The primary electroviscous effect of prolate silica sols

The intrinsic viscosity and the dynamic mobility of four silica sols have been measured as a function of the ionic strength. It was found that intrinsic viscosity decreased with increasing ionic strength, which we attribute to the primary electroviscous effect. The geometry and the charge of the particles were fitted using experimental viscosity, light scattering, and dynamic mobility data, where the intrinsic viscosity measured at the highest ionic strength for a given sol was used as input data in our analysis. Further, the boundary element (BE) method was used to calculate the primary electroviscous effect and electrophoretic mobility of charged prolate ellipsoids. These calculations were then compared with experimental data, and the primary electroviscous effect was subtracted from the intrinsic viscosity at a given ionic strength, which led to a slightly altered geometry of the particles. This revised geometry was used as input data using the BE method, and the procedure was repeated iteratively until agreement was obtained at high ionic strength. In general, good agreement between theory and experiment was found.     

The Primary Electroviscous Effect: Thin Double Layers (akappa>1) and a Stern Layer

The primary electroviscous effect due to the charge clouds surrounding spherical charged particles suspended in an electrolyte was studied by Hinch and Sherwood (J. Fluid Mech. 132, 337 (1983)) in the limit of double layers thin compared to the particle radius a. Here we introduce the effect of a dynamic Stern layer into that analysis, in order to explain the numerical results of Rubio-Hernández et al. (J. Colloid Interface Sci. 206, 334 (1998)) in terms of the ratio of the tangential ionic fluxes within the charge cloud to those within the Stern layer. The predictions of the asymptotic analysis are compared with those of numerical computations. The thickness of the charge cloud is characterized by the Debye length kappa(-1). If akappa>10 the predictions of the asymptotic analysis exhibit the same qualitative behavior as the numerical results, but akappa>1000 is required to achieve quantitative agreement to within 2.5%. Copyright 2000 Academic Press.     

Electroviscous Effect in Dilute Suspensions of Alumina

A study on the electroviscous effect of alumina suspensions has been made. At the low volume fraction of the particles studied here only a first-order effect was detected. Ubbelohde-type capillary viscometers have been used. A simple method to determine the hydrodynamic constant k(1) has been proposed. The experimental primary electroviscous coefficients corresponding to different electrolyte concentrations have been compared with two different theoretical approachs (I. G. Watterson, and L. R. White, J. Chem. Soc. Faraday Trans. 2 77, 1115 (1981); F. J. Rubio-Hernández, E. Ruiz-Reina, and A. I. Gómez-Merino, J. Colloid Interface Sci. 206, 334 (1998)) and the results suggest that the presence of a dynamic Stern layer plays a certain role in this effect. Copyright 2000 Academic Press.     

An experimental test of Booth's primary electroviscous effect theory

The primary electroviscous effect has been investigated in dilute suspensions of titanium oxide (anatase), the viscosities of which were measured by means of a capillary viscometer with automatic timing. The linear relation between viscosity and solids volume fraction was first determined at the isoelectric point of the particles when the particles are uncharged, and the electroviscous contribution to the intrinsic viscosity was then determined at other values of pH. Booth's theory (Proc. R. Soc. London Ser. A203, 533 (1950)) agrees well with the experimental results when the particle zeta potential is small and the double layer is thin (kappa alpha approximately 7.3), but agreement is poor when the double layer is thick (kappa alpha approximately 0.6).     

A STUDY OF THE PRIMARY ELECTROVISCOUS EFFECT IN PYREX GLASS SUSPENSIONS.

An experimental investigation on the electrokinetic phenomenon known as primary electroviscous effect is described for suspensions of Pyrex glass, a highly charged and well known material. By means of an automatic method, the viscosity of the suspensions is measured for different volume fractions of solids, at various electrolyte concentrations and pH values. These measurements allow the estimation of the electroviscous coefficient, p. The electrophoretic mobility was determined for the same systems and zeta potential calculated from these experimental data in order to carry out the comparison between the measured values of p and different theoretical predictions. A qualitative agreement between theory and experiment was found in many cases, but the rigorous theories seem to systemmatically underestimate the experimental p values. The reasons for this disagreement are discussed in addition to the general trends of the electrokinetic behaviour of Pyrex glass.     

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.     

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.     

Electroviscous effect of moderately concentrated colloidal suspensions: Stern-layer influence

A previous model for the viscosity of moderately concentrated suspensions has been extended. The influence of a dynamic Stern layer (DSL), which produces an additional surface conductance at the electrolyte-particle interface, is included. The theoretical treatment is based on Happel's cell model with Simha's boundary conditions for the interparticle hydrodynamic interactions and on a dynamic Stern-layer model for ionic conduction on the particle surface according to Mangelsdorf and White (ref 39). The results are valid for arbitrary zeta potentials and double-layer thickness. Extensive theoretical predictions are shown and interesting new behaviors are found. The comparison with the results in the absence of additional surface conductance shows a great influence of this mechanism in the energy dissipation during the laminar flow of these suspensions. We conclude that the inclusion of a dynamic Stern layer will be required to match the predictions with the experimental results.     

Primary Electroviscous Effect with a Dynamic Stern Layer: Low kappaa Results

The classical treatments of the primary electroviscous effect show important discrepancies with respect to the experimental data. A possible better agreement may be found if the contribution of the ions adsorbed on the Stern layer, which can move tangentially near the particle surface, is taken into account. This contribution has been incorporated into the Watterson-White theory. A study of the influence of the Stern-layer parameters on the primary electroviscous coefficient has been made. Copyright 2000 Academic Press.     

Dielectric relaxation pattern of dilute colloidal suspensions

An immediate method of analysis of the relaxation characteristics of a colloidal suspension, like of any dielectric, is based on the so-called Cole-Cole representation (imaginary part versus real part) of its complex dielectric constant in a wide frequency range. In this work, we show theoretical plots calculated according to the models developed by DeLacey and White (J Chem Soc Faraday Trans 2 77:2007–2039), and by Rosen et al. (J Chem Phys 98: 4183–4194; this model uses the dynamic Stern layer theory). Both theoretical approaches to the dielectric relaxation pattern of a colloidal suspension are compared to each other, and to experimental data obtained on polystyrene suspensions. Although no significant differences are found between the theoretical predictions of the relaxation patterns (except for the values of the dielectric constant; the DSL model yields higher polarizabilities of the suspensions), none of the models can exactly reproduce the frequency dependence of the dielectric constant of a colloidal system. We propose a modification of DeLacey and White's model to include the possibility that the ionic drag coefficients depend on the ion position in the double layer. The final results show that the general trends of the frequency dependence of the quantities involved are not modified, irregardless of the changes in ionic drag coefficients.     

Viscosity and electrophoretic mobility of cesium fullerenehexamalonate in aqueous solutions--comparing experiments and theories on nanometer-sized spherical polyelectrolyte

The viscosity of aqueous solutions of cesium fullerenehexamalonate T h -C 66(COOCs) 12, a rigid spherical nanometer-sized polyvalent salt, was measured by the Ubbelohde-type viscometer. The measurements were performed without added salt at 25 degrees C in the concentration range between 7 and 320 g/dm (3). THe concentration dependence of the obtained reduced viscosity was compared with the theoretical prediction, taking into account contributions stemming from the intrinsic viscosity, hydrodynamic perturbations of the hypothetically bare fullerenehexamalonate macroion, the primary electroviscous effect, and the secondary electroviscous effect. Using the geometric radius of the bare macroion from the previous measurements of the estimated effective charge of the macroion and from the small-angle X-ray scattering data of the estimated thickness of the compact shell of counterions electrostatically bound to the macroion, a good agreement between theory and the experiment was obtained in the range of the lowest and of the highest concentrations. Electrostatic interactions are identified as the main cause of the increased reduced viscosity at the lowest measured concentrations. At the highest concentrations, electrostatic interactions are effectively screened, and the influence of binary hydrodynamic interactions and perturbations of the hypothetical bare macroion prevails over electrostatic contributions to the increased viscosity. The electrophoretic mobility of the fullerenehexamalonate ion in aqueous salt-free medium was computed with the same value for the radius of the fullerenehexamalonate macroion as that used in the calculation of viscosity. The numerical solution of Ohshima's equation agreed well with the experimental values.     

Dynamic light scattering for characterization of latices

With photon correlation spectrometry the diffusion coefficients of colloid particles in highly diluted aqueous suspensions can be measured and average diameters and polydispersities of the samples can be determined. Electrokinetic and electroviscous effects caused by polarization of the electrostatic double layer influence the diffusion of the particles. The adsorption of macromolecules at the interfaces of the particles results in an increase of the hydrodynamic diameter and a decrease of the diffusion and sedimentation coefficients. The hydrodynamic thicknesses of the polymer layers can be evaluated. The thickness values and their dependences on adsorbed amount and molar mass can only be interpreted by the existence of long tails of the adsorbed macromolecules dangling from the interface into the solution. The resulting conformation model is supported by the new theory of Scheutjens-Fleer. Special importance have those tails for the interaction of particles and their stability and flocculation in disperse systems.     

The primary electroviscous effect of polystyrene latexes

An investigation on the primary electroviscous effect of polystyrene latexes has been made. Capillary viscometers of Ubbelohde type have been used. The comparison of the results obtained with the theories allow us to conclude that the effect is underestimated for low electrolyte concentrations. We suggest that this underestimation is due to an additional surface conductance into the electric double layer. This interpretation is consistent with previous studies on electrophoretic mobility of the same system.     

The primary electroviscous effect in colloidal suspensions

Although a well-defined electrokinetic phenomenon, the primary electroviscous effect in dilute colloidal suspensions is still an unsolved problem. Most of the experimental tests of the different theories that we have studied have shown a lack of agreement. We have developed, during the last years, new theoretical approaches obtaining, finally, a much better agreement with the experimental results. The corrections are defined in two lines: first, it is accepted that ions present into the Stern layer, in which the fluid is stagnant, can tangentially move; second, it is accepted that the hydrodynamic interaction between colloidal particles exists although the suspensions are extremely diluted. The remarkable conclusion of our work is that the combination of both corrections should give correct theoretical results.     

The adsorption structure of nonionic surfactant on the sessile mercury electrode in a thin liquid film

In relation to a colloid stability, the adsorption structure of the Stern layer on a sessile mercury electrode in a thin liquid film of nonionic surfactant was investigated by measuring the double layer capacitance. The Stern capacitance on the electrode in the film could be detected when the measuring frequency used was low, for the resistance of the film was not extremely high but of the order of several thousand ohm. It was found that the adsorption structure of nonionic surfactant in the thin liquid film shows a stratification different from that of bulk.     

Electroviscous effect on the streaming current in a pH-regulated nanochannel

Accurate and rapid estimation of the streaming current in nanochannels is crucial for the development of the nanofluidics based power generation apparatus. In this study, an analytical model is developed for the first time to examine the electroviscous effect on the streaming current/conductance in a pH-regulated nanochannel by considering practical effects of multiple ionic species, surface chemistry reactions, and the Stern layer. Predictions from the model are in good agreement with the experimental results of the streaming conductance in silica nanochannels available in the literature. The electroviscous effect could have a significant reduction of ca. 30% in the streaming conductance at medium pH and low salt concentration.     

Improved understanding of the effect of electrical double layer on pressure-driven flow in microchannels

Traditionally, the effects of electrical double layer on pressure-driven flow in microchannels were modeled by using the Poisson-Boltzmann equation and the fluid momentum equation with a flow-induced body force term. Such a model, however, usually underestimate the electrical double layer effects on the flow. In this study, a theoretical model of the electrical double layer field is developed to provide a better understanding of the electrical double layer effects. The electrical potential and ionic concentration distribution in dilute solutions in small microchannels are investigated by numerically solving this new model. This newly developed model predicted the deficit of counter-ions in the bulk liquid region due to the accumulation of counter-ions in the EDL region, and the surplus of co-ions in the bulk liquid region due to rejection of the co-ions in the EDL region. The presence of the net charges in the bulk liquid region is responsible for the strong electroviscous effects in dilute solutions in small microchannels.     

Electroviscous sphere-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged spherical particle and a charged plane wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from Cox's general theory [R.G. Cox, J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential and electroviscous flow field. It is a priori assumed that the double layer thickness surrounding each charged surfaces is much smaller than the particle size. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the sphere are explicitly determined analytically for small particle-wall distances, but low and intermediate Peclet numbers.     

The electrokinetic properties of latex particles: comparison of electrophoresis and dielectrophoresis

A comprehensive study of the AC and DC electrokinetic properties of submicrometre latex particles as a function of particle size and suspending medium conductivity and viscosity is presented. Electrophoretic mobility and dielectrophoretic cross-over results were measured for particle diameters ranging from 44 to 2000 nm. The zeta potentials of the particles were calculated from the electrophoretic mobility data for different suspending medium conductivities, using various models, with and without the inclusion of surface conduction. The dielectrophoretic data was analysed to derive values for the Stern layer conductance and zeta potentials.     

The influence of stern layer conductance on the dielectrophoretic behavior of latex nanospheres

The influence of the Stern layer conductance on the dielectrophoretic behavior of sub-micrometer-sized latex spheres is examined. The dielectrophoretic response of the particles is measured and analyzed in terms of a model of surface conductance divided into discrete components related to the structure of the double layer. The effect of both co- and counterions in the bulk solution on the Stern layer conductance is demonstrated.