A cell model theory of the shear viscosity of a concentrated suspension of interacting spheres in a non-Newtonian fluid

A theoretical approach to the shear viscosity of concentrated suspensions of small particles in a non-Newtonian fluid has been developed using a cell theory model involving particle-particle interaction. The cell theory of Frankel and Acrivos was first generalized to power-law fluid matrices without particle interaction. Particle-particle interaction was then taken into consideration. The theory suggests that the flow behavior of such systems at low shear rates is chiefly dependent upon non-hydrodynamics interparticle interaction such as van der Waals—London and electrostatic forces which induce flocculation and yield stresses. The flow properties at high shear rates are determined by hydrodynamics interaction essentially dependent upon particle concentration and shape.     

Shear behaviour of biopolymer suspensions with spheroidal and cylindrical particles

The rheological behaviour of suspensions is influenced by many parameters, one of which is the particle shape. For rigid particle suspensions a number of studies demonstrate the effects of the particle aspect ratio. Indeed, fibres are widely used as rheology modifiers in different materials such as synthetic polymers. This work is concerned with testing the hypothesis that regularly shaped particles with aspect ratios larger than one that are made of gelled biopolymers could be used as rheology modifiers for biopolymer solutions. Biopolymers, and mixtures thereof are a widely used ingredient in foods and other products with structure functionality. Tailoring rheology modifiers by morphology offers an alternative to using different biopolymers. It is demonstrated how biopolymer suspensions with regular spheroidal, or cylindrical particle shapes can be produced by gelling the droplet phase of a liquid two phase biopolymer mixture in a shear field. Biopolymers were chosen such that gelation is initiated by cooling. Shear-cooling at constant stresses leads to the formation of ellipsoidal particles. Cylindrical particles can be generated by stepping up the shear stress prior to gelation, i.e., stretching the droplet phase into fibrils, and trapping the shape prior to break-up through gelation. Morphologies and steady shear rheological data for suspensions of the two biopolymers gellan and κ-carrageenan with an internal phase volume of 0.2 are reported. The influence of particle shape on relative viscosity is pronounced. At high shear stresses particle orientation leads to decreased viscosity with increasing particle aspect ratio. In the low shear region, higher aspect ratio suspensions show higher viscosities. Additionally, the material properties, including the interfacial tension, which influence the suspension morphology are reported. Received: 3 March 2000 Accepted: 22 August 2000     

In situ flow visualization of capillary flow of concentrated alumina suspensions

A new approach was taken to understand the flow behavior of concentrated particle suspensions in pressure-driven capillary flow. The flow of concentrated alumina suspensions in a slit channel was visualized and quantitatively analyzed with modified capillary rheometer. The suspensions showed complex flow behaviors; unique solid–liquid transition and shear banding. At low flow rates, 55 vol% alumina suspension showed a unique transient flow behavior; there was no flow at first and continuous change of flow profile was observed with time. At low shear rates in particular, the suspensions exhibited shear-banded flow profile which could be divided into three regions: the region with low flow rate near the wall, the region with rapid increase of flow velocity to maximum, and the region of velocity plateau. Based on both flow visualization and measurement of shear stress, it was found that the shear-banded flow profile in pressure-driven slit channel flow was strongly correlated with shear stress. The banding in pressure-driven flow was different from that in Couette flow. The banding of concentrated alumina suspensions was unique in that sluggish velocity profile was pronounced and two inflection points in velocity profile was exhibited. In this study, shear banding of concentrated alumina suspensions in slit channel flow was visualized and quantitatively analyzed. We expect that this approach can be an effective method to understand the flow behavior of particulate suspensions in the pressure-driven flow which is typical in industrial processing.     

A self-similar behavior for the relative viscosity of concentrated suspensions of rigid spheroids

A viscosity model for suspensions of rigid particles with predictive capability over a wide range of particle volume fraction and shear conditions is of interest to quantify the transport of suspensions in fluid flow models. We study the shear viscosity of suspensions and focus on the effect of particle aspect ratio and shear conditions on the rheological behavior of suspensions of rigid bi-axially symmetric ellipsoids (spheroids). We propose a framework that forms the basis to microscopically parameterize the evolution of the suspension microstructures and its effect on the shear viscosity of suspensions. We find that two state variables, the intrinsic viscosity in concentrated limit and the self-crowding factor, control the state of dispersion of the suspension. A combination of these two variables is shown to be invariant with the imposed shear stress (or shear rate) and depends only on the particle aspect ratio. This self-similar behavior, tested against available experimental and numerical data, allows us to derive a predictive model for the relative viscosity of concentrated suspensions of spheroids subjected to low (near zero) strain rates. At higher imposed strain rates, one needs to constrain one of the state variables independently to constrain the state of dispersion of the suspension and its shear dynamic viscosity. Alternatively, the obtained self-similar behavior provides the means to estimate the state variables from the viscosity measurements made in the laboratory, and to relate them to microstructure rearrangements and evolution occurring during deformation.     

Microstructure of shear-thickening concentrated suspensions determined by flow-USANS

Reversible shear thickening in colloidal suspensions is a consequence of the formation of hydroclusters due to the dominance of short-ranged lubrication hydrodynamic interactions at relatively high shear rates. Here, we develop and demonstrate a new method of flow-ultra small angle neutron scattering to probe the colloidal microstructure under steady flow conditions on length scales suitable to characterize the formation of hydroclusters. Results are presented for a model near hard-sphere colloidal suspension of 260 nm radius (10% polydisperse) sterically stabilized silica particles in poly(ethylene glycol) at shear rates in the shear thinning and shear thickening regime for dilute, moderately concentrated, and concentrated (ordered) suspensions. Hydrocluster formation is observed as correlated, broadly distributed density fluctuations in the suspension with a characteristic length scale of a few particle diameters. An order–disorder transition is observed to be coincident with shear thickening for the most concentrated sample, but the shear-thickened state shows hydrocluster formation. These structural observations are correlated to the behavior of the shear viscosity and discussed within the framework of theory, simulation, and prior experiments.     

Investigating the transient response of a shear thickening fluid using the split Hopkinson pressure bar technique

The split Hopkinson pressure bar (SHPB) technique is implemented to evaluate the transient response of a colloidal suspension exhibiting shear thickening at strain rates and timescales never before explored in a laboratory instrument. These suspensions are shown to exhibit a discontinuous transition from fluid-like (shear thinning) to solid-like (shear thickening) behavior when evaluated using rotational rheometry. The effect of loading rate on this transition time is studied for a particle volume fraction of 0.54 using the SHPB technique. It is shown that the time required for transition to occur decreases logarithmically with loading rate. From these results, we conclude that transition is not triggered by a characteristic shear rate, but rather a critical shear strain is required. Results from SHPB experiments performed up to Peclet numbers of order 10⁷ are presented and discussed for 0.50, 0.52, and 0.54 particle volume fraction suspensions.     

Shear viscosity of suspensions of aligned non-Brownian fibres

We report on the steady-state shear viscosity of suspensions of fibres dispersed in Newtonian fluids, in a wide range of volume fractions throughout the dilute and semi-dilute regimes. We show that the apparent shear-thinning behaviour, which is sometimes observed in the semi-dilute regime at intermediate shear rates, is an experimental artefact due to the presence of transient clusters of entangled fibres in the suspensions. At high shear rates, the fibres are aligned and the suspensions exhibit Newtonian behaviour. In this regime, the viscosity is a function of volume fraction and fibre aspect ratio only. The data can be rescaled onto a universal curve using a variable that accounts for the average contribution of the particles to the bulk stress. All these results are discussed in relation to recent theories. Received: 19 January 1999 Accepted: 17 June 1999     

Shear thickening in electrically-stabilized colloidal suspensions

A theory is presented for the onset of shear thickening in colloidal suspensions of particles, stabilized by an electrostatic repulsion. Based on an activation model, a critical shear stress can be derived for the onset of shear thickening in dense suspensions for a constant potential and a constant charge approach of the spheres. Unlike previous models, the total interaction potential is taken into account (sum of attraction and repulsion). The critical shear stress is related to the maximum of the total interaction potential scaled by the free volume per particle. A comparison with experimental investigations shows the applicability of the theory.     

Electrorheology of dilute suspensions induced by hydrodynamic instability

The viscosity behavior in electric fields was measured for dilute suspensions of p-[perfluoro(2-isopropyl-1,3-dimethyl-1-butenyl)oxy]benzoic acid particles (PFNA) in silicone oils. The application of electric fields causes a viscosity increase in a wide range of shear rates. Since the electrorheological (ER) effect is much stronger at low shear rates, the flow becomes shear-thinning. However, contrary to conventional ER suspensions which are reversibly converted between Newtonian fluids and Bingham solids, the PFNA suspensions are fluids even in electric fields. When the particle concentration is increased to 5 wt.%, the ER effect reaches saturation. Further increase does not contribute to additional viscosity enhancement. These results cannot be explained through the chain formation mechanism established for conventional systems. After the ER experiments, the bob surface of the rheometer is covered with several stripes of aggregated particles. Although the strength of electric and shear fields is constant in the rheometer, the periodic structure may be formed in the flow of electrified suspensions. When a dielectric liquid is subjected to high electric fields, the secondary motion of liquid can be induced by the Coulomb force acting on free charge. The electrohydrodynamic (EHD) convection is responsible for the periodic distribution of particles concentration. The ER effect of PFNA suspensions may be generated by a combined effect of EHD convection and external shear.     

Rheological behavior of needle-like hydroxyapatite nano-particle suspensions

We describe here the preparation and rheological behavior of stable suspensions of needle-like hydroxyapatite nanoparticles dispersed in organic media, including methylethylketone (MEK), polycaprolactone (PCL) solutions in MEK, and PCL melt. These suspensions are the main ingredients in preparing certain biodegradable orthopedic materials that have some advantages over traditional implants. Rheological properties were experimentally determined at shear rates approaching those used in the processing methods such as roll coating, extrusion, and pultrusion. Analysis of the flow behavior suggests possible shear alignment at high Pe number (Pe ≈ 6,000). The linear viscoelastic properties and the paste-like behavior suggest the formation of a network as the particle content increases. These results are critical in designing a process for making composite materials containing highly oriented anisotropic particles.     

Shear-thickening behavior of polymethylmethacrylate particles suspensions in glycerine–water mixtures

The rheological behavior of polymethylmethacrylate (PMMA) particles suspensions in glycerine–water mixtures has been investigated by means of steady and dynamic rheometry in this work. The shear rheology of these suspensions demonstrates a strong shear thickening behavior. The variations of shear viscosity with the volume fraction and ratios of glycerine to water are discussed. The effect of volume fraction can be qualitatively explained using a clustering mechanism, which attributes the phenomena to the formation of temporary, hydrodynamic clusters. The influence of interactions between glycerine–water mixtures and PMMA particles on shear thickening is investigated by varying the ratio of glycerine to water. In addition, the reversible and thixotropic properties of suspensions of PMMA dispersed in glycerine–water (3:1) mixtures are also investigated, and the results demonstrate the excellent reversible and thixotropic properties of PMMA particle suspensions.     

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     

Überlegungen zur Scherviskosität von Suspensionen aufgrund einer Dimensionsanalyse

Dimensional analysis of the motion of solid particles suspended in a fluid phase shows that the macroscopic relative shear viscosity of suspensions generally depends not only on the volume concentration and particle shape but also on two Reynolds numbers and a dimensionless sedimentation number. These dimensionless numbers are formed using parameters characterizing the structure and motion of the suspension at the microscopic level. The analysis was based on the assumptions that the dispersed particles are rigid and sufficiently large that Brownian motion may be neglected, that the continuous fluid phase is Newtonian and that the interactions between particles and between particles and fluid phase are only hydrodynamic. The Reynolds numbers describe the influence of the inertial forces at the microscopic level, and the sedimentation number the influence of gravity. The dimensionless numbers can be neglected if their values are much smaller than one. For each of the dimensionless numbers both the shear rate and the particle size influence the shear viscosity. Thus sedimentation number is large for low shear rates, whereas the Reynolds numbers are large for high shear rates. The viscosity function for one suspension can be transformed into the viscosity function for another suspension with geometrically similar particles but of a different size. The scale-up rules are derived from the requirement that the relevant dimensionless numbers must be constant. The influence of non-hydrodynamic effects at the microscopic level on the shear viscosity can be detected by deviations from the derived scale-up rules.     

On the elastic properties of model suspensions as investigated by creep recovery measurements in shear

 The elastic properties of model suspensions with spherical monodisperse hydrophilic glass spheres that were dispersed in a Newtonian liquid were determined in creep and creep recovery measurements in shear with a magnetic bearing torsional creep rheometer. The creep and creep recovery measurements were performed depending on the applied level of shear stresses ranging from 0.19 Pa to 200 Pa. Since the recoverable creep compliances of the chosen suspending medium (i.e. a low molecular weight polyisobutylene) were far below the lower limit of the resolution of the creep rheometer it can be considered to behave as purely viscous. By applying a large shear stress in the creep tests the investigated suspensions with a volume fraction of Φ _t =0.35 behave as Newtonian liquids, too. For these suspensions no significant recoverable creep compliances could be detected, as well. In contrast to the Newtonian state of suspensions at high shear stresses, where a shear induced ordering of the particles can be expected, a non-Newtonian behaviour arises by applying a very low shear stress in the creep test. In this state large recoverable creep compliances were detected for the suspensions. The magnitude of the recoverable creep compliances of the suspensions exceeded the largest creep compliances of polymer melts that are reported in the literature by more than two decades. From the results obtained by creep recovery measurements with a magnetic bearing torsional creep rheometer it can clearly be concluded that the particle structure present in the chosen model suspension gives rise to a pronounced elasticity. Received: 21 November 2000 Accepted: 12 July 2001     

Brownian dynamics simulations for suspension of ellipsoids in liquid crystalline phase under simple shear flows

Brownian dynamics simulations of shear flows are carried out for various suspensions of ellipsoids interacting via the Gay-Berne potential. In this simulation all the systems of the suspension are in a liquid crystalline phase at rest. In a shear flow they exhibit various motions of the director depending on the shear rate: the continuous rotation, the intermittent rotation, the wagging-like oscillation, and the aligning. The director is almost always out of the vorticity plane when it rotates, that is the kayaking. The number density of the system and the inter-particle potential intensity significantly affect the shear rate dependence of orientation. In particular, the continuous rotation of director is maintained to higher shear rates for the system with a stronger potential. Furthermore, the rheological properties are examined. The shear-thinning in viscosity is observed, but the negative first normal difference is not obtained.     

Strain-thickening transition in ferric-oxide suspensions under oscillatory shear

Shear-strain-thickening transition under oscillatory flow was observed in flocculated ferric-oxide suspensions in mineral oil. The value of the dynamic modulus of the suspensions that was measured at small strain amplitude after cessation of shear also became higher when the strain amplitude of the applied shear had been within or above the transition region.The ferric-oxide powders used were an acicular submicron maghemite (magnetic) and the hematite (non-magnetic) that was converted from the maghemite by heat treatment. The powders were treated with a dispersing agent and the suspensions were prepared in 33% by particle weight. The strain-thickening transition was observed in both the magnetic and the non-magnetic suspensions. However, the onset of the strain-thickening in the magnetic suspension was found at about one decade larger strain amplitude than that in the non-magnetic analog suspension, indicating particle interactions affect to the appearance of the phenomenon.A qualitative interpretation was made in view of site percolation for the enhancement of modulus at rest after the application of the large-amplitude oscillatory shear, where the process of the strain-thickening transition under shear and the development of the modulus after stopping the shear was described with a floc model in which the flocculation phase dilates as a result of the reduction of the particle linkages under higher shear.     

Extensional rheology of a shear-thickening cornstarch and water suspension

A filament-stretching rheometer is used to measure the extensional viscosity of a shear-thickening suspension of cornstarch in water. The experiments are performed at a concentration of 55 wt.%. The shear rheology of these suspensions demonstrates a strong shear-thickening behavior. The extensional rheology of the suspensions demonstrates a Newtonian response at low extension rates. At moderate strain rates, the fluid strain hardens. The speed of the strain hardening and the extensional viscosity achieved increase quickly with increasing extension rate. Above a critical extension rate, the extensional viscosity goes through a maximum and the fluid filaments fail through a brittle fracture at a constant tensile stress. The glassy response of the suspension is likely the result of jamming of particles or clusters of particles at these high extension rates. This same mechanism is responsible for the shear thickening of these suspensions. In capillary breakup extensional rheometry, measurement of these suspensions demonstrates a divergence in the extensional viscosity as the fluid stops draining after a modest strain is accumulated.     

Reological behaviour of concentrated monodisperse suspensions as a function of preshear conditions and temperature: an experimental study

 The influence of preshearing on the rheological behaviour of model suspensions was investigated with a stress-controlled cone-and-plate rheometer. The used matrix fluids showed Newtonian behaviour over the whole range of applied shear stresses. Highly monodisperse spherical glass spheres with various particle diameters were used as fillers. By applying steady preshearing at a low preshear stress, where a diffusion of particles can be expected, it was found for all model suspensions investigated at volume fractions ranging from 0.20 to 0.35 that the time-temperature superposition in the steady shear and in the dynamic mode holds within the chosen temperature range. Furthermore, all presheared model suspensions displayed a high and a low frequency range which are either separated by a shoulder or by a plateau value of G′ at intermediate frequencies. It could clearly be demonstrated that the low frequency range strongly depends on the preshear conditions. Hence, the features observed in the low frequency range can be attributed to a structure formation of a particulate network. In the high frequency range a frequency-dependent behaviour was observed which obeys the classical behaviour of Newtonian fluids (G′∝ω², G′′∝ω). The resulting temperature shift factors from the dynamic and the steady shear mode are identical and independent of the volume fraction and the particle size of the filler. Received: 29 November 2000 Accepted: 12 July 2001     

Dynamics and rheology of a dilute suspension of dipolar nonspherical particles in an external field: Part 1. Steady shear flows

Suspensions of small nonspherical particles having dipolar moments exhibit non-Newtonian behavior under the influence of shear and external fields. Numerical methods are presented for calculating the rheological and rheo-optical properties of dilute suspensions of Brownian particles having permanent dipoles subject to time-dependent shear and external fields. The numerical methods employ the Galerkin method of weighted residuals to solve the differential equation for the particle orientation distribution function. The steady-state shear flow intrinsic viscosity of suspensions of particles with sufficiently extreme aspect ratio is predicted to exhibit a maximum value attained for intermediate shear rates at selected field orientations. These numerical results provide valuable insight into the coupling which occurs between the effects of rotary Brownian motion, the hydrodynamic resistance of nonspherical particles, and the external torque exerted on dipolar particles. The results are applicable to both suspensions of magnetic particles and electrically dipolar particles.     

Solutions of xanthan gum/guar gum mixtures: shear rheology,porous media flow,and solids transport in annular flow

Mixtures of xanthan and guar gum in aqueous solution were studied in two flow situations: simple shear and porous media. In addition, solids transport in vertical annular flow of sand suspensions was explored. The zero shear rate viscosity of the solutions displayed a pronounced synergy: the viscosity of the mixture is higher than that of the polymer solutions in a wide range of relative concentrations of the two polymers, in agreement with previous literature. However, at relatively high shear rates, the viscosity approaches the value of the more viscous xanthan gum solutions at mass fractions of xanthan gum between 0.1 and 0.15, and the degree of synergy substantially decreases. Stress relaxation experiments in simple shear indicate that the polymer mixtures exhibit a well-defined yield stress after relaxation that is absent in solutions of pure polymers. In porous media flow experiments, a synergistic behavior mimicking the shear flow results was obtained for the polymer mixtures at low shear rates. However, at a critical shear rate, the apparent viscosity in porous media flows exceeds the shear viscosity due to the elongational nature of flow in the pores. The solids transport capacity in annular flows is well-represented by trends in shear viscosity and stress relaxation behavior. However, the lack of viscosity synergy at high shear rates limits the applicability of the mixtures as a way to improve solids suspension capacity in annular flows.