density. This change, in turn, resulted in sedimentation of the complex drops to form several high internal ratio morphologies in an SO continuous emulsion in the lower part of the test tube, among them a W/VO/SO emulsion. Finally, an inversion took place into an SO/VO/W double emulsion forming a separate bottom layer.     

Existence of hydration forces in the interaction between apoferritin molecules adsorbed on silica surfaces

The atomic force microscope, together with the colloid probe technique, has become a very useful instrument to measure interaction forces between two surfaces. Its potential has been exploited in this work to study the interaction between protein (apoferritin) layers adsorbed on silica surfaces and to analyze the effect of the medium conditions (pH, salt concentration, salt type) on such interactions. It has been observed that the interaction at low salt concentrations is dominated by electrical double layer (at large distances) and steric forces (at short distances), the latter being due to compression of the protein layers. The DLVO theory fits these experimental data quite well. However, a non-DLVO repulsive interaction, prior to contact of the protein layers, is observed at high salt concentration above the isoelectric point of the protein. This behavior could be explained if the presence of hydration forces in the system is assumed. The inclusion of a hydration term in the DLVO theory (extended DLVO theory) gives rise to a better agreement between the theoretical fits and the experimental results. These results seem to suggest that the hydration forces play a very important role in the stability of the proteins in the physiological media.     

Colloid vibration potential and ion vibration potential in a dilute suspension of spherical colloidal particles

A general electroacoustic theory is presented for the macroscopic electric field in a dilute suspension of spherical colloidal particles in an electrolyte solution, which consists of the colloid vibration potential (CVP) and the ion vibration potential (IVP), induced by an oscillating pressure gradient field due to an applied sound wave. This is a unified theory that unites previous theories for CVP and those for IVP. Approximate analytic expressions are derived for CVP and IVP. The obtained IVP expression agrees with Debye's formula that is corrected by taking into account the force acting on the electrolyte ions as a result of the pressure gradient in the sound wave. The obtained CVP expression is correct to the first order of the particle zeta potential and applicable for arbitrary kappaalpha, where kappa is the Debye-Hückel parameter and alpha is the particle radius. It is found that an Onsager relation holds between CVP and dynamic electrophoretic mobility. It is also shown that the CVP from particles with very small kappaalpha approaches IVP; that is, in the limit of very small kappaalpha a particle behaves like an ion.     

Electrophoresis of a concentrated spherical dispersion at arbitrary electrical potentials

The electrophoretic behavior of a concentrated spherical dispersion is investigated theoretically. The present analysis extends those in the literature in that both the surface potential of a particle and the strength of the applied electric field are arbitrary and both the effects of double-layer polarization and the overlapping between neighboring double layers are taken into account. Results based on these conditions are highly desirable since they cover essentially all the possible experimental conditions in practice. We show that, for a fixed surface potential and strength of applied electric field, the higher the concentration of particle, the smaller the mobility. Counterions are found to accumulate at the downstream side of a particle. Double-layer polarization is inappreciable if either it is thick or the concentration of the particle is high.     

Field-induced alignment of a smectic-A phase: a time-resolved x-ray diffraction investigation

The field-induced alignment of a smectic-A phase is, in principle, a complicated process involving the director rotation via the interaction with the field and the layer rotation via the molecular interactions. Time-resolved nuclear magnetic resonance spectroscopy has revealed this complexity in the case of the director alignment, but provides no direct information on the motion of the layers. Here we describe a time-resolved x-ray diffraction experiment using synchrotron radiation to solve the challenging problem of capturing the diffraction pattern on a time scale which is fast in comparison with that for the alignment of the smectic layers. We have investigated the alignment of the smectic-A phase of 4-octyl-4(')-cyanobiphenyl by a magnetic field. The experiment consists of creating a monodomain sample of the smectic-A phase by slow cooling from the nematic phase in a magnetic field with a flux density of 7 T. The sample is then turned quickly through an angle phi(0) about an axis parallel to the x-ray beam direction but orthogonal to the field. A sequence of two-dimensional small angle x-ray diffraction patterns are then collected at short time intervals. Experiments were carried out for different values of phi(0), and at different temperatures. The results show that the alignment behavior changes fundamentally when phi(0) exceeds 45 degrees, and that there is a sharp change in the alignment process when the temperature is less than 3 degrees C below the smectic-A-nematic transition. The results of the x-ray experiments are in broad agreement with the NMR results, but reveal major phenomena concerning the maintenance of the integrity of the smectic-A layer structure during the alignment process.     

Electrophoresis of a concentrated dispersion of spherical particles in a non-Newtonian fluid

Electrophoresis is one of the most widely used analytical tools for the quantification of the charged conditions on the surface of fine particles including biological entities. Although it has been studied extensively in the past, relevant results for the case when the dispersion medium is non-Newtonian are very limited. This may occur, for example, when the concentration of the dispersed phase is not low, which is not uncommon in practice. Here, the electrophoresis of a concentrated spherical dispersion in a Carreau fluid is analyzed theoretically under the conditions of low electric potential and weak external applied electrical field. A pseudospectral method coupled with a Newton-Raphson iteration procedure is used to solve the electrokinetic equations describing the phenomenon under consideration. We conclude that the more significant the shear thinning effect of the fluid, the larger the mobility, and this phenomenon is pronounced for the case when the double layer surrounding a particle is thin. We show that if the double layer is thin and the effect of shear thinning is significant, a second vortex can be observed in the neighborhood of a particle.     

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.     

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.     

Electroosmosis through a Cation-Exchange Membrane: Effect of an ac Perturbation on the Electroosmotic Flow

The viscous behavior of oil-in-water (O/W) emulsions is studied over a broad range of dispersed-phase concentrations (φ) using a controlled-stress rheometer. At low-to-moderate values of φ (φ<0.60), emulsions exhibit Newtonian behavior. The droplet size does not exert any influence on the viscosity of Newtonian emulsions. However, at higher values of φ, emulsions exhibit shear-thinning behavior. The viscosity of shear-thinning emulsions is strongly influenced by the droplet size; a significant increase in the viscosity occurs when the droplet size is reduced. With the decrease in droplet size, the degree of shear thinning in concentrated emulsions is also enhanced. The viscosity data of Newtonian emulsions are described reasonably well by the cell model of Yaron and Gal-Or (Rheol. Acta 11, 241 (1972)), which takes into account the effects of the dispersed-phase concentration as well as the viscosity ratio of the dispersed phase to continuous phase. The relative viscosities of non-Newtonian emulsions having different droplet sizes but the same dispersed-phase concentration are scaled with the particle Reynolds number. The high shear viscosities of non-Newtonian emulsions can be predicted fairly well by the cell model of Yaron and Gal-Or (Rheol. Acta 11, 241 (1972)). Copyright 2000 Academic Press.     

Rheology of double emulsions

New equations for the viscosity of concentrated double emulsions of core-shell droplets are developed using a differential scheme. The equations developed in the paper predict the relative viscosity (eta(r)) of double emulsions to be a function of five variables: a/b (ratio of core drop radius to shell outer radius), lambda(21) (ratio of shell liquid viscosity to external continuous phase viscosity), lambda(32) (ratio of core liquid viscosity to shell liquid viscosity), phi(DE) (volume fraction of core-shell droplets in double emulsion), and phi(m)(DE) (the maximum packing volume fraction of un-deformed core-shell droplets in double emulsion). Two sets of experimental data are obtained on the rheology of O/W/O (oil-in-water-in-oil) double emulsions. The data are compared with the predictions of the proposed equations. The proposed equations describe the experimental viscosity data of double emulsions reasonably well.     

Electrophoresis of a colloidal sphere in a spherical cavity with arbitrary zeta potential distributions

An analytical study is presented for the quasi-steady electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity when the surface potentials are arbitrarily nonuniform. The applied electric field is constant, and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and the gap width between the surfaces. The presence of the cavity wall causes three basic effects on the particle velocity: (1) the local electric field on the particle surface is enhanced or reduced by the wall; (2) the wall increases the viscous retardation of the moving particle; and (3) a circulating electroosmotic flow of the suspending fluid exists because of the interaction between the electric field and the charged wall. The Laplace and Stokes equations are solved analytically for the electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the particle are obtained. To apply these formulas, one has to calculate only the monopole, dipole, and quadrupole moments of the zeta-potential distributions at the particle and cavity surfaces. It is found that the contribution from the electroosmotic flow developing from the interaction of the imposed electric field with the thin double layer adjacent to the cavity wall and the contribution from the wall-corrected electrophoretic driving force to the particle velocities can be superimposed as a result of the linearity of the problem.     

Electrical potential distribution over the bilayer lipid membrane due to amphiphilic ion adsorption

Potential drops at the boundary of the bilayer lipid membrane (BLM) due to amphiphilic anion (dodecylsulfate) adsorption have been investigated. The magnitude of these drops was determined by different experimental methods: inner field compensation (IFC), electrophoretic mobility and current relaxation (tetraphenylboron and dipicrylamine were taken as probe anions).The boundary potential (BP) drops (IFC method) do not depend on the electrolyte concentration for neutral membranes. The ζ-potential values in the same conditions are considerably smaller than the BP drops measured by the IFC method. The potential drops, determined with the help of the initial BLM conductivity changes (current relaxation method) coincide with the BP drops (IFC method). The adsorption of amphiphilic ions leads to a decrease in the rate constant of the movement of hydrophobic ions through the BLM (current relaxation method).To explain the results obtained, it is suggested that a potential drop due to amphiphilic ion adsorption is located not only in the diffuse double layer, but also in a layer inside the membrane. The latter is not screened by electrolyte solution ions and could not be registered by the electrophoretic method.     

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.     

Laser diffraction estimation of particle size distribution of slightly water-soluble drugs coexisting with additives: application to solid dosage forms.

A simple and quantitative evaluation method for particle size distribution (fx(r)) of slightly water-soluble drugs dispersed in an aqueous medium together with other water-insoluble additives was developed using a laser diffraction method. The particle size distribution function of the powder mixture, (f(r)), was assumed as f(r) = phi x.fx(r) + phi a.fa(r), where phi is the volume fraction of each component dispersed in a measurement medium and fa(r) is the distribution function of another water-insoluble additive "a". In order to calculate fx(r) from f(r), it is necessary to know the density of drug and additive in the measurement medium, d(x) and d(a), but this is difficult to determine since particles usually swell in the medium. Thus, a method was developed to use their relative value, delta a (= da/dx). As a practical application, oxolinic acids (OA) of three sizes (OA-S (about 2 microns), OA-M (about 7 microns) and OA-L (about 24 microns)) were used as model drugs. delta a values were determined for various additives using the mixture of OA-S and each additive. Then, using delta as, fx(r) of OA-M or OA-L in the mixture containing OA-M or OA-L and additives was calculated from the f(r) experimentally determined for the mixture. They agreed well with their original distributions. The method was applied to some dosage forms, and the results obtained had good correlation with those from turbidity, wet sieving or dissolution test.     

Dynamic electrophoretic mobility of spherical colloidal particles in salt-free concentrated suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.