Dynamic properties of shear thickening colloidal suspensions

The transient shear rheology (i.e., frequency and strain dependence) is compared to the steady rheology for a model colloidal dispersion through the shear thickening transition. Reversible shear thickening is observed and the transition stress compares well to theoretical predictions. Steady and transient shear thickening are observed to occur at the same value of the average stress. The critical strain for shear thickening is found to depend inversely on the frequency at fixed applied stress for low frequencies (high strains), but is limited to an apparent minimum critical strain at higher frequencies. This minimum critical strain is shown to be an artifact of slip. Lissajous plots illustrate the transition in material properties through the shear thickening transition, and the energy dissipated by a shear thickening suspension is analyzed as a function of strain amplitude.     

Linear and non-linear rheological behaviour of cement and silica suspensions. Effect of polymer addition

Oil well cement pastes and model silica suspensions demonstrate similar rheology: in oscillatory shear, beyond a critical stress, a sharp transition is ob- served between gel and liquid behaviour. In creep tests, an apparent yield stress and shear-thinning are followed by the appearance of shear thickening. The minimum viscosity measured in steady shear is close in value to the complex viscosity obtained from oscillatory measurements. The observations can be explained by the formation of liquid trapping aggregates whose compactness may be estimated by fitting the Tsenoglou model, and whose cohesion is reflected in the rigidity of the gel and in the critical strain (or stress) of gel dissolution. Substituting cement or silica particles by polymer redispersible powder causes a decrease of the storage modulus in the gel state and a lower viscosity, while leaving the general features of the flow curve unchanged. Decrease in material rigidity may be due to a weaker inter-particle attraction generated by the polymer presence. The decrease in viscosity is explained by a lessening of water entrapped within the aggregates, which now contain polymer particles which are less hydrophilic than either cement or silica.     

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.     

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     

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.     

The role of solution structure in apparent thickening behavior of dilute peo/water systems

An experimental investigation was undertaken to determine the role of solution structure on the apparent thickening exhibited by “dilute” polyethylene oxide/water solutions in extensional flow. Measurements of apparent relative viscosity were obtained as a function of wall shear rate for solutions flowing from a reservoir through a 0.1 mm internal diameter tube. As the wall shear rate was increased, slightly shear thinning behavior was observed up until a critical wall shear rate was exceeded at which point a large increase in relative viscosity was seen. Other researchers have observed these apparent thickening effects and have interpreted them in terms of individual polymer molecules undergoing coil-stretch transitions. However, in the systems used in this study, the critical wall shear rate and the degree to which relative viscosity increased wer both seen to be strong functions of solution aging time and concentration. These results are inconsistent with the simple picture of individual polymer coils undergoing a coil-stretch transition and instead are consistent with the picture of aggregated systems or micronetworks being stretched from their equilibrium configurations.     

An apparent viscosity function for shear thickening fluids

A new apparent viscosity function for shear thickening fluids is proposed, contemplating the three characteristic regions typically exhibited by these materials: slight shear thinning at low shear rates, followed by a sharp viscosity increase over a threshold shear rate value (critical shear rate), and a subsequent pronounced shear thinning region at high shear rates. The proposed function has a continuous derivative, making it appropriate in numerical simulations. Moreover, the function is shown to provide an excellent fit to several independent experimental data sets.     

Rheology for deposition control of polymer-amended oil sands tailings

Mineral slurries may be dewatered to the point that they manifest non-Newtonian behavior. Many such slurries exhibit both thixotropic and hysteric behavior in their rheology, which has important implications for managing their deposition in tailings impoundments. This paper characterizes the rheology of a mineral slurry with relatively high clay content, which is treated with a high molecular weight anionic polymer to induce flocculation. The rheology exhibits viscosity bifurcation behavior similar to pure clay, including shear history-dependent apparent yield stress values. Rheometry results are presented including stress growth, controlled stress tests, and oscillatory rheometry, all using a vane fixture. The measured rheology is modeled using a previously published viscosity bifurcation model that accounts for hysteresis in the apparent yield stress. The rheology results are used semi-quantitatively to explain deposition rate-dependent behavior seen in flume tests. The geometry of tailings in flume tests with relatively slow deposition is affected by the presence of deposited tailings that have come to rest sufficiently to manifest the yield stress of initially fully structured material, rather than the lower value yield stress that characterizes when the material first comes to a stop. This full recovery of the yield stress seems to be particularly important to managing surface deposition, as zones of tailings that have stopped moving substantially steepen the slope of deposits near the deposition point.     

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     

Time-dependent plane Poiseuille flow of a Johnson–Segalman fluid

We numerically solve the time-dependent planar Poiseuille flow of a Johnson–Segalman fluid with added Newtonian viscosity. We consider the case where the shear stress/shear rate curve exhibits a maximum and a minimum at steady state. Beyond a critical volumetric flow rate, there exist infinite piecewise smooth solutions, in addition to the standard smooth one for the velocity. The corresponding stress components are characterized by jump discontinuities, the number of which may be more than one. Beyond a second critical volumetric flow rate, no smooth solutions exist. In agreement with linear stability analysis, the numerical calculations show that the steady-state solutions are unstable only if a part of the velocity profile corresponds to the negative-slope regime of the standard steady-state shear stress/shear rate curve. The time-dependent solutions are always bounded and converge to different stable steady states, depending on the initial perturbation. The asymptotic steady-state velocity solution obtained in start-up flow is smooth for volumetric flow rates less than the second critical value and piecewise smooth with only one kink otherwise. No selection mechanism was observed either for the final shear stress at the wall or for the location of the kink. No periodic solutions have been found for values of the dimensionless solvent viscosity as low as 0.01.     

Extensional rheology of concentrated poly(ethylene oxide) solutions

The shear and extensional rheology of three concentrated poly(ethylene oxide) solutions is examined. Shear theology including steady shear viscosity, normal stress difference and linear viscoelastic material functions all collapse onto master curves independent of concentration and temperature. Extensional flow experiments are performed in fiber spinning and opposed nozzles geometries. The concentration dependence of extensional behavior measured using both techniques is presented. The zero-shear viscosity and apparent extensional viscosities measured with both extensional rheometers exhibit a power law dependence with polymer concentration. Strain hardening in the fiber spinning device is found to be of similar magnitude for all test fluids, irrespective of strain rate. The opposed nozzle device measures an apparent extensional viscosity which is one order of magnitude smaller than the value determined with the fiber spinline device. This could be attributed to errors caused by shear, dynamic pressure, and the relatively small strains developed in the opposed nozzle device. This instrument cannot measure local kinematics or stresses, but averages these values over the non-homogenous flow field. These results show that it is not possible to measure the extensional viscosity of non-Newtonian and shear thinning fluids with this device. Fiber spin-line experiments are coupled with a momentum balance and constitutive model to predict stress growth and diameter profiles. A one-mode Giesekus model accurately captures the plateau values of steady and dynamic shear properties, but fails to capture the gradual shear thinning of viscosity. Giesekus model parameters determined from shear rheology are not capable of quantitatively predicting fiber spinline kinematics. However, model parameters fit to a single spinline experiment accurately predict stress growth behavior for different applied spinline tensions.     

Study of geometry effects in torsional rheometry of fibre suspensions

This work concerns the problem of measuring the viscosity of a suspension of fibres that are not short compared to the dimensions of the measurement device. We have examined various geometry effects in shear using parallel-plate and cone-and-plate configurations. Steady state viscosity, transient viscosity and first normal stress difference have been studied. Silicone oil with milled glass fibres at 8 vol.% was used as a model fibre suspension. The conventional parallel-plate geometry exhibits a significant gap dependence of the apparent viscous response. Too small gaps constrain the fibre rotations, thus lowering the initial stress peak and delaying the development of steady state. Too large gaps lead to a loss of liquid at the sample perimeter, which reduces the apparent steady state viscosity. The steady state response, however, seems to be correct for gaps in the range 1–2 mm when the maximum fibre length is 1.5 mm. The cone-and-plate geometry is less sensitive to large gaps. Too small a gap at the (truncated) cone apex leads to anomalous response due to bridging of the gap by fibres. The use of unusually large plates (100 mm diameter) and different cone angles and truncations was explored. It was shown that cone-and-plate configurations of large diameter and large truncation can effectively decrease the geometry disturbances both due to fibre bridging at the cone apex and loss of liquid at the edge.     

The role of the mathematical mean value theorem (MVT) in rheometry: an easy way to convert apparent flow curves into correct ones

The mean value theorem of integral calculus guarantees that the apparent viscosity η _a can easily be converted into the correct viscosity η. For ordinary liquids there is a direct identity between η _a and η but the apparent shear rate (or apparent shear stress) has to be shifted to the representative shear rate γ˙^ (or representative shear stress τ^). A model free approximation scheme is introduced which implies a constant shift factor. The corresponding approximation for η is acceptable for liquids most commonly encountered. For plastic fluids the relation between η and η _a is more complex since it involves a function depending upon α; the yield stress relative to the maximum stress within the viscometer. Using the same approximation scheme as before the shift factor will involve α as well. The corresponding approximation of η is shown to be acceptable for the whole range of α. Received: 7 February 2000/Accepted: 15 February 2000     

A non‐linear dynamical system approach to finite amplitude Taylor‐Vortex flow of shear‐thinning fluids

The effect of shear thinning on the stability of the Taylor–Couette flow is explored for a Carreau–Bird fluid in the narrow‐gap limit. The Galerkin projection method is used to derive a low‐order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional non‐linear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the circular Couette flow, becomes lower as the shear‐thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow, which coincides with the onset of a supercritical bifurcation. Comparison with existing measurements of the effect of shear thinning on the critical Taylor and wave numbers show good agreement. The Taylor vortex cellular structure loses its stability in turn, as the Taylor number reaches a critical value. At this point, an inverse Hopf bifurcation emerges. In contrast to Newtonian flow, the bifurcation diagrams exhibit a turning point that sharpens with shear‐thinning effect. Copyright © 2004 John Wiley & Sons, Ltd.     

Specific rheology – morphology relationships for some blends containing LCPs

For the blend melts of isotropic polysulfone (PSF) and LC polyester (PES), differing in viscosity more than 10 times, the flow curves with maxima were observed in cone and plate geometry. The low shear rate branch is located near the PSF flow curve, and the high shear rate branch is close to the PES flow curve. At high strains, the formation of the ring-like morphology of the blend sample, accompanied by appearance of maximum on flow curve, was registered. The scaling analysis of the reasons for the ring morphology formation was based on stretching of the large, low-viscous LC droplet, embedded to the high-viscous polymer matrix, in a homogeneous shear field. It was shown that, if the critical Taylor radius is not exceeded, the droplet may form the closed torus. Under strong flows, the PSF melt manifests the “spurt effect”, consisting of a drastic increase of the shear rate when the critical value of the shear stress is reached. The pattern of the blend flow curves with maxima may be explained by a vanishing PSF input to the total shear stress, inherent for blends, while the PES melt continues to be in a liquid state and, consequently, is responsible for the blend viscosity at the high shear rates. The presence of regular heterogeneities in the blend in the form of LC rings may initiate the rupture of the entanglements network of the matrix PSF (close to LC rings) under strong shear flows. The appearance of the low-viscous “cracks” at the critical shear stress will diminish the contribution of the PSF to the blends rheological response. Received: 20 April 1999 Accepted: 28 January 2000     

Normal stress effects in the gravity driven flow of granular materials

In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined plates. We assume that the granular materials can be represented by a modified form of the second grade fluid where the viscosity depends on the shear rate and volume fraction and the normal stress coefficients depend on the volume fraction. We also propose a new isotropic (spherical) part of the stress tensor which can be related to the compactness of the (rigid) particles. This new term ensures that the rigid solid particles cannot be compacted beyond a point, namely when the volume fraction has reached the critical/maximum packing value. The numerical results indicate that the newly proposed stress tensor has obvious and physically meaningful effects on both the velocity and the volume fraction fields.     

Influence of medium viscosity and adsorbed polymer on the reversible shear thickening transition in concentrated colloidal dispersions

The influence of medium viscosity on the onset of shear thickening of silica dispersions is investigated with two different methods. In the first method, the sample temperature is varied over a narrow range for two different suspensions. For the first suspension, the stress at the onset of shear thickening, or the critical stress, was found to be independent of sample viscosity, and the shear viscosity scaled with Peclet number, as expected. The critical stress for the second suspension was not independent of sample viscosity, and the Peclet number scaling was only moderately successful. The differences were attributed to changes in particle interactions with temperature. In the second method, the molecular weight of an oligomeric silicone oil medium is varied. In principle, this method should maintain constant chemical interactions as medium viscosity varies; however the polymer is found to adsorb onto the silica surface and delay shear thickening to higher stresses with increasing molecular weight. The critical stress for the highest molecular weight systems, which is highly dependent on particle loading, overlays with an effective volume fraction based on the hydrodynamic diameter of the polymer-stabilized colloids. The results of both methods suggest that if all other properties of the dispersion are held constant, critical stress is independent of medium viscosity.     

The effect of volume relaxation on elastohydrodynamic lubrication

In elastohydrodynamic lubrication (EHD) three important non-Newtonian effects arise. These are volume viscoelasticity, shear viscoelasticity, and the variation of viscosity with shear rate. All these effects tend to decrease the shear stress or traction.In this paper the effect of volume relaxation of EHD is examined using experimental viscosity data obtained in a simple viscometric flow. It is shown that the viscosity of a fluid during EHD is unlikely to reach its equilibrium value. Approximations to the viscosity as a function of time lead to the conclusion that volume and shear viscoelasticity have effects which are of the same order of magnitude and will be difficult to separate except by an exact knowledge of the shear rate and pressure profiles.     

A parameter investigation of shear-induced coalescence in semidilute PIB–PDMS polymer blends: effects of shear rate, shear stress volume fraction, and viscosity

In this work, drop coalescence of polymer blends under shear flow in a parallel flow apparatus was investigated by optical sectioning microscopy. In each experiment, shear rate was set at values low enough to avoid any break-up phenomena. The time evolution of the drop size distribution was determined by motorized sample scanning and iterative acquisition of stacks of images along sample depth. Drop size and location in the acquired images was found by automated image analysis techniques. A systematic experimental campaign to investigate the effects of shear rate (in the range 0.1–0.5 s⁻¹), volume fraction (2.5–10%), and viscosity of the two phases (3–63 Pa s) at different viscosity ratio (0.1–2.3) was carried out. By comparing data from different experiments, it was found that at any strain value, the average drop size decreases monotonically with the shear stress, calculated as the product of shear rate and matrix viscosity. Furthermore, the coalescence rate slowed down with increasing viscosity ratio. Overall, these results provide an extensive set of data, which can be used as a benchmark for modeling shear-induced coalescence in polymer blends.Paper presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.