Role of Electrostatic Repulsion on the Viscosity of Bidisperse Silica Suspensions

The flow behavior of bidisperse aqueous silica suspensions has been studied at different electrolyte concentrations as a function of shear rate, total volume fraction of the particles, and volume ratio of small to large particles. It is shown that the range of the electrostatic repulsion plays an important role in determining the viscosity of the suspension. Binary mixtures of particles of longer range repulsive forces showed higher viscosities than the suspensions of shorter range electrostatic interactions. Bimodal suspensions of long-range interactions showed non-Newtonian behavior over wider ranges of shear due to the deformation of the ionic cloud around the particles, which is larger in these systems. The viscosity of bimodal suspensions used in this study was scaled with respect to the viscosity of the related monosized systems and the viscosity of one bimodal suspension at a fixed total volume fraction of the particles, employing our earlier scaling method. The model normalizes the effect of colloidal forces by introducing a scaling factor that collapses the data into a single curve for bimodal suspensions of a particular size ratio, and it is shown that the model is valid for systems with both short-range and long-range repulsive forces. Copyright 1999 Academic Press.     

Molecular-dynamics simulation of model polymer nanocomposite rheology and comparison with experiment

The shear-rate dependence of viscosity is studied for model polymer melts containing various concentrations of spherical filler particles by molecular-dynamics simulations, and the results are compared with the experimental results for calcium-carbonate-filled polypropylene. Although there are some significant differences in scale between the simulated model polymer composite and the system used in the experiments, some important qualitative similarities in shear behavior are observed. The trends in the steady-state shear viscosities of the simulated polymer-filler system agree with those seen in the experimental results; shear viscosities, zero-shear viscosities, and the rate of shear thinning are all seen to increase with filler content in both the experimental and simulated systems. We observe a significant difference between the filler volume fraction dependence of the zero-shear viscosity of the simulated system and that of the experimental system that can be attributed to a large difference in the ratio of the filler particle radius to the radius of gyration of the polymer molecules. In the simulated system, the filler particles are so small that they only have a weak effect on the viscosity of the composite at low filler volume fraction, but in the experimental system, the viscosity of the composite increases rapidly with increasing filler volume fraction. Our results indicate that there exists a value of the ratio of the filler particle radius to the polymer radius of gyration such that the zero-shear-rate viscosity of the composite becomes approximately independent of the filler particle volume fraction.     

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.     

Use of a Cross-Sectional Model for Determining Rheology in Settling Slurries: Effect of Solvent,Particle Size,and Density

Transport models for partially settling slurries need accurate rheology correlations, particularly describing viscosity relationship to the particle concentration. A method is needed to untangle the effects of settling on apparent viscosity and the real effects of particle concentration on viscosity during rheology measurements. Our approach is based on model inversion of a cross-section model for the vertical particle concentration gradient and the local rheologies in the gap of a Couette type rheometer, established by a balance between gravitational particle settling and shear induced migration of the particles. The Krieger-Dougherty rheology correlation with adjustable parameters has been applied, where the parameters are determined by minimizing the difference between the measured viscosity data and those calculated by the model. Fairly mono-disperse silver coated polystyrene particles with two sizes and densities were used in both the aqueous and oil phase. In the raw data an apparent shear thinning tendency is observed. Through the model inversion process, this is accounted for by the shear dependent settling and the steep increase of viscosity with particle concentration. Maximum packing fraction was obtained through settling experiments. The difference between this value and the maximum packing fraction from the model inversion was less than 3% for oil-based suspensions. The larger difference was found for smaller particle size in water which is attributed to the larger effect of interparticle forces.     

Flow properties of freshly prepared ettringite suspensions in water at 25 degrees C

The rheology of a complex, heterogeneous mineral colloid was rationalised using models devised for model rod systems. Mixing a calcium hydroxide slurry with an aluminium sulphate solution produces a suspension of rod-shaped ettringite particles. Ettringite rod suspensions exhibit non-Newtonian flow behaviour, which depends on the shape of the particles, their size distribution, concentration and surface properties as well as the suspension medium characteristics. We have measured the shear viscosity of suspensions of ettringite rods with a median aspect ratio, r(i) approximately 8, at 25 degrees C as a function of particle volume fraction, phi, in the range 0.0001-0.08. It was found that the viscosity of the suspensions increased with phi, and showed a marked change of slope at phi approximately 0.01, which we identified as the minimum overlap concentration phi(*). Above phi(*), the system is in the semi-dilute regime. At phi>phi(*), when Pe(rot)>1, hydrodynamic interactions between rods become increasingly significant, and we observe shear-thinning behaviour. The high effective hydrodynamic volume of rotating rods, resulting in much lower values of the maximum packing fraction, phi(c), than for spheres, dominates the rheological behaviour of ettringite suspensions.     

A novel procedure able to predict the rheological behavior of trifunctional epoxy resin/hyperbranched aliphatic polyester mixtures

A hyperbranched polymer (HBP), based on a highly branched polyester, was added to a trifunctional triglycidyl-p-aminophenol (TGAP) epoxy resin as a possible route to increase the toughness of the resin. Different amounts of the HBP, up to 26.5% wt. of resin, were dispersed in the TGAP resin. The rheological behavior of the formulations produced was studied as function of the shear rate and the filler content using a cone and plate rheometer. The rheological behavior of the TGAP resin, initially Newtonian, was modified displaying a pseudo-plastic trend when the hyperbranched polymer was added. An increase in the viscosity of the resin was observed with increasing volume fraction of the filler. The Cross equation was used to predict the viscosity of each formulation as a function of the shear rate. A novel procedure was developed to predict the viscosity of each mixture as a function of the filler volume fraction. This could be employed to provide quantitative information on the filler volume fraction in epoxy/HBP systems, necessary to achieve the characteristic viscosity values corresponding to the typical shear rates for a specific processing technology.     

Permeation models for mixed matrix membranes

Permeation models for mixed matrix membranes (MMMs) are discussed. A new model is proposed for the effective permeability of a species in MMMs. The model takes into account the presence of interfacial layer (shell) at the surface of the core filler particles. According to the proposed model, the relative permeability (Pr) of a species in MMM, defined as permeability in MMM divided by matrix permeability, is a function of five variables, namely: ratio of interfacial shell-to-core particle radii (delta), ratio of interfacial shell-to-matrix permeabilities (lambdaIm), ratio of core particle-to-interfacial shell permeabilities (lambdadI), volume fraction of composite core-shell particles (phi), and maximum packing volume fraction of particles (phim). The predictions of the model are discussed and compared with available experimental data on permeability and selectivity of mixed matrix membranes.     

Effect of pH on deagglomeration and rheology/morphology of aqueous suspensions of goethite nanopowder

The kinetics of deagglomeration in diluted suspensions of goethite nanopowder, as well as the rheology and morphology of the resulting suspensions, strongly depends on pH. At pH 3, nanopowder can be dispersed as separate nanoparticles, and the resulting suspension is Newtonian, with the viscosity only marginally higher than the viscosity of water. At pH between 5 and 12, nanoparticles tend to reaggregate and form weak aggregates/flocs. Morphology changes from a Newtonian suspension of primary nanoparticles to a non-Newtonian, shear-thinning suspension of large, porous, interconnected flocs with the yield stress reaching a maximum at an isoelectric point. The effect of pH on morphology and rheology is reversible, and as pH is reduced to 3, the suspension becomes Newtonian, with viscosity marginally higher than the viscosity of water. The rheological models based on DLVO theory do not allow prediction of the effect of pH on viscosity and yield stress, but the flow curves of goethite suspensions can be described by a fractal model with five adjustable parameters.     

Investigation of shear thinning behavior and microstructures of MWCNT/epoxy and CNF/epoxy suspensions under steady shear conditions

This report investigates the steady-state viscosities of multiwall carbon nanotube (MWCNT)/epoxy and carbon nanofiber (CNF)/epoxy suspensions with varying filler concentrations under different shear rates at various temperatures. In situ observation of filler networks suggests the build-up of shear induced MWCNT and CNF agglomerates at low shear rates, which correlates with the measured shear thinning behavior. The agglomeration process in MWCNT/epoxy suspensions is enhanced at lower shear rates in the case of higher temperatures, whereas, at high shear rates, both nano-fillers show good dispersion. Shear thinning behavior is observed for both types of fillers, and shear thinning exponential parameters are evaluated as a function of filler content. The shear thinning exponent increases in conjunction with increase in filler content, but it is found to saturate at a specific value, independently of filler material. Finally, the micromechanical elasticity-based analogy model is applied to the prediction of steady state shear viscosity of suspensions at higher shear rates with the assumption of complete dispersion and alignment of individual nano-fillers in suspensions. The predicted viscosities and the experimental data at higher shear rates are compared. The results conclude that fairly good agreement can be seen for the cases of CNF/epoxy suspensions at lower temperatures, whereas MWCNT/epoxy suspensions and CNF/epoxy suspensions at higher temperatures show discrepancy between the prediction and the experimental data.     

1H-NMR Relaxation of Water Molecules in the Aqueous Microcrystalline Cellulose Suspension Systems and Their Viscosity

An intensive study for aqueous microcrystalline cellulose (MCC) suspensions was carried out in view of the relationship between a viscosity and a 1H spin-spin relaxation time (T2) of water. An investigation was carried out for four suspension systems with the different particle size distributions. The proton mole ratio () of bound water against MCC particles and T2 of bound water (T2,b) were evaluated from the T2 values obtained by Carr-Purcell- Meiboom-Gill (C.P.M.G) method and those by solid echo method, respectively. As a result of these analyses, the T2,b value for the aqueous MCC suspension was evaluated as 5 × 10–3 s and it was found that the system having a larger tended to show a higher viscosity. By relating the above results to the observation of the suspensions by an optical microscope, it was concluded that a network formed by MCC particles plays an important role in generating a high viscosity of MCC suspension, and that an averaged mobility of water molecules is sensitively affected by the network structure.     

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.     

A hybrid rheological model for particulate suspension in zeolite crystal growth

A hybrid constitutive model is developed to represent the thixotropic behavior of particulate suspension during zeolite crystallization from solution. This model is valid over the complete solid fraction range typical for such a process. It employs two internal variables, agglomeration and contiguity, to describe the degree to which the gel particles form short- and long-range networks. The contiguity is used to weigh the effects of hydrodynamic to chain-like network deformation on the suspension viscosity. Heterogeneous nucleation and surface reaction-controlled crystal growth are assumed to describe the evolution of microstructure and solid fraction of gel and crystals. Such a model successfully captures the thixotropic behavior of zeolite particulate suspension by comparison of the predictions with a set of experimental data.     

Rheology of binary colloidal structures assembled via specific biological cross-linking

The selectivity and range of energies offered by specific biological interactions serve as valuable tools for engineering the assembly of colloidal particles into novel materials. In this investigation, high affinity biological interactions between biotin-coated "A" particles (RA = 0.475 microm) and streptavidin-coated "B" particles (RB = 2.75 microm) drive the self-assembly of a series of binary colloidal structures, from colloidal micelles (a large B particle coated by smaller A particles) to elongated chain microstructures (alternating A and B particles), as the relative number of small (A) to large (B) particles (2 < or = NA/NB < or = 200) is decreased at a low total volume fraction (10(-4) < or = phiT < or = 10(-3)). At a significantly higher total volume fraction (phiT > or = 10(-1)) and a low number ratio (NA/NB = 2), the rheological behavior of volume-filling particle networks connected by streptavidin-biotin bonds is characterized. The apparent viscosity (eta) as a function of the shear rate gamma, measured for networks at phiT = 0.1 and 0.2, exhibits shear-rate-dependent flow behavior, and both the apparent viscosity and the extent of shear thinning increase upon an increase of a factor of 2 in the total volume fraction. Micrographs taken before and after shearing show a structural breakdown of the flocculated binary particle network into smaller flocs, and ultimately a fluidlike suspension, with increasing shear rate. Rheological measurements provide further proof that suspension microstructure is governed by specific biomolecular interactions, as control experiments in which the streptavidin molecules on particles were blocked displayed Newtonian flow behavior. This investigation represents the first attempt at measuring the rheology of colloidal suspensions where assembly is driven by biomolecular cross-linking.     

Electrorheological properties and microstructure of silica suspensions

We present experimental and theoretical results on the electrorheological response and microstructure of colloidal suspensions composed of silica nanoparticles dispersed in a silicon oil, as a function of electric field strength and silica water content. Using small-angle neutrons scattering experiments, we determined the evolution of the static structure factor of the suspensions when an electric field is applied. Experimental data were fitted with model calculations using the Percus-Yevick solution for Baxter's hard-sphere adhesive potential. The obtained stickiness parameter is directly related to the polarization interactions that depend on the water content of silica particles. The influence of the polarization interparticle potential on the rheology of the silica dispersions was investigated in a second time. A microscopic theory for the shear viscosity of adhesive hard-sphere suspensions was successfully used which describes the steady shear viscosity of suspension in terms of the fractal concept.     

Viscosity of concentrated colloidal suspensions: comparison of bidisperse models

In this paper, recent advances in the study of rheological behavior of concentrated bimodal suspensions are briefly reviewed. The predictive models are divided into two categories, namely, the effective volume fraction (or hard sphere scaling) approach and the separation of contributions approach. Predictions of both approaches are compared with experimental data of electrostatically and sterically stabilized suspensions. It is shown that the predictions of both hard sphere scaling and the scaling method of Zaman and Moudgil (J. Colloid Interface Sci. 212 (1999) 167) to separate the contributions of fine and coarse particles are in good agreement with the experimentally observed results. The approach by Dames, Morrison, Wilenbacher (Rheol. Acta 40 (2001) 434) to separate the hard-sphere and non-hard-sphere contributions is investigated using the aqueous silica and polystyrene suspensions respectively. A good agreement is shown for aqueous silica suspensions. However, significant differences between the predictions and experimental data are found for the sterically stabilized polystyrene suspensions, suggesting a more generalized expression is needed. As an attempt to classify the models on the viscosity of colloidal suspensions, the present study will provide guidelines for interpretation of experimental results and for the development of more comprehensive predictive methodologies for polydispersed colloidal dispersions.     

Influence of interparticle interaction effects on the rheological properties of low density polyethylene filled with glass beads

The rheological properties of Low-density polyethylene (LDPE) compounds with different fractions of glass beads have been investigated by means of high pressure capillary rheometry. The purpose of this study is to find a functional approach for describing the flow behaviour of suspensions as a function of the volumetric filler content and the applied shear stress or shear rate, respectively. The flow behaviour of suspensions is influenced by interaction effects, which are dependent on the filler particle, its volume content and particle size. While small glass beads exhibit pronounced interparticle interaction effects even at low volumetric filler concentrations, large glass beads show a plateau of negligibly interactions up to approx. 20% volumetric filler content. With introducing a generalized interaction function the flow behaviour of the tested suspensions could be described with reasonable accuracy in consideration of the transition from negligible to pronounced interactions.     

Viscoelasticity and Stokes-Einstein relation in repulsive and attractive colloidal glasses

We report a numerical investigation of the viscoelastic behavior in models for steric repulsive and short-ranged attractive colloidal suspensions, along different paths in the attraction strength vs packing fraction plane. More specifically, we study the behavior of the viscosity (and its frequency dependence) on approaching the repulsive glass, the attractive glass, and in the reentrant region where viscosity shows a nonmonotonic behavior on increasing attraction strength. On approaching the glass lines, the increase of the viscosity is consistent with a power-law divergence with the same exponent and critical packing fraction previously obtained for the divergence of the density fluctuations. Based on mode-coupling calculations, we associate the increase of the viscosity with specific contributions from different length scales. We also show that the results are independent of the microscopic dynamics by comparing Newtonian and Brownian simulations for the same model. Finally, we evaluate the Stokes-Einstein relation approaching both glass transitions, finding a clear breakdown which is particularly strong for the case of the attractive glass.     

Dispersion of Silica Fines in Water-Ethanol Suspensions

The dispersion of silica fines in water-ethanol suspensions has been studied through the measurement of settling efficiency, wetting rate, zeta potential, and viscosity. The measurements were performed on two silica samples with mean volumetric diameters of 5.02 and 0.272 &mgr;m at different fractions of ethanol in water-ethanol suspensions. The results have demonstrated that the dispersion stability of the silica suspensions increased as the fraction of ethanol increased and reached to maximum at the fraction of 50%, followed by a decline. The stability was stronger in a pure ethanol suspension than in a pure water suspension. It was observed that the stability closely correlated with the lyophilicity of the particles, but was not predominated by the surface charge of the particles as predicted by the DLVO theory. Viscosity measurements have been used to estimate the solvation film thickness on silica particles immersed in water-ethanol suspensions, on the basis of Einstein's theory of the viscosity of dispersions. It was found that the solvation film thickness on silica fines in a water-ethanol (1 : 1) suspension is about double that in a pure water suspension and about 1.4-fold that in a pure ethanol suspension, respectively, which well explains the dispersion behaviors of the silica fines in the water-ethanol suspensions because a thicker solvation film will cause a stronger disjoining pressure to prevent the proximity of the particles. Copyright 2001 Academic Press.     

Rheological behavior of organic suspensions of fluorapatite

A fluorapatite suspension prepared in the azeotrope methyl ethyl ketone-ethyl alcohol (MEK:EtOH) in the presence of the phosphoric ester was investigated. Electrical conductivity, adsorption isotherms, and sedimentation technique showed that the amount of phosphoric ester adsorbed on the fluorapatite surface was equal to, or higher than, 1 wt%. This dispersant concentration led to a good particle packing. The rheological properties of fluorapatite suspensions were studied as a function of phosphoric ester concentration. The data obtained from the viscosity measurements and those previously collected correlated well. In the case of suspensions prepared with 60 wt% in fluorapatite, the dispersion was optimal for a phosphoric ester content of about 1.3 wt%.     

Re-entrant kinetic arrest and elasticity of concentrated suspensions of spherical and nonspherical repulsive and attractive colloids

We have designed and studied a new experimental colloidal system to probe how the weak shape anisotropy of uniaxial particles and variable repulsive (Coulombic) and attractive (van der Waals) forces influence slow dynamics, shear elasticity, and kinetic vitrification in dense suspensions. The introduction of shape anisotropy dramatically delays kinetic vitrification and reduces the shear elastic modulus of colloidal diatomics relative to their chemically identical spherical analogs. Tuning the interparticle interaction from repulsive, to nearly hard, to attractive by increasing suspension ionic strength reveals a nonmonotonic re-entrant dynamical phase behavior (glass-fluid-gel) and a rich variation of the shear modulus. The experimental results are quantitatively confronted with recent predictions of ideal mode coupling and activated barrier hopping theories of kinetic arrest and elasticity, and good agreement is generally found with a couple of exceptions. The systems created may have interesting materials science applications such as flowable ultrahigh volume fraction suspensions, or responsive fluids that can be reversibly switched between a flowing liquid and a solid nonequilibrium state based on in situ modification of suspension ionic strength.