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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Bidisperse electrorheological fluids using hydrolyzed styrene-acrylonitrile copolymer particles: synergistic effect of mixed particle size

Monodisperse micron-sized styrene-acrylonitrile copolymer (SAN) particles with three different sizes (about 5, 10, and 15 microm) were prepared by a two-step seeded polymerization and used for a study of bidisperse electrorheological (ER) suspensions. The effect of the particle size and the size-mixing fraction on ER properties was studied with varying the size of these monodisperse copolymer particles. When the two particle sizes were mixed, the suspension generally showed a decrease in the shear yield stress, reaching a minimum value. However, a bidisperse ER suspension of large particles containing a small fraction of fine particles showed an interesting synergy effect of size mixing on ER response, giving enhanced yield stresses over the other size-mixing fractions. This synergistic ER suspension also showed a great increase in the viscoelastic property. The current density of suspensions was maximum at the synergistic bidisperse suspension. This synergy effect in a particular bidisperse suspension was investigated in view of the structure model consideration and was concluded to be due to a close packing and a peculiar structural ordering at an optimum size ratio and mixing fraction.     

Effect of pH and Salt on Rheological Properties of Aerosil Suspensions

Ionic strength and pH will influence the zeta potential of suspended particles, and consequently particle interactions and rheological properties as well. In this study the rheological properties and aggregation behaviour of Aerosil particles dispersed in aqueous solutions with various pH and salt concentration were studied. The potential energy was estimated by the DLVO theory and short range hydration forces and compared to the experimentally determined zeta potential. The strongest attraction between particles occurs at the isoelectric point (pH 4) and resulted in large aggregates, which gave relatively higher values of viscosity, yield stress, moduli, and shear thinning effects. The relative viscosity as a function of volume fraction was fitted to the Krieger and Dougherty model for all the suspensions. Oscillation measurements showed that the suspensions display elastic behaviour at low pH and viscous behavior at high pH. Furthermore, suspensions with high salt content had higher storage moduli. A power law dependency of storage moduli with volume fraction could be used to indicate the interaction strength between particles.     

Effect of associating polymer on the viscosity behavior of suspensions consisting of particles with different surface properties

Associating polymers which consist of water-soluble long-chain molecules containing a small fraction of hydrophobic groups (hydrophobes) behave as flocculants in aqueous suspensions. The effects of associating polymers on the rheological behavior are studied for single suspensions of particles with hydrophilic and hydrophobic surfaces, and their mixtures. For particles with hydrophilic surfaces, the suspensions are highly flocculated by a bridging mechanism, because the water-soluble chains adsorb onto hydrophilic surfaces. On the other hand, the particles with hydrophobic surfaces cannot be dispersed in water without polymer and the additions of a small amount of polymer are required for preparation of homogeneous suspensions. The associating polymer acts as a dispersant at low concentrations. However, further additions of polymer lead to a drastic increase in viscosity. Since the hydrophobes on one end of molecules adsorb onto hydrophobic surfaces and other hydrophobes tending from the particles can form micelles, the particles are connected by linkage of interchain associations. By mixing two suspensions of particles with hydrophilic and hydrophobic surfaces, the viscosity is substantially reduced and the flow becomes nearly Newtonian. The associating polymer in complex suspensions acts as a binder between the hydrophilic and hydrophobic surfaces. The hetero-flocculation which leads to the formation of composite particles may be responsible for the viscosity reduction of complex suspensions.     

Effect of Particle Size Distribution on the Rheology of Dispersed Systems

The rheological properties of aqueous polystyrene latex dispersions from three synthetic batches, with nearly the same z-average particle sizes, 400 nm, but varying degrees of polydispersity, 0.085, 0.301, and 0.485, respectively, were systematically investigated using steady-state shear and oscillatory shear measurements. The particles were sized with photon correlation spectroscopy and transmission electron microscopy and were stabilized sterically with PEO–PPO–PEO triblock copolymer (Synperonic F127). Results from steady-state shear measurements show that the viscosities of the systems exhibit shear-thinning behavior at high solid fractions. However, the degree of shear thinning depends on the breadth of particle size distribution, with the narrowest distribution suspension exhibiting the highest degree of shear thinning. The Herschel–Bulkley relationship best describes the flow curves. The relative viscosities as a function of volume fraction data were compared, and it was found that the broadest distribution suspension had the lowest viscosity for a given volume fraction. In addition, the data were fitted to the Krieger–Dougherty equation for hard spheres. A reasonable agreement of theory with experiment is observed, particularly and surprisingly for the very broad distribution. However, when the contribution to the volume due to the adsorbed polymer layer is considered, the agreement between experiment and theory becomes closer for all the suspensions, although the agreement for the broad distribution suspension is now worse. Fitting the Dougherty–Krieger theory to the experimental data based on our experimental maximum packing fractions gives very good agreement for all the systems studied. From oscillatory shear measurements, the moduli were obtained as a function of frequency at various latex volume fractions. The results show general change of the dispersions from viscous (G" > G′) at low volume fractions (0.25–0.30) to moderately elastic (G′ > G") at moderately high volume fractions (0.41–0.45). The change at this concentration level is likely due to some compression and interpenetration of the stabilizing polymer chain at the periphery, indicating the dominance of the interparticle forces. Overall, the very broad distribution was found to have the lowest elastic modulus for a given volume fraction.     

Phonons in suspensions of hard sphere colloids: volume fraction dependence

The propagation of sound waves in suspensions of hard sphere colloids is studied as a function of their volume fraction up to random close packing using Brillouin light scattering. The rich experimental phonon spectra of up to five phonon modes are successfully described by theoretical calculations based on the multiple scattering method. Two main types of phonon modes are revealed: Type A modes are acoustic excitations which set up deformations in both the solid (particles) and the liquid (solvent) phases; for type B modes the stress and strain are predominantly localized near the interface between the solid particles and the surrounding liquid (interface waves). While the former become harder (increase their effective sound velocity) as the particle volume fraction increases the latter become softer (the corresponding sound velocity decreases).