Primary electroviscous effect in a dilute suspension of soft particles

A theory for the primary electroviscous effect in a dilute suspension of soft particles (i.e., particles coated with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution is presented. The general expression for the effective viscosity eta s of the suspension and the primary electroviscous coefficient p, which is further expressed in terms of a function L, is given. On the basis of the general expressions, we derive approximate analytic expressions for eta s and p, which are applicable when the density of the fixed charges distributed within the surface layer is low. Further we obtain a simple approximate analytic expression (without involving numerical integrations) for p applicable for most practical cases. It is found that the function L exhibits a minimum when plotted as a function of kappa a (kappa is the Debye-Hückel parameter and a is the particle core radius), unlike the case of a suspension of hard particles, in which case L decreases as kappa a increases, exhibiting no minimum. The presence of a minimum for the case of a suspension of soft particles is due to the fact that L is proportional to 1/kappa 2 at small kappa a and to kappa 2 at large kappa a. Because of the presence of this minimum, the difference in L between soft and hard particles becomes very large for large kappa a.     

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.     

The electroviscous effect in ethylcellulose latex suspensions. Effect of ionic strength and correlation between theory and experiments

 This article describes an experimental and theoretical investigation of the so-called primary electroviscous effect, i.e., the increase in suspension viscosity due to the existence of an electrical double layer around the particles. By measuring the viscosity of ethylcellulose latex suspensions, the electroviscous coefficient, the quantity measuring the effect, was estimated for different concentrations of 1-1 electrolyte in the dispersion medium. These data were compared with the predictions of Watterson and White's model, using the zeta potential of the particles deduced from electrophoretic mobility measurements. It was found that the theory considerably underestimates the effect. In an attempt to improve the agreement between data and predictions, the model was generalized to include the possibility (dynamic Stern layer) that ions in the inner part of the double layer have nonzero mobility. The general theory, however, predicts even lower values of the electroviscous coefficients, thus increasing the separation between calculated and measured electroviscous coefficients. A careful analysis of the ionic concentrations and velocity profiles with and without dynamic Stern layer corrections can account for this fact, but leaves unsolved the problem of the large discrepancies found in the theoretical explanation of the strength of the electroviscous effect. Received: 19 October 1999/Accepted: 17 December 1999     

Primary electroviscous effect in a dilute suspension of charged mercury drops

The standard theory of the primary electroviscous effect in a dilute suspension of charged spherical rigid particles in an electrolyte solution (Watterson, I. G.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1981, 77, 1115) is extended to cover the case of a dilute suspension of charged mercury drops of viscosity eta(d). A general expression for the effective viscosity or the electroviscous coefficient p of the suspension is derived. This expression tends to that for the case of rigid particles in the limit of eta(d) --> infinity. We also derive an approximate analytical viscosity expressions applicable to mercury drops carrying low zeta potentials at arbitrary kappaa (where kappa is the Debye-Hückel parameter and a is the drop radius) and to mercury drops as well as rigid spheres with arbitrary zeta potentials at large kappaa. It is shown that the large-kappaa expression of p for rigid particles predicts a maximum when plotted as a function of zeta potential. This result for rigid particles agrees with the exact numerical results of Watterson and White. It is also shown that in the limit of high zeta potential the effective viscosity of a suspension of mercury drops tends to that of uncharged rigid spheres given by Einstein's formula (Einstein, A. Ann. Phys. 1906, 19, 289), whereas in the opposite limit of low zeta potential the effective viscosity approaches that of a suspension of uncharged liquid drops derived by Taylor (Taylor, G. I. Proc. R. Soc. London, Ser. A 1932, 138, 41).     

The electroviscous force between charged particles: beyond the thin-double-layer approximation

We have investigated the hydrodynamic drag force between charged particles in electrolyte solutions, specifically the electroviscous force that arises from the distortion of the electrical double layers by the flow field. We report an improvement on the thin-double-layer theory (S.G. Bike, D.C. Prieve, J. Colloid Interface Sci. 136 (1990) 95-112), using a more accurate boundary condition for the radial charge current. The differences become important when the double layers start to overlap. We have found that nonlinear hydrodynamic effects are small, whereas nonlinear electric effects can be significant, in some instances leading to qualitatively different behavior. If the ion diffusivities are highly asymmetric, the electroviscous force can be reduced by an order of magnitude when there is an excess of the mobile ions in the double layer. The common supposition that there are substantial differences in the electroviscous force predicted by constant-charge and constant-potential boundary conditions is incorrect; our calculations show that it is an artifact introduced by the Debye-Hückel approximation.     

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 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.     

Cell models for the primary electroviscous effect

The primary electroviscous effect in a nondilute suspension of charged spherical particles is studied by means of cell models. The governing equations are derived, and then analytic results are obtained by restricting attention to the limit of thin double layers, small Hartmann and Peclet numbers, and small potentials. Previous work has assumed that the velocity at the outer boundary of the cell is identical to the imposed flow, as proposed by Simha (J. Appl. Phys. 1952, 23, 1020). Results with this boundary condition are compared against those predicted when the tangential shear stress on the outer boundary is assumed to be unperturbed, as proposed by Happel (J. Appl. Phys. 1957, 28, 1288). Both the hydrodynamic and electroviscous contributions to the effective viscosity are smaller with the Happel boundary condition, showing that such cell models offer a range of predictions and should be used with caution.     

Electroviscous cylinder-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged cylindrical particle and a charged plane boundary 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 R.G. Cox's general theory [J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential, and electroviscous flow field. It is assumed a priori that the double layer thickness surrounding each charged surface is much smaller than the length scale of the problem. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the cylinder are explicitly determined analytically for small particle-wall distances for low and intermediate Peclet numbers. It is found that the tangential force usually increases the drag above the purely hydrodynamic drag, although for certain conditions the drag can be reduced. Similarly the normal force is usually repulsive, i.e., it is an electrokinetic lift force, but under certain conditions the normal force can be attractive.     

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 Forces on a Charged Cylinder Moving Near a Charged Wall

The refined theory of the electroviscous lift forces is presented for the case when the separation distance between the particle and the wall is larger than the double-layer thickness. The theory is based on the lubrication approximation for motion of a long cylinder near a solid wall in creeping flow. The approximate analytical formula for the lift force valid for Pe相似文献   

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.     

Primary electroviscous effect in a suspension of charged porous spheres

Primary electroviscous effect for a dilute suspension of porous spheres with fixed volumetric charge density is investigated theoretically. In the absence of flow, the electrical potential and solution charge density are assumed to satisfy the linearized Poisson-Boltzmann equation. With incorporation of the electrical body force, the Brinkman equation and the Stokes equation are used to govern the fluid flow inside and outside a sphere. The theory is formulated by assuming weak deviation of the charge cloud from its equilibrium state. However, the electrical body force is not restricted to be small compared to the viscous force in the fluid momentum equation. The results show that the double layer distortion is increased with increasing particle permeability, thereby enhancing the relative importance of its stress contribution. Nonetheless, the intrinsic viscosity remains a decreasing function of permeability, similar to the case of uncharged particles.     

Structure of colloid silica determined by viscosity measurements

The viscosity of nanosized colloid silica suspensions, used as binders in the investment casting, was determined as a function of their weight fraction reaching 52%. A new capillary viscometer was used whose construction eliminated sedimentation effects. The experiments have been carried out at fixed pH 10.0 and controlled ionic strength. It was found that for a low silica concentration range (weight fraction below 5%) the suspension viscosity increased more rapidly than the Einstein theory predicts. This anomalous behavior could not be explained in terms of the primary electroviscous effect predicted to be a few orders of magnitude smaller as observed. This discrepancy was accounted for by postulating a fuzzy, gel-like structure of colloid silicas used in our experiments. Hence, the apparent hydrodynamic radius of silica particles in aqueous suspensions was found to be larger than the primary particle size in accordance with previous observations. Based on this postulate, an apparent density of the silica sols was found to be 1.32-1.37 g/cm(3) instead of 2.2-2.32 g/cm(3) as determined from the suspension dilution method. This behavior was interpreted in terms of the core/shell model with high shell porosity, reaching 85%. Similarly, for higher concentration ranges, silica viscosity increased more rapidly with increased sol concentration than predicted by the Batchelor model derived for hard particles. The deviation was attributed to the secondary electroviscous effect stemming from the electrostatic interactions among silica particles in sheared suspensions. This effect has quantitatively been interpreted in terms of Russel's theory. On the other hand, for the high concentration range the experimental results were well accounted for by the Dougherty-Krieger model. By exploiting our experimental findings a sensitive method of determining the structure and apparent density of silica sols in aqueous media was proposed.     

Intrinsic viscosity of aqueous suspensions of cellulose nanofibrils

Cellulose nanofibrils (CNF) from wood fibers are of increasing interest to industry because they are from renewable sources and are biodegradable. Owing to their high aspect ratio, they produce viscous suspensions and stiff gels that are strengthened by interfibrillar hydrogen bonds. In this study, the viscosity of aqueous CNF suspensions, at dilute concentrations ( \(nL^{3}<1\) ), was measured at various pH values by addition of HCl, and at various ionic strengths by addition of NaCl and \(\hbox {CaCl}_{2}\) . The results show that the primary electroviscous effect significantly increases the intrinsic viscosity. The intrinsic viscosity under conditions where the surface charge of nanofibrils is fully screened is in good agreement with the predictions of classical theory for dispersions of rodlike particles at low shear rates. Increasing the ionic strength up to \(\kappa d\approx 1\) decreases the intrinsic viscosity; at \(\kappa d>1\) , the intrinsic viscosity increases because of fibril aggregation and increase of the effective volume fraction.     

海藻酸钠在KCl水溶液中的粘度行为

通过测定海藻酸钠水溶液的特性粘数及在低高于强度的条件下其浓度与比浓粘度关系曲线上的峰值，系统地研究了KCl浓度在2×10（－5）－0.5mol·L（-1）范围内对海藻酸钠溶液粘度行为的影响．根据Odijk－Skolnick－Fixman理论和Rinaudo的处理方法，从理论上对海藻酸钠溶液的粘度行为进行了探讨．研究结果表明：聚电解质溶液的电粘滞效应可使用静电相关长度得到合理解释     

软段含羧基的水性聚氨酯物性研究

合成了单官能团小分子物质封端的软硬段皆含羧基的脂环族水性聚氨酯(PU),研究了反离子种类、固含量、外加小分子盐/酸、pH值对水性PU的粘度、粒径、CMC和电导率的影响,同时,比较了不同软段分子量水性PU分散液pH临界值和CMC的差异.实验结果表明,随固含量升高,PU分散液体系粘度增大,当固含量为30wt%时,粘度比固含量20wt%的体系粘度增大约20倍;随小分子盐NaCl的加入,PU分散液电粘滞效应逐渐消失,电导率呈现先减小后增大的趋势,随NaCl的加入/软段分子量提高,PU分散体系的CMC值减小,钙离子对PU粒子扩散双电层的破坏作用更加明显.随pH值的增大,PU分散液体系粒径减小,电导率则升高,随软段分子量提高,pH临界值增大,PU分散体对外加小分子酸存在缓冲作用.     

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.     

Electrophoresis of concentrated mercury drops

The electrophoretic behavior of concentrated monodispersed, positively charged mercury drops is investigated theoretically. The present study extends previous analyses by considering arbitrary surface potentials, double-layer polarization, and the interaction between adjacent double layers. The coupled equations describing the spatial variations in the flow field, the electric field, and the concentration field are solved by a pseudo-spectral method. For a low surface potential phi(r), the mobility increases monotonically with kappaalpha; kappa and alpha are respectively the reciprocal Debye length and the radius of a mercury drop. For medium and high phi(r), the mobility curve has a reflection point, which arises from the interaction of adjacent double layers, for kappaalpha. Also, if phi(r) is high, the mobility curve may exhibit a local minimum as kappaalpha varies. This phenomenon is pronounced if the concentration of the dispersed phase is high. If the double layer is thick, the mobility increases with phi(r), and the reverse is true if it is thin. We show that the higher the concentration of the dispersed phase the smaller the mobility, and as kappaalpha becomes large the mobility approaches a constant value, which is independent of the concentration of the dispersed phase. The mobility of mercury drops is larger than that of the corresponding rigid particles.     

Estimation of aspect ratio of cellulose nanocrystals by viscosity measurement: influence of surface charge density and NaCl concentration

Cellulose nanocrystals (CNCs) with similar size and various surface charge densities were prepared by sulfuric acid hydrolysis and NaOH desulfation. The influence of surface charge density and NaCl concentration on the intrinsic viscosity of CNC suspensions and predicted aspect ratio were investigated by Ubbelohde viscometer. With decreased CNC surface charge density, the intrinsic viscosity initially decreased due to the electric double layers on the CNC surface and subsequently increased due to CNC aggregation. To screen electroviscous effect, NaCl was added into CNC suspensions. With increased NaCl concentration, the intrinsic viscosity of CNC suspensions first decreased and then increased. The aspect ratios of CNCs predicted by Batchelor equation from the minimum intrinsic viscosity were consistent with that measured by transmission electron microscopy. Suspensions of CNCs with higher surface charge density needed less NaCl to obtain minimum intrinsic viscosity. The NaCl content that should be added to the suspension to predict the actual physical aspect ratio of CNC can be estimated by Debye–Hückel theory, assuming that the Debye length is equal to the CNC diameter.