New measurements of the flow-curves for Carbopol dispersions without slip artefacts

The thickening properties of many commercial thickeners are difficult to measure because of wall slip artefacts. Here we report a series of experiments on a typical thickener where these artefacts have been successfully eliminated. As a result, complete, steady-state flow-curves of aqueous Carbopol 980 (the toxicologically preferred version of the older and more well-known Carbopol 940) dispersions are reported for a range of concentrations of 0.045–1.0 wt%. The vane-and-basket flow geometry was used to avoid slip problems at low shear stress, with the geometry housed in a TA AR1000-N controlled-stress rheometer, whilst a Haake RV2 viscometer with an SV2P and MV2P concentric-cylinder geometries were used at higher shear rates. The flow-curves obtained show a smooth but steep transition from a very high Newtonian viscosity at low shear stress to a much lower viscosity at high shear stress. No real yield stresses were detected, but the higher shear rate results can be fitted to the Herschel-Bulkley model, which assumes an apparent yield stress. The various model parameters are displayed as a function of Carbopol concentration. Received: 29 November 2000/Accepted: 26 February 2001     

Linear viscoelastic behavior of copper phthalocyanine dispersions used in printing inks

In this paper we describe the linear viscoelastic properties of copper phthalocyanine (CuPCN) dispersions that are used in the manufacturing of offset lithographic printing inks. Transmission electron microscopy shows that the primary pigment particles are rod-like and have sizes in the range of 10 to 300 nm. Steady shear measurements show that the dispersions are Newtonian at a pigment volume fraction of 0.073 and become increasingly shear thinning as the pigment volume fraction is increased. The strong shear-thinning nature of these dispersions can be attributed to the highly flocculated nature of the dispersions, which is due to interparticle attractions. The structural complexity of the dispersions also results in an unexpected linear viscoelastic response. While at low frequencies (0.1 and 1.0 Hz) the ex tent of the linear region decreases with increasing pigment concentration, at a higher frequency (10 Hz) the extent of the linear region increases with increasing pigment concentration. This increase in the linear region with increasing pigment concentration suggests that at higher frequencies the dispersion is less brittle, and that the rheological behavior is dominated by intra-aggregate associations. In addition, frequency sweeps show that the dispersions behave like a viscoelastic liquid at low pigment concentrations. However, at higher pigment concentrations (yet significantly lower than the maximum packing fraction) the dispersions behave like a cross-linking polymer at its gel point.     

Anomalous rheology of polypyrrole nanoparticle/alginate suspensions: effect of solids volume fraction, particle size, and electronic state

The rheology of dispersions of polypyrrole (PPY) nanoparticles (nPPY) is compared to that of micron-sized PPY particles (CPPY), each suspended in aqueous sodium alginate. With increasing PPY volume fraction, the Newtonian viscosity of the CPPY/alginate suspensions exhibits a ??normal?? increase, whereas that of the nPPY/alginate suspensions decreases to a minimum and then increases again. Enhanced elasticity, indicative of agglomerate formation via bridging interactions with the alginate, is observed only in the CPPY rheology. By comparing doped versus dedoped nPPY particles, and investigating the effect of nPPY particle size, we conclude that the negative viscosity change of the nPPY dispersions is due to adsorption of a dense layer of alginate, resulting in a decrease in bulk alginate concentration. The viscosity upturn at higher nPPY volume fractions indicates the onset of particle agglomeration via bridging interactions with alginate. The results demonstrate improved dispersability of both doped and dedoped nPPY over CPPY particles.     

体积分数对基于沸石和硅油的悬浮液的电流变性能的影响

用 HAAKE RV2 0型流变仪 ,在不同外加电场强度和不同颗粒体积分数下测试了基于沸石和硅油的电流变液的剪切应力变化 .结果表明 :随着外加电场强度升高 ,电流变液的零电场粘度急剧增加 ,电流变液的剪切屈服应力增加 ;随着电流变液中沸石颗粒体积分数升高 ,电流变液的剪切屈服强度急剧上升 .这种变化可以用颗粒间作用力与颗粒间距的关系、单位面积的颗粒链数目变化以及多体作用对电流变液性能的影响来解释     

Electrical double layer and rheological properties of yttria-stabilized zirconia suspensions in solutions of high molecular weight polyacrylic acid polymers

This work deals with the effect of the adsorption of two high molecular weight polyacrylic acid polymers (Carbopol) on the interfacial properties, and the rheology of aqueous zirconia suspensions. Since the Carbopol-covered particles can be thought of as soft colloids, Ohshimas theory was used to gain information on the surface potential and the charge density of the polymer layer (Ohshima H (1995) Electrophoretic mobility of soft particles. Colloids Surf A Physicochem Eng Aspects 103:249–255). The effect of the pH of the solution on the double layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The electrokinetic properties of the suspensions are studied for different pH and Carbopol concentrations in solution in order to investigate the possible stabilization of the suspensions by electrostatic repulsion between the particles. The rheological behavior of the suspensions was investigated in steady-state and dynamic conditions, and the corresponding yield stress and storage modulus were obtained in absence and presence of polymer in solution. The competition between bridging flocculation provoked by polymer adsorption and electrosteric stabilization determines the rheological properties of the suspensions. In the pH range investigated, bridging flocculation predominates at the neutral pH because of the graft of the uncoiled polymer to more than one particle, while at the extreme pH values (pH 3, pH 9) steric or electrosteric stabilization seems to be the predominant mechanism that explains the rheological results. These facts were confirmed by estimating the zirconia particle (or aggregate) diameter in the liquid medium by means of light scattering measurements.     

Effect of polymer bridging on rheological properties of dispersions of charged silica particles in the presence of low-molecular-weight physically adsorbed poly(ethylene oxide)

 The effect of a low-molecular-weight physically adsorbed poly(ethylene oxide) on the rheological behavior of aqueous dispersions of silica particles (as a model system) has been investigated. Particular attention is given to the evolution of the rheological behavior with increasing polymer concentration in the system at different volume fractions of the particles. Experiments were performed in the absence of salt and just the pH of the dispersion was adjusted to 9.5, a condition at which the system is electrostatically stable and electrostatic repulsive forces are long range in nature. It was observed that the shear viscosity and the linear viscoelastic functions of the dispersion at 55 vol% increase initially through the addition of polymer, reach a maximum, and then decrease to a minimum with further addition of polymer to the system. At higher polymer concentrations, there may be an increase in the viscosity of the dispersion owing to an increase in the concentration of free polymer chains in the medium causing depletion flocculation in the system. The increase in the rheological behavior of the dispersion at low polymer coverage is attributed to polymer bridging flocculation caused by a low-molecular-weight poly(ethylene oxide) in the system. Comparison of the data given here with the results of earlier studies on the viscosity behavior of the system in the presence of salt (0.01 M) indicates that the range of the electrostatic repulsion has a significant role in the rheological behavior of the system. Received: 7 February 2001 Accepted: 18 October 2001     

An investigation of squeeze flow as a viable technique for determining the yield stress

A systematic study of squeeze flow (SF) was performed on different concentrations of Carbopol with varying yield stresses. A sample of constant volume was placed between two parallel plates and a series of constant force steps applied, following the plate separation as a function of time. Precise rheological measurements of the model yield stress fluids were performed in addition to the well-controlled SF tests. These rheological measurements were used in conjunction with the SF equations to determine the time-dependent plate separation, allowing a direct comparison of theory and experiment throughout the entire test. The limiting height achieved during constant force SF reveals information about the yield stress of the fluid as predicted by the theory. It appears that by carefully controlling the experimental conditions of the squeeze test one can obtain yield stress values that agree with the rheological measurements within 10%. Additionally, the validity of the lubricational theory was tested; not only for the determination of the yield stress but throughout the flow as well.     

The rheology of strongly-flocculated suspensions

The rheology of strongly-flocculated dispersions of colloidal particles has been investigated at particle concentrations where a continuous network is formed rather than a collection of discrete flocs. Such networks are shown to possess a true yield stress in both shear and in uniaxial compression (as realised in a centrifuge). Properties measured as a function of particle concentration and particle size include the yield stresses in shear (σ_y) and compression (P_y); the limiting and strain-dependent, instantaneous shear moduli G_O and G(γ); the elastic recovery at finite strains, and the rate of centrifugally-driven compaction. The yield stresses and moduli appear to show a power-law dependence on particle concentration with G_O and P_y, having the same power-law index and σ_y a somewhat lower one. The data are in part consistent with predictions based on the idea that the networks have a heterogeneous structure comprising a collection of interconnected fractal aggregates. The behaviour as a function of particle size and concentration is however not completely scaleable as might be expected on this basis. Thus, whereas the shear yield stress could be scaled to remove its dependence on particle radius a and volume fraction φ (over the measured range 0.25 μm ⩽ a ⩽ 3.4 μm; 0.05 ⩽ φ ⩽ 0.25) as could the strain dependent modulus (0.25 ⩽ a ⩽ 1.3 μm; 0.08 ⩽ 0.25), the particle-size and concentration dependence of P_y and G_O could only be scaled for particles with radii between 0.16 and 0.5 μm, smaller and larger particles having different and much higher power-law index in respect of their concentration dependencies. In the case of the smaller particles the failure of the scaling is thought to be due to an anomaly since these particles distort significantly under the influence of the strong van der Waals forces and this causes the aggregates to be more compact then they otherwise would be. The reasons for the failure at larger sizes is not clear.     

Effects of particle softness on the rheology and yielding of colloidal glasses

We studied the linear and nonlinear rheology of colloidal glasses consisting of hard spheres and soft core-shell particles at several volume fractions to explore the effects of particle softness on the mechanical properties and yielding. Creep and recovery and oscillatory shear measurements were used to determine the shear elastic modulus and the yield strain. Both hard and soft sphere glasses exhibited ‘entropic cage elasticity’ below random close packing, whereas for compressed soft spheres at higher effective volume fractions, the yield strain was determined by shell elasticity. The shear modulus followed a strong increase with volume fraction for hard spheres and a much weaker one for soft particles reflecting their interparticle potential. Nonlinear effects, revealed as strong distortions of the stress signal during yielding, were analyzed via Fourier transform rheology and Lissajous plots. The significant contribution of the nonlinearities was analyzed in terms of strain softening and hardening mechanisms within a cycle of oscillation and discussed in relation to particle softness.     

A review on wall slip in high solid dispersions

High solid dispersions are soft materials made of colloidal or non-colloidal particles dispersed at high volume fractions in a liquid matrix. They include hard sphere glasses, colloidal pastes, concentrated emulsions, foams, and vesicles. These materials are prone to exhibit different kinds of flow heterogeneities: shear banding, wall slip, and fracture. While wall slip is often considered as a nuisance by experimentalists, it appears to be a fundamental component to the way that high solid dispersions respond to mechanical deformation. Moreover, the ability of soft materials to slip onto surfaces allows them to move readily and efficiently in many natural phenomena and industrial processes. This review surveys recent developments and current research in the field. Topics like wall slip detection and control, microscopic modeling for rigid and soft particles materials, and the relation between wall slip and other flow heterogeneities are discussed. We also identify important open issues for future research.     

Rheological characterization of bimodal colloidal dispersions

In order to investigate the effect of the particle size distribution on the rheological properties of concentrated colloidal dispersions both steady-state shear and oscillatory measurements have been performed on well-characterized bimodal dispersions of sterically stabilized PMMA particles. Replacing a minor amount of large particles by small ones in a concentrated dispersion, keeping the total effective volume fraction constant, decreases the viscosity quite drastically. On the other hand, replacing a small amount of small particles by big ones hardly effects the viscosity at all. This behavior can be attributed to the deformability of the stabilizing polymer layer. A procedure is proposed to calculate the limiting viscosities in a bimodal colloidal dispersion starting from the characteristics of the monodisperse systems. A good agreement has been obtained between the calculated values and the experimental results. The linear viscoelastic properties of the concentrated dispersions have been investigated by means of oscillatory measurements. The plateau values of the storage modulus for the bimodal dispersions decrease with an increasing fraction of the coarse particles. By substituting the bimodal dispersion by an equivalent monodisperse system the storage modulus can be superimposed on the values for the monodisperse suspensions when plotted as a function of the mean interparticle distance.     

Rheological properties of suspensions of the green microalga Chlorella vulgaris at various volume fractions

A systematic study of the rheological properties of solutions of non-motile microalgae (Chlorella vulgaris CCAP 211-19) in a wide range of volume fractions is presented. As the volume fraction is gradually increased, several rheological regimes are observed. At low volume fractions (but yet beyond the Einstein diluted limit), the suspensions display a Newtonian rheological behaviour and the volume fraction dependence of the viscosity can be well described by the Quemada model (Quemada, Eur Phys J Appl Phys 1:119–127, 1997). For intermediate values of the volume fraction, a shear thinning behaviour is observed and the volume fraction dependence of the viscosity can be described by the Simha model (Simha, J Appl Phys 23:1020–1024, 1952). For the largest values of the volume fraction investigated, an apparent yield stress behaviour is observed. Increasing and decreasing stress ramps within this range of volume fractions indicate a thixotropic behaviour as well. The rheological behaviour observed within the high concentration regime bears similarities with the measurements performed by Heymann and Aksel (Phys Rev E 75:021505, 2007) on polymethyl methacrylate suspensions: irreversible flow behaviour (upon increasing/decreasing stresses) and dependence of the flow curve on the characteristic time of forcing (the averaging time per stress values). All these findings indicate a behaviour of the microalgae suspensions similar to that of suspensions of rigid particles. A deeper insight into the physical mechanisms underlying the shear thinning and the apparent yield stress regime is obtained by an in situ analysis of the microscopic flow of the suspension under shear. The shear thinning regime is associated to the formation of cell aggregates (flocs). Based on the Voronoi analysis of the correlation between the cell distribution and cell sizes, we suggest that the repulsive electrostatic interactions are responsible for this microscale organisation. The apparent yield stress regime originates in the formation of large-scale cell aggregates which behave as rigid plugs leading to a maximally random jammed state.     

Steady shear rheology of dilute polystyrene particle gels

This paper describes an experimental study on dispersions of monodisperse polystyrene (PS) spheres with a typical radius of 1 μm, dispersed in an electrolyte at high ionic strength, screening the electrostatic repulsion. These suspensions gelate at rest even at low volume fractions of PS particles. The density of the particles is matched with the solvent by using deuterium oxide for volume fractions φ≤0.117. Steady-state flow curves, viscosity as a function of shear rate, are measured and reported for 0.014<φ<0.322. The measured flow curves are analyzed on the basis of two models: 1. In the giant floc model (van Diemen and Stein 1983, 1984; Schreuder et al. 1986, 1987; Laven et al. 1988), at low shear rates, the shear is not distributed homogeneously but is limited to certain shear planes; the energy dissipation during steady flow is due primarily to overcoming the viscous drag on the suspended particles during motion caused by encounters of particles in the shear planes. Though this model was developed for higher solid volume fractions (0.35–0.425), we found that it also describes the rheology of dilute particle gels for 0.15≤φ≤0.3, using the same values for the parameters in the model as in the high solid volume fraction region. For φ<0.15, the model also describes the data if the fraction of distance by which a moving particle entrains its neighbors, is assumed to increase in this φ region. 2. The model of de Rooij (de Rooij et al. 1993, 1994) considers aggregates in shear flow to be monodisperse impermeable spheres with a fractal structure. The permeability is taken into account by considering a hydrodynamic radius smaller than the gyration radius in the Krieger-Dougherty expression for the hydrodynamic contribution to the viscosity. Through the use of a yield criterion the aggregate radius is modeled as a function of shear rate. We found that the model describes our experimental results, with a combination of parameter values used already by de Rooij, but only for φ<0.15. Received: 7 May 1998 Accepted: 22 December 1998     

Physical characterisation and yield stress of a concentrated Miscanthus suspension

We present yield stress measurements of a concentrated suspension of Miscanthus x giganteus, a biomass substrate for the production of biofuels and chemicals. The particle porosity and the apparent solid packing fraction are quantified, and a simple relationship between volume and mass fractions proposed. The relationship between yield stress and solid concentration was measured with the maximum torque method of Dzuy and Boger (J Rheol 27: 321–349, 1983) for concentrations between 11 and 15 %, just below maximum packing. In the range of concentrations considered, the measured dependence of the yield stress on concentration appears to be significantly stronger than that reported for corn stover, a plant for which reliable data is available: the apparent power law exponent is found to be larger than 10, while the corresponding exponent reported for corn is in the range 4–6. We argue that differences in particle rigidity between corn and Miscanthus may play a role in explaining this result.     

Rheological properties of suspensions of TiO2 particles in polymer solutions. 1. Shear viscosity

This paper presents results on the rheological behaviour of suspensions of two kinds of TiO₂ particles in two different polymer solutions. The particles differ in their hydrophilic or hydrophobic properties. The dispersing media are a solution of high molecular weight polyisobutylene in decalin and a solution of a low molecular weight polybutene in decalin. The concentrations of polymer are adjusted in order to get the same zero shear viscosity. The shear viscosity measurements display an apparent yield stress in some cases. The existence and the values of the yield stress depend on the volume fraction of solid particles and on the type of particles. The evolution of the intrinsic viscosity and of the maximum packing fraction vs the shear rate is interpreted in terms of evolution of the size and of the shape of aggregates of particles under shear. The effect of temperature on the development of the yield stress is also discussed. The results are completed by microscopic observations.     

Dispersion Stability and Transport of Nanohybrids through Porous Media

Single-walled carbon nanotube-silica nanohybrid particles are a very promising material that could be used for enhanced oil recovery because of their interfacial activity. To demonstrate the basic principle, aqueous nanohybrid particle dispersions were evaluated by looking at the effect of pH, surfactant, and polymer. The results showed that pH did not have significant effect on the dispersion stability of nanohybrid particles. Although surfactant could improve the dispersion stability, it reduced the interfacial activity of the nanohybrid particles, causing them to stay in the aqueous phase. The best nanohybrid particle dispersion stability was found upon polymer addition, where the dispersions were stable for more than a week even at low polymer concentration (50?ppm). One-dimensional sand-pack studies were performed to evaluate the flow of the nanohybrid particles through porous media. The results showed that most of the nanohybrid particles (>99%) could pass through a column packed with glass beads while a measurable fraction of the particles was retained in the column packed with crushed Berea. When the columns contained a residual saturation of decane, additional nanohybrid particles were retained at the oil/water interface in both glass beads and crushed Berea sand media. The sand pack studies showed that not only can the nanohybrid particles flow through porous media but also about half of the particles injected will go the O/W interface when the porous medium contains a residual saturation of hydrocarbon, where they could be used to support a catalytic conversion of components of the oil in reservoirs.     

Viscosity of suspensions in polymeric solutions

Viscosities of suspended particles in polymeric solutions depend upon dissolved polymer concentration, volume fraction of particles and shear rate. In this analysis of viscosity data, relative viscosity was defined as the ratio of suspension viscosity to solution viscosity at the same shear stress rather than shear rate. These relative viscosities reached asymptotic values at high shear stress for all concentrations of dissolved polymer and for all particle loadings. At a given particle loading, the asymptotic values of relative viscosity were nearly independent of the concentration of dissolved polymer. Realtive viscosities were correlated with volume fraction by the one-constant equation of Maron and Pierce.     

Normal stress distribution in highly concentrated suspensions undergoing squeeze flow

Using pressure-sensitive films, the normal stress distribution is measured in suspensions of glass spheres in a Newtonian liquid undergoing constant-force squeeze flow. At volume fractions of solids up to 0.55, the normal stress distribution is independent of volume fraction and almost identical to the parabolic pressure distribution predicted for Newtonian fluids. However, at higher volume fractions, the normal stresses become an order of magnitude larger near the center and very low beyond that region. At these high volume fractions, the normal stresses decrease in the outer regions and increase in the inner regions as the squeezing proceeds. The normal stress distribution that results when the glass spheres without any fluid are subjected to squeeze flow is very similar to that for suspensions with volume fractions above 0.55, suggesting that the cause for the drastic changes in the normal stress distribution is the jamming of the particles in the suspension.     

Numerical investigation of plate edge and slot size effects in low yield stress measurements with a slotted plate device

There is a need for accurate yield stress measurements, especially in the case of low yield stress complex materials such as biological samples. This task cannot be accomplished with conventional rotational rheometers due to significant wall slip effects and the necessity to operate the device at very low shear rates, often beyond the limit that such rheometers can achieve. In this paper, we focused on the slotted plate method proposed recently for low yield stress measurements. Using computational fluid dynamics, we studied the effects of plate geometry on the measurement accuracy of the slotted plate method. Results of this study indicate that both wall slip effects and pressure drag force can be substantially reduced by adopting a thin plate with sharp front and rear edges, high slot area ratio, and large number of slots. If the plate has 30° triangular edges, a slot area ratio of 80%, and 12 slots, the slotted plate method overpredicts the yield stress of a 0.09 wt.% Carbopol dispersion (yield stress of 9.17 Pa) by only 8.4% under no-slip conditions and underpredicts the yield stress by 12.3% under free-slip conditions. Similar results were obtained for human saliva characterized by a very low yield stress (0.073 Pa).     

Rheology of concentrated microgel solutions

Viscosity, modulus, and yield stress for 0–6 wt% aqueous solutions of Carbopol 941 were investigated using constant shear rate, constant shear stress, and dynamic oscillatory experiments. The microgel character of the polymer was evident from the solid-like behavior of the solutions above 1 wt%. Yield stress increased with concentration, but yield occurred at a critical shear strain of 40%, independent of concentration. The static stress-strain relationship became non-linear at ~ 25% strain, in fair agreement with the onset of non-linear response in the storage modulus at ~ 10% strain. Small strain moduli from static and low frequency measurements agreed rather well; modulus values obtained from the recoverable strain after yielding were 30–40% smaller. Solutions flowed at near-constant stress in the low shear rate regime; at higher rates the stress increases with shear rate more rapidly. The viscosity did not obey the Cox-Merz rule. Steady-state viscosity scaled with polymer concentration to the 3/4 power. Results were interpreted using a cellular, deformable sphere model for the polymer, in analogy to emulsions and foams.