Rheological behaviour of a filled wax system

The temperature dependent rheological behaviour of a pigment filled wax system is investigated in a cone-and-plate viscometer over a range of shear rates from 60 to 10 000 s^–1. A strong influence of water adsorbed by the pigment on rheological properties of the filled system can be found. The increase of the yield stress and the viscosity at low shear rates can be related to a build-up of pigment structures due to growing water content. The flow behaviour can be described by the Casson equation as well as by the Herschel-Bulkley equation.Both formulations are compared and discussed. The Casson model is evaluated more closely by the calculation of characteristic structural parameters of the suspension which are critically discussed.Dedicated to Prof. Dr. Joachim Meissner on the occasion of his retirement from the chair of polymer physics at the Eidgenössische Technische Hochschule (ETH), Zürich.     

Rheological properties of disperse systems at low shear stresses

Three-dimensional network structures can be built up in disperse systems due to long-range colloidal interactions between the dispersed particles. The rheological behaviour of such coagulation structures has been studied by means of creep and recovery experiments at low shear stresses, i.e. by measuring the shear strain as a function of time under constant stress and after removal of stress. Measurements of this type give insight into the elastic and viscous deformations and the retardation times necessary to reach equilibrium or steady-state conditions.Results obtained with dispersions of pigments in polymer solutions and with monodisperse polymer latexes indicate the existence of an equilibrium state at low shear stresses with a predominant elastic deformation and a high viscosity suggesting that the disperse systems investigated do not behave exactly as rigid gels but apparently exhibit a dynamic equilibrium of structural break-down and formation under applied stress. This behaviour is approximately described by a 4-parameter-model with an instantaneous and a steady-state compliance, one retardation time, and a viscosity.At higher shear stresses thixotropic structural break-down occurs resulting in a transition from the rheological behaviour described here to a liquid-like state with a comparatively low viscosity. In this stress range the viscoelastic properties become strongly time-dependent.These measurements give evidence of the presence of two types of deformation: an instantaneous, purely elastic deformation attributable to the unperturbed coagulation structure and the creep-recovery behaviour of an elastic liquid apparently related to the breaking and re-forming of bonds.     

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.     

A structural model for thixotropy of colloidal dispersions

The present study proposes a structural model to describe the thixotropic behavior of colloidal dispersions. This model uses structural viscosity and elasticity as internal parameters, and predicts the evolution of shear stress when shear rate varies over time. Viscosity represents the structural level of colloidal aggregates and is dependent upon their alignment. Changes in alignment are linked to changes in shear rate, are regarded as instantaneous and are not believed to cause thixotropic behavior. Only changes in the structural level or structural viscosity and in the elastic deformation of colloidal aggregates cause measurable thixotropic behavior. Variations in structural viscosity over time, and at a fixed shear rate, follow a first-order kinetic equation based on two characteristic thixotropic times. This model incorporates several parameters, which are fitted independently by the appropriate rheological tests, in order to avoid any mathematical coupling. This model has been tested in 3 wt% Laponite aqueous dispersions using different ionic strengths.     

Rheology of brown coal-water suspensions

Techniques for measuring the fundamental flow properties of as-mined Victorian brown coal suspensions are developed. Flow properties are presented for Morwell, Yallourn and Loy Yang coals as a function of concentration for fixed particle size distribution. Even at the relatively low solids concentration of 20 to 30 percent by weight, the suspensions exhibit complex non-Newtonian characteristics. Generally at high concentration, the suspensions are thixotropic with a shear rate dependent viscosity and exhibit a yield stress. The inherent thixotropy of the coals can be exploited and it is technically but perhaps not economically feasible to transport the as-mined coals in a pipeline. The power requirement to pump the coals in a pipeline is found to be 10 to 30 times that required to pump black coal in the Black Mesa pipeline in the U.S.A. The differences in the rheological properties of the three coals is related to the surface properties of the coal particle — expressed in terms of carboxylate and inorganic cation content, and to differences in the pore volume of the coals. The flow characteristics of one coal can be converted to that of another simply by varying either the carboxylate or ionic content of the suspension.     

Rheology of oil-in-water emulsions

The effect of interfacial tension on the steady-flow and dynamic viscoelastic behavior of emulsions are studied experimentally. At very low inter-facial tensions and low volume fractions, the viscosity decreases with increasing shear rate and becomes constant at high shear rates. The high-shear-rate Newtonian viscosity is not affected by interfacial tension, but the transition from pseudoplastic to Newtonian flow shifts to lower shear rates as the interfacial tension decreases. At an interfacial tension of 5 × 10^–3 Nm^–1, the viscosity decreases, passes through a minimum, and then increases as the shear rate is increased. The dilatant behavior may be attributed to elastic responses of interfaces during collision of drops. At high volume fractions, the emulsions show remarkable elasticity resulting from the interfacial energy associated with deformation of liquid films. The modulus and viscosity are proportional to interfacial tension and inversely proportional to drop size.     

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     

Droplet deformation of a strongly shear thinning dense suspension of polymeric micelles

We investigated the deformation of a strong shear thinning droplet undergoing simple shear flow in a Newtonian liquid. The droplet was an aqueous solution of poly(ethylene oxide) end capped with an alkyl group that forms spherical micelles in aqueous solution. At high concentrations and below a critical temperature, the jammed micelles showed strong shear thinning behaviour, and neither a yield stress nor a Newtonian viscosity was observed. At small shear rates, the droplet rotated and aligned in the flow, but did not deform or only very weakly. At high shear rates, the droplet deformation increased with increasing shear rate. The deformed droplet did not relax after the shear was stopped except for a modest rounding of the edges. For each shear rate, an apparent viscosity, η _ad, of the equivalent Newtonian droplet was calculated assuming affine deformation. η _ad showed a power law dependence on the capillary number Ca with an exponent of − 1.8 and was larger than the shear viscosity of the micelle suspension at the same shear rates. The results were explained by the existence of a strong gradient of the viscosity inside the droplet leading to a very low viscosity fluid layer near the droplet/matrix interface.     

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear‐induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear‐induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse‐flux model. Semi‐implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Rheology and flow-birefringence from viscoelastic polymer-clay solutions

 The shear orientation of viscoelastic clay-polymer solutions was investigated by means of rheology and flow birefringence (Δn). The polymer chains are in dynamic adsorption/desorption equilibrium with the clay particles to form a “network”. The elastic behavior of the network was characterized by constant stress, oscillatory shear, and stress relaxation experiments. Constant stress experiments indicated a yield stress upon which shear flow started and no strain recovery could be observed. Oscillatory shear experiments showed a broad elastic region followed by flow when a critical strain was reached. Stress relaxation experiments showed several relaxation times when the same critical strain was reached. Experiments under steady flow characterized the transient behavior of the network. With increasing steady shear rate a pronounced minimum in birefringence was observed at a critical shear rate. The shear rate dependent viscosity showed near power law behavior and no corresponding critical feature. While birefringence detects orientational effects on a microscopic length scale, rheology averages over macroscopic changes in the sample. The same degree of orientation could be achieved under constant shear rate or constant stress conditions. Received: 25 January 2001 Accepted: 22 May 2001     

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.     

The effect of parallel combined steady and oscillatory shear flows on blood and polymer solutions

Human blood at physiological volume concentration exhibits non-Newtonian and thixotropic properties. The blood flow in the microcirculation is pulsatile, initiated from the heart pulse and can be considered as superposition of two partial flows: a) a steady shear, and b) an oscillatory shear. Until now steady and viscoelastic behavior were separately investigated. Here we present the response to the combination of steady and oscillatory shear for human blood, a high molecular weight aqueous polymer solution (polyacrylamide AP 273E) and an aqueous xanthan gum solution. The polyacrylamide and xanthan solutions are fluids that model the rheological properties of human blood. In general, parameters describing blood viscoelasticity became less pronounced as superimposed steady shear increased, especially at low shear region and by elasticity, associated with reduction in RBC aggregation. The response of polymer solutions to superposition shows qualitative similarities with blood by elasticity, but their quantitative response differed from that of blood. By viscosity another behavior was observed. The superposition effect on viscous component was described by a modified Carreau equation and for the elastic component by an exponential equation.Paper in part presented at the Symposium on Rheology and Computational Fluid Mechanics dedicated to the memory of Prof. A. C. Papanastasiou, University of Cyprus, Nicosia, July 4–5, 1996     

Performance modeling and analysis of blood flow in elastic arteries

Nomenclature　　τ　　wallshearstressγshearrateτy yieldstressηc Cassonviscosityktheconsistencyindexnnon_Newtonianindexτp shearstressofthepthelementωangularvelocityRvessel’sradiusCwavespeedM　　magneticparameter (Hartmannnumber)u,w　velocitycomponentinther_andz_directions,respectivelyP　　pressureα　　unsteadinessparameter k , R meanparametersTp relaxationtimeofthepthelementρ densityIntroductionTheimportancetoatherogenesisofarterialflowphenomenasuchasflowseparation ,recirculationands…     

Strain stiffening of non-colloidal hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region

Concentrated hard sphere suspensions often show an interesting nonlinear behavior, called strain stiffening, in which the viscosity or modulus starts to increase at critical strain amplitude. Sudden increase of rheological properties is similar to shear thickening; however, the particle dynamics in the strain stiffening under oscillatory shear flow does not necessarily coincide with the mechanism of shear thickening under step shear flow. In this study, we have systematically investigated the nonlinear rheology of non-colloidal (>1???m) hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region in order to better understand the strain stiffening behavior. The suspensions near liquid-and-crystal coexistence region are known to locally form the closed packing structure. The critical strain amplitude which is the onset of strain stiffening was different for the storage and loss modulus. But they converged to each other as the suspension forms a more crystalline structure. The critical strain amplitude was independent of medium viscosity, imposed angular frequency, and particle size, but was strongly dependent upon particle volume fraction. The onset of strain stiffening was explained in terms of shear-induced collision due to particle motion in the closed packing structure. Nonlinear stress wave-forms, which reflect the micro-structural change, were observed with the onset of strain stiffening. During the strain stiffening, enhanced elastic stress before and after flow reversal was observed which originates from changes in the suspension microstructure. Nonlinearity of the shear stress in terms of Fourier intensity was extremely increased up to 0.55. Beyond the strain stiffening, the suspension responded liquid-like and the nonlinearity decreased but the elastic shear stress was still indicating the microstructure rearrangement within a cycle.     

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.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 2. High shear limit behavior

It is shown that in a truly bimodal coal-water slurry the hydrodynamic interactions between the coarse particles impose on the fine fraction a shear rate higher than that applied externally by the viscometer walls. A semi-empirical function of the coarse volume fraction is obtained for this correction factor to the applied shear rate. The derivation of this shear correction factor is based on lubrication concepts and introduces the maximum packing fraction,ø _m, at which flow can take place.ø _m is obtainable from a simple dry packing experiment. It is shown that the contribution of the coarse particles to the viscosity rise can be successfully described by a viscosity model employing the same concepts used to derive the shear correction factor. The bimodal model is applied in the high shear limit to polymodal coal slurries with a continuous particle size distribution. In the model, the contribution of the coarse particles to the viscosity rise is taken from separate viscosity measurements for the coarse coal particles, while the contribution to the viscosity of the fine coal particles is taken to be that given by the measured viscosity of colloidal suspensions of monomodal rigid spheres. It is shown that there is a ratio of coarse to fine fraction volumes in the continuous size distribution, corresponding to a specific separating particle size, for which the measured viscosities of the polymodal slurries match almost perfectly over the whole solids volume fraction range with the viscosity values obtained using the bimodal approach. The match is found to be relatively insensitive to the precise value of the separating particle size.     

Steady and transient shear flows of polystyrene solutions I: Concentration and molecular weight dependence of non-dimensional viscometric functions

Start up from rest and relaxation from steady shear flow experiments have been performed on monodisperse polystyrene solutions with molecular weight ranging from 1.3 × 10⁵ to 1.6 × 10⁶ and concentration c ranging from 5% to 40%. A method of reduced variables based on the use of a characteristic time τ_w is proposed. τ_w is defined as the product of zero shear viscosity with the steady state elastic compliance.Reduced steady and transient viscometric functions so obtained depend on the ratio M/M_e (where M_e is the entanglement molecular weight). Limiting forms are obtained when M/M_e ? 18. In steady flow, a simple correlation is found between shear and normal stresses.In stress relaxation experiments, independent of shear rate, the long-time behaviour can be characterised by a single relaxation time τ₁, which is identical for shear and normal stresses. τ₁ can be simply related to the zero shear rate viscosity and the limiting elastic compliance.     

Rheology of milled black cumin (Nigella sativa L.)

Black cumin (Nigella sativa L.) paste is a local food in the Middle East, which is produced from dehulled black cumin seeds. The rheological properties of a commercial black cumin paste in the temperature range of 5-40 °C have been studied. Shear-thinning flow behavior with a yield stress was observed for the samples tested. The Herschel-Bulkley model described well the flow curves of the black cumin pastes at different temperatures. It was found that the yield stress, the consistency coefficient, and the flow behavior index decrease with temperature. As far as the effect of steady shearing on the rheological properties of black cumin paste is concerned, the structural kinetic approach was used to predict the thixotropic behavior. It was found that the thixotropic behavior of black cumin paste increases with increasing shear rate and is mitigated by increasing temperature. The completely destructed black cumin paste flow curves were also measured after subjecting the samples to a high shear rate for 2 h. The flow curves of the completely destructed samples were modeled well by the Herschel-Bulkley model. A comparison between the fresh and the completely destructed black cumin paste results at different temperatures revealed that there was a systematic difference, such that the completely destructed paste showed lower yield stress and flow behavior index, and showed a greater consistency coefficient.