Thixotropy, yielding and ultrasonic Doppler velocimetry in pulp fibre suspensions

This paper reports thixotropy in concentrated pulp fibre suspensions and studies their transient flow behaviour using conventional rheometry coupled with a velocimetry technique. Specifically, an ultrasonic Doppler velocimeter is used in conjunction with a rate-controlled rheometer to deduce the local velocity profiles of pulp fibre suspensions. Pulp suspensions are found to exhibit a plateau in their flow curves where a slight increase in the shear stress generates a jump in the corresponding shear rate, implying the occurrence of shear banding. The velocity profiles were found to be discontinuous in the vicinity of the yielding radius where the Herschel–Bulkley model failed to predict the flow. Shear history and the time of rest prior to the measurement were found to play a significant role on the rheology and the local velocity profiles of pulp suspensions.     

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.     

Fibre suspension rheology: effect of concentration, aspect ratio and fibre size.

Viscosity data for fibre suspensions are produced using cone-and-plate geometry of enhanced dimensions for the reduced influence of fibre-wall interactions. Semi-concentrated suspensions of monodisperse polyamide fibres in silicone oil, with a variety of fibre concentrations (2, 5 and 8%), lengths and diameters, were studied. The suspension viscosity was measured in a range of shear stress in order to study the stress dependence. The study here focuses on the nature of the forces and interactions that contribute to the suspension viscosity. The results show that at sufficiently high stress levels, the suspension viscosity tends to reach a steady-state. At very low stress levels the suspension viscosity increases over time, most likely due to structures formed by adhesive forces. At higher concentrations, the viscosity depends on the absolute size of the fibres, again indicating the presence of non-hydrodynamic interactions.     

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     

Rheological behavior of concentrated suspensions as affected by the dynamics of the mixing process

The rheological characterizations of concentrated suspensions are generally carried out assuming “well-mixed” suspensions. However, the variation of the concentration distributions of the ingredients of the formulation, i.e., the “goodness of mixing”, the size and shape distributions of the particle clusters and the rheological behavior of the suspension all depend on the thermo-mechanical history that the suspension is exposed to during the mixing process. Here, various experimental tools are used for the characterization of the degree of mixedness (concentration distributions) of various ingredients along with the characterization of rheological material functions, wall slip behavior and the maximum packing fraction of a graphite/elastomer suspension. The degree of mixedness values of the ingredients of the suspensions processed using batch and continuous processes and under differing operating conditions were characterized quantitatively using wide-angle X-ray diffraction and thermo gravimetric analysis and were elucidated under the light of the electrical properties of the suspension as affected by the mixing process. Upon achieving better homogeneity of the graphite particles and the binder and decreases in the size and breadth of the size distributions of particle clusters (as inferred from electrical measurements and maximum packing fraction values), the elasticity (storage modulus) and the shear viscosity (magnitude of the complex viscosity from small-amplitude oscillatory shear and shear viscosity from steady torsional and capillary rheometry) of the suspension decreased significantly and the wall slip velocity values increased. These findings demonstrate the intimate relationships that exist between the rheological behavior of concentrated suspensions and the thermo-mechanical history that they are exposed to during the processing stage and suggest that the preparation conditions for suspensions should be carefully selected and well documented to achieve reproducible characterization of rheological material functions.     

Rheology of pulp suspensions using ultrasonic Doppler velocimetry

Conventional rheometry coupled with local velocity measurements (ultrasonic Doppler velocimetry) are used to study the flow behaviour of various commercial pulp fibre suspensions at fibre mass concentrations ranging from 1 to 5 wt.%. Experimental data obtained using a stress-controlled rheometer by implementing a vane in large cup geometry exhibits apparent yield stress values which are lower than those predicted before mainly due to existence of apparent slip. Pulp suspensions exhibit shear-thinning behaviour up to a high shear rate value after which Newtonian behaviour prevails. Local velocity measurements prove the existence of significant wall slippage at the vane surface. The velocimetry technique is also used to study the influence of pH and lignin content on the flow behaviour of pulp suspensions. The Herschel–Bulkley constitutive equation is used to fit the local steady-state velocity profiles and to predict the steady-state flow curves obtained by conventional rheometry. Consistency between the various sets of data is found for all suspensions studied, including apparent yield stress, apparent wall slip and complete flow curves.     

On the behaviour of gelled fibre suspensions in steady shear

The shear rheological properties of suspensions of gelled agar fibres in a low viscosity Newtonian matrix fluid were investigated. Two classes of fibres, low aspect ratio fibres and high aspect ratio fibres with an aspect ratio of the order of 10 and 100 respectively were included in the investigations. For all fibre phase volumes investigated, from as low as 0.01 upwards, the flow curves are characterised by an apparent yield stress followed by shear-thinning which was independent of the fibre aspect ratio. Based on our analysis of the flow curves, we conclude that the high aspect ratio fibres behave like flexible threads in contrast to the low aspect ratio fibres whose high shear relative viscosity is successfully described by a relation for long rigid rods. These findings are supported by flow visualisation using an optical shearing stage coupled to a light microscope.     

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.     

Packing properties of binary mixtures in disordered sphere systems

Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio. A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity. The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by “large–small” contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems.     

Packing properties of binary mixtures in disordered sphere systems

Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,     

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.     

Free-surface flow of concentrated suspensions

Free-surface flows of concentrated suspensions exhibit many interesting phenomena such as particle segregation and surface corrugation. In this work the flow structures associated with free-surface has been studied experimentally. The free-surface velocity for neutrally buoyant suspension of uniform spheres in a gravity driven inclined channel flow was determined by particle imaging velocimetry (PIV) technique. Experiments were carried out for concentrated suspensions with particle fractions ? ranging from 0.40 to 0.50. The measured velocities show blunted profile in the channel. The blunting of the velocity profile increases with the particle concentration. The rms velocity fluctuations measured at the free-surface progressively increase with particle fraction ? and are linear in shear rate γ. The surface roughness were characterized by analyzing the power spectral density of the refracted light from the free-surface. The characteristics observed are in support of earlier findings.     

One-step,in situ jamming point measurements by immobilization cell rheometry

Dense colloidal suspensions are processed in a wide variety of industries. Challenges for pumping suspensions and slurries at high concentrations include shear thickening and dilation, which can have deleterious consequences. These systems are shear sensitive close to the jamming point, meaning that a significant increase in high shear viscosity can be observed with just a few percent change in volume fractions. Therefore, accurate and rapid determination of the jamming point can greatly aid formulation. Typically, conventional rheometry identifies the jamming point by a time-consuming process, whereby multiple flow curves of suspensions of different volume fraction are measured and extrapolated to the volume fraction where the viscosity diverges. We present an alternative approach for rapid, one-step, experimental determination of the jamming point for aqueous suspensions. The procedure monitors the shear stress under constant shear stress or shear rate as the sample is dewatered using immobilization cell rheometry, until the viscosity diverges. The method is validated by comparing the results of this work with conventional rheometry for a model suspension. Then it is applied to examine the effect of grafting a short-chain polymer to particles, comprising an industrial suspension of silica-coated titania. Polymeric coating of the particles increases the jamming concentration and mitigates shear thickening, qualitatively consistent with predictions from simulations.

A new method is designed to extract the jamming point of a suspension. The procedure monitors the effective viscosity under prescribed shear conditions as the suspension is dewatered using immobilization cell rheometry. The geometry moves down to accommodate solvent evaporation, until the viscosity diverges, and the jamming point is reached.

     

The normal stress behaviour of suspensions with viscoelastic matrix fluids

 We investigate the variations in the shear stress and the first and second normal stress differences of suspensions formulated with viscoelastic fluids as the suspending medium. The test materials comprise two different silicone oils for the matrix fluids and glass spheres of two different mean diameters spanning a range of volume fractions between 5 and 25%. In agreement with previous investigations, the shear stress–shear rate functions of the viscoelastic suspensions were found to be of the same form as the viscometric functions of their matrix fluids, but progressively shifted along the shear rate axis to lower shear rates with increasing solid fraction. The normal stress differences in all of the suspensions examined can be conveniently represented as functions of the shear stress in the fluid. When plotted in this form, the first normal stress difference, as measured with a cone and plate rheometer, is positive in magnitude but strongly decreases with increasing solid fraction. The contributions of the first and the second normal stress differences are separated by using normal force measurements with parallel plate fixtures in conjunction with the cone-and-plate observations. In this way it is possible for the first time to quantify successfully the variations in the second normal stress difference of viscoelastic suspensions for solid fractions of up to 25 vol.%. In contrast to measurements of the first normal stress difference, the second normal stress difference is negative with a magnitude that increases with increasing solid content. The changes in the first and second normal stress differences are also strongly correlated to each other: The relative increase in the second normal stress difference is equal to the relative decrease of the first normal stress difference at the same solid fraction. The variations of the first as well as of the second normal stress difference are represented by power law functions of the shear stress with an unique power law exponent that is independent of the solid fraction. The well known edge effects that arise in cone-and-plate as well as parallel-plate rheometry and limit the accessible measuring range in highly viscoelastic materials to low shear rates could be partially suppressed by utilizing a custom- designed guard-ring arrangement. A procedure to correct the guard-ring influence on torque and normal force measurements is also presented. Received: 20 December 2000 Accepted: 7 May 2001     

Shear-induced changes of electrical conductivity in suspensions

The effect of shear on electrical conductivity (rheo-conduction) is studied to give information about particle behaviour in suspensions. Past work is reviewed, and expressions are derived for the rheo-conduction of a suspension of nonconducting spheroids in a conducting matrix for current flow, parallel and normal to the suspension flow direction. A simple apparatus to study rheo-conduction in pipe flow is described, and measurements of steady and time-dependent effects are reported for various suspensions of colloidal particles. Suspensions of anisometric rod- and platelike particles at low concentrations showed rheo-conductive changes of sign, magnitude and relaxation that were consistent with the particle shape, concentration and interactions. The rheo-conductive response decreased with increasing volume fraction for platelike kaolinite particles, attributed to orientational jamming. Spherical latex particles gave unexpected rheo-conductive changes consistent with shear disruption of a conductive network of particles. It is concluded that rheo-conduction measurements are a useful adjunct to conventional rheometry.     

Bidisperse polymeric mixtures for independent control of viscosity and elasticity

 It is known that the zero shear viscosity of a polydisperse melt of linear polymers depends only on its weight-average molecular weight, whereas its recoverable compliance increases with polydispersity. These facts can be exploited to design model viscoelastic fluids using mixtures of short and long chains of the same homopolymer (bidisperse mixtures). The composition required to obtain a bidisperse mixture with the desired viscosity can be calculated from the molecular weights of the components, and the known relationship between viscosity and weight-average molecular weight. The terminal viscoelastic properties of such a bidisperse mixture are estimated from theoretical predictions for the compliance of bidisperse mixtures available in the literature. These predictions suggest that the elasticity of bidisperse mixtures can be varied independent of their viscosity by appropriately choosing the molecular weights of their components and their composition. This strategy is applied here on bidisperse mixtures of monodisperse 1,4-polyisoprene, which are shown to display second-order fluid behavior over a reasonable range of accessible shear rates. The same procedure is also applied to mixtures of PDMS polymers which are not particularly monodisperse. Rheological measurements show that the elasticity of these polyisoprene and PDMS mixtures can indeed be varied without changing their viscosity. Such materials are ideally suited to study structure-rheological properties relationships in blends of immiscible viscoelastic fluids. Received: 12 April 2001 Accepted: 28 August 2001     

Direct measurements of shear-induced particle migration in suspensions of bimodal spheres

A variety of studies reported in the literature have established that initially well mixed suspensions subjected to non-homogeneous shear flows attain an anisotropic particulate structure. It has also been shown that non-homogeneous shearing causes suspensions of unimodal spheres to demix, i.e., gradients in solids concentration are formed. The objective of this study was to determine the effect of non-homogeneous shear flows on suspensions of bimodal particles, and specifically, to determine if the solids concentration gradients which develop are accompanied by size segregation of the coarse with respect to the fine fraction. We used the simplest and most direct methods to determine the relative solids concentrations: visual observation of tracer particles in transparent suspensions and physical separation of the coarse and fine solid fractions. Three different types of non-homogeneous shear flows were examined, and in each case the data support two main conclusions: 1) suspended particles migrate from regions of high shear rate to regions of low shear rate, and 2) the coarse fraction of particles migrates much faster than the fine fraction, leading to size segregation of initially well-mixed suspensions. While the former conclusion is consistent with other studies reported in the literature, to our knowledge this paper provides the first data supporting and, to a limited extent, quantifying the latter conclusion.     

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     

Transport of Neutrally Buoyant and Dense Variably Sized Colloids in a Two-Dimensional Fracture with Anisotropic Aperture

The transport of monodisperse as well as polydisperse colloid suspensions in a two-dimensional, water saturated fracture with spatially variable and anisotropic aperture is investigated with a particle tracking model. Both neutrally buoyant and dense colloid suspensions are considered. Although flow and transport in fractured subsurface formations have been studied extensively by numerous investigators, the transport of dense, polydisperse colloid suspensions in a fracture with spatially variable and anisotropic aperture has not been previously explored. Simulated snapshots and breakthrough curves of ensemble averages of several realizations of a log-normally distributed aperture field show that polydisperse colloids exhibit greater spreading than monodisperse colloids, and dense colloids show greater retardation than neutrally buoyant colloids. Moreover, it is demonstrated that aperture anisotropy oriented along the flow direction substantially increases colloid spreading; whereas, aperture anisotropy oriented transverse to the flow direction retards colloid movement.     

Brownian dynamics simulation for suspensions of oblong-particles under shear flow

Computer simulations of the shear flow for the suspensions of oblong-particles were performed using nonequilibrium Brownian Dynamics (BD). The model particle is a rigid body made up of linearly connected spheres with the interparticle potential of a repulsive Lennard-Jones potential. The length-over-width ratios of the oblong-particles used in the present calculations are 5/3 and 3. In the concentrated suspensions high orientation is easily induced by shear at low shear rates. The systems of the oblong-particles exhibit the structural transition that causes the significant change in the rheological properties at high shear rates. Furthermore, the dependence of the length-over-width ratio of the particle is examined. Received: 16 June 1997 Accepted: 3 February 1998