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The rheology of suspensions showing discontinuous shear thickening (DST) is well documented in conventional rheometer with rotating tools, but their study in capillary flow is still lacking. We present results obtained in a homemade capillary rheometer working in an imposed pressure regime. We show that the shape of the experimental curve giving the volume flow rate versus the wall stress in a capillary can be qualitatively reproduced from the curve obtained in rotational geometry at imposed stress but instead of a sharp decrease of the volume flow rate observed at a critical stress, this transposition predicts a progressive decrease in flow rate. The Wyart-Cates theory is used to reproduce the stress-shear rate curve obtained in rotational geometry and then applied to predict the volume flow rate at imposed pressure. The theoretical curve predicts a total stop of the flow at high stress, whereas experimentally it remains constant. We propose a modification of the theory which, by taking into account the relaxation of the frictional contacts in the absence of shear rate, well predicts the high stress behavior. We also hypothesized that the DST transition propagates immediately inside the capillary, once the wall shear stress has reached its critical value: $\tau_R=\tau_c$, even if the internal shear stress $\tau(r, Comment: Rheologica Acta, Springer Verlag, 2021

The rheological characterization of concentrated suspensions is complicated by the heterogeneous nature of their flow. In this contribution, the shear viscosity and wall slip velocity are quantified for highly concentrated suspensions (solid volume fractions of 0.55–0.60, D4,3 ~ 5 µm). The shear viscosity was determined using a high-pressure capillary rheometer equipped with a 3D-printed die that has a grooved surface of the internal flow channel. The wall slip velocity was then calculated from the difference between the apparent shear rates through a rough and smooth die, at identical wall shear stress. The influence of liquid phase rheology on the wall slip velocity was investigated by using different thickeners, resulting in different degrees of shear rate dependency, i.e. the flow indices varied between 0.20 and 1.00. The wall slip velocity scaled with the flow index of the liquid phase at a solid volume fraction of 0.60 and showed increasingly large deviations with decreasing solid volume fraction. It is hypothesized that these deviations are related to shear-induced migration of solids and macromolecules due to the large shear stress and shear rate gradients.

In this work, the rheological response and sedimentation stability of micron-sized flake-shaped carbonyl iron (CI) water-based magnetorheological (MR) fluid were investigated using iron nanopowder with hydrophilic carbon shell as an additive. The rheological behaviors of MR fluid containing 1 wt% iron nanopowder were measured with and without a magnetic field under shear rate, shear strain, and shear stress sweep mode using a parallel plate rotational rheometer. The magnetic field strength was varied from 0 to 131 kA/m, and in the presence of magnetic field strength, micron flake-shaped CI and iron nanopowder particles lead to form a robust columnar structure. It was observed that using 1 wt% of iron nanopowder with hydrophilic carbon shell, the rheological responses and sedimentation stability of MR suspension were enhanced. We fitted the shear stress as a function of shear rate curves using the Bingham-plastic flow model, which shows a good agreement with the experimental results. We find that yield stress obtained in shear rate sweep mode was larger than that in the shear strain and shear stress sweep mode because, in shear strain and shear stress mode, the responding strain (or stress) may be unable to follow the stress (or strain) applied and a smaller value of strain (or stress) was observed. The amplitude sweep reveals a transition from viscoelastic-to-viscous behavior at the critical strainγcrt = 0.1%. The storage modulus (G') of the MR fluid showed a stable plateau region over the small strain area γ ≤ γcrt and G'independent of strain amplitude. The frequency sweep demonstrated that storage moduli (G') exhibit elastic response and stable plateau region over the entire frequency range, suggesting the distinguished solid-like behavior of the MR fluid.

In this study, the analytical Herschel-Bulkley fluid model of a monotube mixed mode MR damper was examined. The MR damper was modeled and simulated by using computational fluid dynamics (CFD) and magnetic finite elements analysis (FEA). The magnetic effects were modeled in a coupled manner with CFD. The actual rheological data was used in the CFD solver to find the cell-based viscosity by using a shear stress interpolation method. The MR damper was manufactured, and experiments were conducted to find the force-displacement and force-velocity correlations, and a good agreement was found between the numerical results and experimental data. The experimental results were also compared with analytical and numerical models under various current values. The CFD results are valuable in predicting the actual characteristics of the non-Newtonian flow inside an MR damper, and it can be used for various non-Newtonian fluid CFD models.

The data set of steady and transient shear data reported by Santangelo and Roland Journal of Rheology 45: 583–594, (2001) in the nonlinear range of shear rates of an unentangled polystyrene melt PS13K with a molar mass of 13.7 kDa is analysed by using the single integral constitutive equation approach developed by Narimissa and Wagner Journal of Rheology 64:129–140, (2020) for elongational and shear flow of Rouse melts. We compare model predictions with the steady-state, stress growth, and stress relaxation data after start-up shear flows. In characterising the linear-viscoelastic relaxation behaviour, we consider that in the vicinity of the glass transition temperature, Rouse modes and glassy modes are inseparable, and we model the terminal regime of PS13K by effective Rouse modes. Excellent agreement is achieved between model predictions and shear viscosity data, and good agreement with first normal stress coefficient data. In particular, the shear viscosity data of PS13K as well as of two polystyrene melts with M = 10.5 kDa and M = 9.8 kDa investigated by Stratton Macromolecules 5 (3): 304–310, (1972) agree quantitatively with the universal mastercurve predicted by Narimissa and Wagner for unentangled melts, and approach a scaling of Wi−1/2at sufficiently high Weissenberg numbers Wi. Some deviations between model predictions and data are seen for stress growth and stress relaxation of shear stress and first normal stress difference, which may be attributed to limitations of the experimental data, and may also indicate limitations of the model due to the complex interactions of Rouse modes and glassy modes in the vicinity of the glass transition temperature.Graphical abstract

We report on the rheology of isotropic and nematic aqueous solutions of a sulfonated all-aromatic polyamide, poly(2,2′-disulfonyl-4,4′-benzidine terephthalamide) (PBDT), that forms high-aspect-ratio rod-like assemblies. For quiescently isotropic solutions, the concentration dependence of the zero-shear viscosity, longest relaxation time, and terminal modulus shows deviations in comparison to the Doi-Edwards theory for hard rods. For quiescently nematic solutions, we characterize the flow behavior through steady-state and transient nonlinear rheological measurements in conjunction with small-angle neutron scattering under shear. The steady-state flow curve is characterized by two anomalous shear thickening responses, one at moderate shear rates and the other immediately prior to flow alignment at high shear rates. We assign the origin of these shear thickening response to director “kayaking” and “out-of-plane steady” states, using predictions from prior high-resolution numerical simulations of sheared nematic rods. Utilizing transient shear flow reversals and step-down experiments, we characterize the oscillatory response of the nematic director through these flow regimes. When the first normal stress difference is plotted versus the shear stress during a transient step-down, the so-called dynamic stress path, the counterclockwise versus clockwise rotation has previously been shown to reveal the relative dominance of viscous versus elastic contributions to the stress tensor, respectively. Our measurements strongly suggest that the anomalous shear thickening behavior in nematic PBDT solutions arises from viscous stresses developed as the ensemble of rods undergoes periodic oscillatory motion under shear, rather than elastic stresses due to broadening of the orientational distribution function.

Rheometry ever since made part of soil physical characterization, but only since the availability of highly sensitive rheometers, amplitude sweep tests (AST) and thixotropy tests are conducted on structured and homogenized soil, mostly one the base of few or one rheological parameter. Comprehensive and simultaneous analysis of different parameters has not been done yet, though it offers valuable clues to the highly complex soil processes and their multidimensional (spatial, temporal, and stress-rate-dependent) interferences, especially with regard to the role of the most important soil aggregation factors, i.e., soil organic matter (SOM) and water content. Consequently, we conducted a strain-controlled AST under varying normal stresses σn on different soil aggregate fractions of either high or low SOM content and at different water contents. We determined shear stress τ, loss and storage modulus G″ and G′, respectively, and their ratio, tan δ, at the end of the linear viscoelastic range (LVR) and the yield point (YP) as well as the strain at which they occurred. In addition, we analyzed tan δ curves for dilatancy, and classified shear failure behavior (plastic or brittle). Viscoelasticity parameters were mostly affected by SOM (i.e., electrostatical attractive forces) and strain (spatial impact), while shear stress parameters altered with SOM, σn, and water content (friction and particle coordination). Based on integrated interpretation of the AST and its resulting parameters, we developed a conceptual framework to be used in future soil (micro)mechanical characterization, where rheological parameters serve as input data to model, e.g., erosion, landslides, or soil deformation under shear.

In this paper, we determine the effect of confinement on the shear flow of concentrated soft microgel particle suspensions. Utilizing a flexure-based microgap rheometer (FMR), aqueous suspensions of swollen P(NIPAM-co-AA) microgel particles of 4μ m diameter at different volume fractions larger than 64 vol% are subjected to shearing deformations between plates separated by gaps of 5–120μ m while monitoring the stress response at different rates. Describing the stress evolution from a balance of elastohydrodynamic lubrication and elastic forces following the approach of Cloitre and Bonnecaze, it could be shown that already below a critical confinement level on the order of 10 particle diameters an increase of the interparticle pressure leads to a rising shear stress at a given rate in the yielded regime. This effect is strongest for particle volume fractions close to the critical closest packing, with two orders of magnitude increase in flow resistance when approaching the single-particle confinement level, whereas this confinement effect on the flow decreases when raising the concentration. Furthermore, it could be shown that, at the onset of the yielding of the suspensions, the confinement is increasing the effective modulus, but not the yield strain.

Solid-liquid separation aims to increase the solids concentration. The dewatering extent can be parameterized through the compressive yield stress, py(ϕ) whereby to further consolidate a suspension, higher stress has to be applied to the material. In a variety of dewatering devices, shear (in addition to unilateral compression) is applied to the material and is demonstrated to be of benefit to the process, albeit without a basis for optimisation. To address this fundamental issue, two novel measurement techniques, namely the Vane-in-a-Filter (ViaF) and the Vane-under-Compressional-Loading (VuCL), are presented, allowing measurement of the shear stress response with different normal loads under fixed solids concentrations. Furthermore, high solid concentration shear yield stress measurements are possible. The results demonstrate that the shear stress response increases with normal load (at a fixed state of compression) and the peak shear stress has a minimum at shear rates of 0.01–0.1 s−1.

We have investigated the rheology and structure of a gel formed from a mixture of non-Brownian particles and two immiscible liquids. The suspension of particles in a liquid undergoes gelation upon the addition of a small content of second, wetting liquid which forms liquid bridges between particles leading to a sample spanning network. The rheology of this gel primarily exhibits a yield stress at low shear rates followed by a linear variation of shear stress at high shear rates. The apparent yield stress extracted from the flow curves increases rapidly with volume fraction of second liquid before saturation, while it exhibits a monotonic increase with increasing particle concentration. Rescaling of the yield stress curves using suitable shift factors results in an empirical expression for the yield stress showing squared dependence on liquid fraction and a rapid increase with particle fraction above a certain value, both combined in a highly nonlinear manner. The microstructural variations with changing secondary liquid content and particle fractions are captured using three dimensional X-ray tomography technique. The microstructure is observed to show increased local compactness with increased liquid content and increased spatial homogeneity with increased particle fractions. The images from X-ray tomography are analysed to obtain the distributions of particle-particle bonds (coordination number) in the system which serve to explain the observed yield stress behavior in a qualitative manner., Comment: 16 pages, 14 figures

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.

In this work, the FENE dumbbell model under small- and large-amplitude oscillatory shear flows using a micro-macro approach is presented. This approach involves the evolution of an ensemble of Brownian Configuration Fields which describes the polymer dynamics of the microscopic scale and the momentum equation describes the macroscopic scale. The Lissajous curves for the shear stress and the first normal stress difference versus the instantaneous strain or strain rate for the elastic or viscous projection are shown. The influences of the solvent/polymer viscosity ratio, the maximum extension length, and the relation between strain rate and frequency are analyzed. An important finding is the self-intersection of the Lissajous curves, which forms secondary loops for short extension lengths and high Weissenberg/Deborah dimensionless numbers ratio.

In this study, rheological behaviors and capillary extrusion flow instabilities of ultra-high molecular weight polyethylene (UHMWPE)/high-density polyethylene (HDPE)/SiO2 composites containing modified nano-SiO2 or pure nano-SiO2 are investigated. Effects of interfacial conditions between the dispersed nano-SiO2 phase and PE matrix on rheological behaviors are analyzed. The results show that modified nano-SiO2 in the PE matrix has a relatively strong interfacial interaction with the polymer chains compared with pure nano-SiO2, thus causing a more pronounced shear thinning behavior and reducing extrudate swell during capillary extrusion. Nanocomposite extrudates experience the transition of smooth- sharkskin- oscillating distortion—overall melt fracture with the increase of shear rate (or shear stress). The interfacial interaction allows a more storage of elastic energy as the melt flow through the die, resulting in sharkskin distortion and oscillating distortion to occur prematurely at critical shear rates. It also restricts the elastic recovery of the melt after leaving the die, thus delaying sharkskin distortion under shear stress. At high shear rates, the modified nano-SiO2 particles begin to roll, and some of the unmodified particles move and embed to the wall. It is believed that the interfacial adsorption effect and the wall-slip effect of nanoparticles exist simultaneously in the whole extrusion process.

Rheological and microstructural properties of welan gum aqueous solutions were studied as a function of polymer concentration in the 0.2–0.6% (m/m) range at fixed temperature 20 °C. Welan gum is an exopolysaccharide produced by Sphingomonas sp. All the systems exhibited a shear thinning and weak gel–like behavior whose parameters were well adjusted to a power law with the concentration. Furthermore, time-concentration superposition methods were carried out to obtain two master curves, one from the flow curves and the other from the mechanical spectra, which made it possible to extend the accessible experimental range. The non-linear viscoelastic properties were also studied by means of parallel superposition tests. The superimposed shear stress induced a change from weak gel to entangled solution behavior. This latter flow behavior is characterized by a frequency crossover that has been shown to have a linear dependence on the superimposed steady-state shear rate. Finally, Cryo-SEM images revealed a network with numerous junction zones between polymer chains.

The role of friction in non-colloidal suspensions is examined with a model which splits the viscosity into a frictionless component (τ*) plus a frictional component which depends on the ratio of the particle pressure (P) to the shear stress (τ). The model needs the input by computation of τ* and P and a suitable choice of particle friction coefficient (μ). It can be extended to elongational flows and cases where sphere roughness is important; volume fractions up to 0.5 are considered. It is shown that friction acts in a feedback or “bootstrap” manner to increase the suspension viscosity. The analysis is also useful for deducing the friction coefficient in suspensions from experimental data. It was applied to several sets of experimental data and reasonable correlations of the viscosities were demonstrated. An example of the correlation for spheres in a silicone oil is shown for volume fractions 0.1–0.5.

Rheological properties of three different nanocomposites, consisting of graphene oxide (GO), reduced graphene oxide (rGO), and polyhedral oligomeric silsesquioxane grafted reduced graphene oxide (rGO-POSS) as nanofillers and polydimethylsiloxane (PDMS), were investigated by large amplitude oscillatory shear (LAOS). The viscoelastic nonlinearity of the three nanofluids groups was studied by Lissajous curves, local nonlinear viscoelastic moduli of an oscillatory shear cycle, and Fourier transform rheology as a function of filler concentration and increasing and decreasing strain magnitude. The nonlinear behavior of the nanofluids was compared to understand the variation of internal microstructures. Firstly, GO/PDMS composites behave with higher moduli and smaller linear viscoelastic range comparing to that of other two composites. Secondly, the elastic stress Lissajous curves of these composites changed from elliptic to rectangular with round the corner with increasing the filler level and strain amplitude. Thirdly, all these three nanofluids exhibited intra-cycle strain stiffening with increasing strains and shear thickening at intermediate strain and then shearing thinning with increasing strain further. Fourthly, higher harmonic intensity of rGO/PDMS increased with increasing strain and came to a plateau, while that of other two nanofluids reached a maximum and then decreased. It suggested that different surface functionalization of nanoparticles will present different rheological behavior due to formed different network and LAOS could be used as a potential helpful method to characterize rheological properties of nanocomposites, especially at higher shear strain.

A novel approach to the analysis of the electrorheological effect is proposed, based on the expansion of dimensionless relative shear stress as function of electric field strength in the power series $$ {\tau}_{\mathrm{rel}}=\frac{\tau_E}{\tau }=1+\frac{\alpha }{\tau }E+\frac{\beta }{\tau }{E}^n $$ . The application of this approach to investigation of the electrorheological effect in suspensions of isotropic and needle-like CeO2 nanoparticles in polydimethylsiloxane has revealed that the polynomial coefficients can be judged as a measure of the efficiency of transformation of electrical energy into mechanical energy. The values of α and β coefficients depend on the shape and concentration of filler particles, as well as on the shear rate. The value and the sign of these coefficients determine both the magnitude of the electrorheological effect and the type of dependence of the shear stress (linear or power law) on the strength of the electric field. It has been shown that the values of α and β coefficients for the electrorheological fluids with needle-like particles are greater than for fluids with isotropic particles (at the same concentration of suspensions), which is associated with the different polarization of particles in the applied electric field.

Shear banding occurs in complex fluids that exhibit a non-monotonic constitutive instability, such as wormlike micelles, and potentially also in polymeric fluids with presumably monotonic constitutive behavior. However, velocity profiles for shear thinning fluids in geometries possessing a stress gradient, such as Taylor-Couette flow, could be misidentified as shear banding. To address this, we present a model-free experimental procedure to distinguish shear banding from strong shear thinning using high-resolution velocimetry. The approach is developed and validated using simulations using the d-Giesekus model and is based upon the behavior of the width of the apparent interface between the high and low shear rate regions. It is then tested using experimental data for model wormlike micellar solutions. The method allows shear banding to be distinguished from shear thinning in cases where this difference is otherwise indistinguishable. As a by-product, it also provides an estimate of the stress diffusivities for shear banding fluids.

Drilling fluids are suspensions of solid particles and present thixotropic and elastoviscoplastic behaviors simultaneously, which turn their rheological characterization into a challenging task. Rotational rheometers are widely employed to determine the properties of these fluids, and one major challenge in rheometric tests carried out with thixotropic fluids is to obtain repeatable results. Submitting the fluid specimen to a known shear history by performing a pre-shear procedure is commonly used to achieve repeatable results with thixotropic fluids. In this paper, the effect of different pre-shearing conditions on the rheological measurements of an oil-based drilling fluid was investigated using cross-hatched parallel plates. Firstly, an adequate aging time to ensure complete fluid restructuring was determined by monitoring the storage modulus, G′, over an oscillatory time sweep experiment. Shear-rate controlled start-up tests were then conducted to evaluate the gel strength and the steady-state shear stress. Nine different pre-shearing conditions were evaluated, and each experiment was performed three times. Finally, the results were analyzed by using two statistical tools: a two-way analysis of variance (ANOVA) and the Tukey’s range test. The analysis shows that despite the good repeatability achieved when the same pre-shear condition is applied, the pre-shearing affects not only the gel strength but also the steady-state shear stress. The ANOVA also revealed that the effect of the pre-shearing shear rate on the fluid rheological behavior is statistically more significant than the effect of the pre-shearing time. The same analysis was performed after 10 s and 10 min of aging, and similar results were obtained.

The rheology and wall slip behavior of several polyisobutylene (PIB) melts with different molecular weights were studied using parallel-plate and capillary rheometry. All PIBs studied were found to slip even at very low wall shear rates. The transition from weak to strong slip (nearly plug flow) was found to occur at a wall shear stress of approximately 0.09 MPa. The slip model developed by Ebrahimi et al. (2015) based on double reptation was used in order to relate the slip velocity, V s, to the molecular weight distribution of the polymers. It was found for the monodisperse polymers (extracted from the general model) that the slip velocity scales with wall shear stress, σ w, and the number average molecular weight as, M n as $$ {V}_{\mathrm{s}}\propto {M}_{\mathrm{n}}^{-2}{\sigma}_{\mathrm{w}}^{1/n} $$ with n equal to the local slope of the flow curve of the corresponding polymer, $$ n\equiv d\left( \log \left({\sigma}_{\mathrm{w}}\right)\right)/d\left( \log \left({\dot{\gamma}}_{\mathrm{w}}\right)\right) $$ . The exponent −2 in the molecular weight dependence for PIBs was found to be the same with those reported for high-density polyethylenes (HDPEs) and polybutadienes (PBDs), suggesting that it is universal for linear polymers.

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.

A stability analysis of planar shear flow shear of a homogeneous, complex fluid predicts that shear banding instabilities can grow in fluids with a shear thinning strength above W c = 1 and dampen out in fluids with W

We report on the interplay between creep and residual stresses in a carbopol microgel. When a constant shear stress $\sigma$ is applied below the yield stress $\sigma_\text{y}$, the strain is shown to increase as a power law of time, $\gamma(t)=\gamma_0 + (t/\tau)^\alpha$, with an exponent $\alpha=0.39\pm 0.04$ that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some typical value $\sigma_\text{c}\simeq 0.2 \sigma_\text{y}$, the microgel experiences a more complex, anomalous creep behaviour, characterized by an initial decrease of the strain, that we attribute to the existence of residual stresses of the order of $\sigma_\text{c}$ that persist after a rest time under a zero shear rate following preshear. The influence of gel concentration on creep and residual stresses are investigated as well as possible aging effects. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems., Comment: 17 pages, 14 figures, Rheologica Acta (2016)

The rheology of fluid fine tailings is studied and compared with that of kaolinite suspensions having the same zeta potential, solid volume fraction and relatively similar particle size distribution. The suspensions were examined under shear and oscillatory deformation fields to investigate their yielding, aging, and steady-state flow behavior under shear rate and stress-controlled conditions. Using dynamic strain sweep experiments, it is shown that the samples exhibit a maximum in their loss modulus during yielding while they exhibit two different regimes of strain dependency in their fluidized regime. Samples are found to exhibit a plateau region in their stress-strain curves measured by the dynamic strain sweep experiments, due to the presence of flow instabilities. Small amplitude oscillatory tests are performed to study aging behavior of the suspensions with different shear histories. The aging process is found to depend strongly on the shear history of the samples prior to rest. Shear flow experiments under stress-controlled conditions show that both suspensions exhibit a plateau in their flow curves where a slight increase of the shear stress results in a dramatic change of the shear rate, implying the occurrence of shear-banding flow instability. This agrees with the behavior observed in the oscillatory deformation mode and implies that below a critical shear stress, no stable flow can be achieved in the suspensions. Fluid fine tailings and kaolinite suspensions are found to exhibit fairly similar rheological behavior, when their zeta potentials, solid volume fractions, and particle size distributions are matched.

New equation for determination of the primary normal stress difference from viscosity curve is proposed, and the methods of calculations with the use of adequate viscosity models are discussed. Comparison of calculated and measured values of primary normal stress difference has shown that the proposed equation describes quite well experimental data but the calculations are not stable. For this reason, the proposed equation along with other equations of this type known from the literature was transformed into shear stress-dependent form. It was shown that such transformation makes it possible to represent the normal stress-to-shear stress ratio (Weissenberg number) as a unique function of the local slope of the flow curve, which is simultaneously temperature invariant. Such representation was confirmed using experimental data for eight systems comprising linear polymers and various measurement temperatures. It was found that new equation in the shear stress-dependent form is numerically stable and provides excellent description of experimental data. The general structure of expressions, which may be used for description of the elasticity of polymer liquids based on the flow curve shape, was discussed from the point of view of dimensional analysis. Obtained results made it possible to modify other expressions known from the literature in such way that they also provide an excellent fit to experimental data.

The steady and transient nonlinear rheological behaviors of dilute rod-like micellar solutions are predicted here with a particular case of the generalized Bautista–Manero–Puig (BMP) model that consists of the upper-convected Maxwell constitutive equation and a dissipative power-dependent kinetic equation, which takes into account the formation and disruption of shear-induced structures (SISs). This model has been derived using the extended irreversible thermodynamic (EIT) formalism. In steady shear, the model predicts a Newtonian region at low shear rates and a characteristic shear rate ( $$ {\dot{\upgamma}}_{\mathrm{c}} $$ ) at which shear thickening develops. In the shear thickening region, the model predicts either a reentrant zone, which is caused by multi-valued shear stresses when the data are collected with a shear stress-controlled mode or a continuous increase in the shear stress-shear rate flow curve, when the data are collected with a shear rate-controlled mode; in this region, two coexisting phases are predicted. The coexisting phases at the same shear rate in the two-phase envelope and the spinodal-like region were evaluated from the extended Maxwell equal-area criterion, which was calculated from the equal values of the two minima of the plot of the extended Gibbs free energy versus shear rate. At higher shear rates, the model predicts a transition to shear thinning, and under transient flows, an induction time and a saturation time are obtained from the predicted and the experimental data as detailed in the text. The magnitudes of both, the induction and the saturation times, diminish as the shear rate departs from $$ {\dot{\upgamma}}_{\mathrm{c}} $$ , but only the induction time decreases according to a power law with shear rate. The conditions under which these rheological responses arise are derived and justified in detail with the BMP model. The model predictions are compared with experimental data of two dilute micellar solutions. The model parameters were determined from a set of independent experiments without fitting.

Systematic rheological characterisation of several injection implants based on hyaluronic acid (Belotero®, Teosyal®, Glytone® and Juvederm® brands) has been carried out. All these dermal fillers are viscoelastic media with the storage modulus exceeding the loss modulus. So at low deformations, they are gel-like materials, but at increasing shear stress, they can flow demonstrating typical non-Newtonian behaviour. In some cases, though not always, the yield stress is expressed rather clearly. The application of the technique of large amplitude oscillation shear (LAOS) allowed us to distinguish two groups of rheological behaviour characterised by shear thinning or strain overshoot. The Belotero® fillers belong to the first group. Similar strong changes in the storage and loss moduli as a function of frequency and fuzzy yielding are characteristic of these materials. The Teosyal® and Juvederm® Voluma filler belong to the second group. Their typical rheological features are existence of the minimum for the frequency dependence of the loss modulus and clearly expressed the yield stress. The Glytone® and Juvederm® Ultra fillers occupy the intermediate position. When the dermal fillers of the second group were diluted, they demonstrated effects similar to the phase separation. As a result of the rheological characterisation, some assumptions have been advanced regarding correlations between the objective rheological parameters of dermal fillers and conditions of their application.

Neglecting of end effects in rotational viscometry introduces 10–30 % error in the estimate of shear stress σ R at surface of rotating cylindrical spindle. Actual values of the correction coefficient c L for a real sensor depend on pseudoplasticity level of a given sample (measured by the flow-behavior index n) and inertia level (measured by the Reynolds number Re). The correction coefficients for the real sensors with coaxial cylinders are calculated by solving the related flow problem for Generalized Newtonian Fluid with power-law viscosity function. In addition to the cylindrical sensors according to ISO 3219 CEN Bruxelles 53:019, (1994) , also some clones with different geometry simplex H = h/R are considered. The results on c L (n, Re, H) are presented as a simple empirical formula for easy use in downstream treatment of primary data using the pseudosimilarity approach.

The stick-slip motion of magnetorheological (MR) fluids under a simple linear shear mode has been experimentally reported. The critical shear strain for the onset of the stick-slip motion decreases logarithmically with the magnetic flux intensity applied. The rate of energy accumulation and releasing during stick-slip motion changed in a power law of the viscosity of the continuous phase in a range of 0.01~1000 mPa S. Different carrier fluids led to different stick-slip characteristics. The stick-slip motion can be fully suppressed with certain carrier fluids. When the MR fluids are in a shear-thickening state, the critical shear strain of the onset of the stick-slip motion is larger than a normal state. But, the relative spike amplitude of the stick-slip remains similar.

The quiescent and shear-induced isothermal crystallization behavior of linear and long-chain branched (LCB) polylactides (PLAs) was investigated at a temperature of 130 °C. LCB-PLAs were produced by the reaction with a multifunctional chain extender, Joncryl©. In quiescent crystallization, the presence of the LCB structure accelerated the nucleation process and reduced the induction time, depending on the level of branching. The impact of shear strain and shear rate on crystallization was also examined. The shear-induced crystallization of the linear and LCB-PLAs was affected by both the total shear strain and shear rate. The crystallization kinetics of the LCB-PLAs was more affected by shear than that of the linear PLA. The crystalline morphology of the linear and LCB-PLAs under quiescent and step shear rate conditions was examined using a Linkam optical shearing system. An increase in the spherulite density was observed in the strained melt of both linear (33 %) and LCB-PLAs (15 %), in comparison with those of unstrained counterparts. Optical micrographs confirmed that the crystal nucleation was affected by the shear flow. Long-chain branching significantly promoted the nucleation density (6.7 times), although it diminished the crystal growth rate from 4.4 to 2.0 μm/min.

Analytical solutions for either the shear stress or the normal stress differences in large-amplitude oscillatory shear flow, both for continuum or molecular models, often take the form of the first few terms of a power series in the shear rate amplitude. Here, we explore improving the accuracy of these truncated series by replacing them with ratios of polynomials. Specifically, we examine replacing the truncated series solution for the corotational Maxwell model with its Pade approximants for the shear stress response and for the normal stress differences. We find these Pade approximants to agree closely with the corresponding exact solution, and we learn that with the right approximants, one can nearly eliminate the inaccuracies of the truncated expansions.

A severe problem to flow assurance occurs when subsea flowlines become blocked with gelled waxy crudes. To design proper surface pump facilities, it is essential to know the minimum pressure required to restart the flow. Simulating and predicting this minimum pressure require the understanding of several physical phenomena, including compressibility, shrinkage, and rheological behavior. This study aims to characterize and simulate the rheological behavior of two commercial waxy crude oils. Based on its survey of the literature, we select the de Souza Mendes and Thompson (2013) model to fit the oil’s behavior and then conduct, using a rheometer, a considerable number of experiments with the selected oils. To verify the solution of our algorithm, we compared our theoretical solutions with some results of the literature. When comparing the simulation with experiments, the model was unable to predict the data perfectly; hence, we propose a modified version without changing the physical meaning of the equations, to improve its predictions. Once any of the empirical parameters were able to influence the elastic behavior in such a way that the shear stress decreased with time, the structural elastic modulus function was modified, which means that the relation of the structure parameter and the storage modulus was modified. One of the interesting results of the analysis is when relating the storage modulus and a new parameter added in the modification, a value was found to be, regardless of the aging time or the oil used, constant.

We derive exact single-point corrections for parallel disk measurements of all four asymptotically nonlinear measures under strain-controlled oscillatory shear. In this regime, sometimes called medium-amplitude oscillatory shear (MAOS), the derivatives appearing in the general stress correction are constant over the range of interest. This enables an exact single-point correction of all four shear stress components and material functions in the asymptotically nonlinear regime. This greatly simplifies the data processing and allows convenient measurements of true nonlinear material functions with parallel disk geometries. We use a strain amplitude expansion for the stress response, introducing a general non-integer strain amplitude scaling for the leading order nonlinearity, σ ∼ γ α , where typically α = 3 has been assumed in the past. The stress corrections are a multiplicative amplification by a factor $f\left (\alpha \right )=\frac {\alpha +3}{4}$ , shown for the first time for all four asymptotically nonlinear coefficients. Experimental measurements are presented for the four asymptotically nonlinear signals on an entangled polymer melt of cis-1,4-polyisoprene, using both parallel disk and cone fixtures. The polymer melt follows a cubic (α = 3) strain amplitude scaling in the MAOS regime. The theoretical corrections indicate a 50 % amplification of the apparent signals measured with the parallel disk fixture. The corrected (amplified) signals match the measurements with the cone.

An analytical solution is obtained for steady flow of Quemada-type fluids in a circular tube driven by a constant pressure gradient. Expressions are derived for velocity distribution and for volumetric flow rate as a function of pressure gradient or wall shear stress.

In this paper, an exact analytical solution for creeping flow of Bingham plastic fluid passing through curved rectangular ducts is presented for the first time. The closed form of axial velocity distribution, flow resistance ratio, and wall shear stress are derived using bounded Fourier transformation. An extensive investigation on mutual effects of Hedstrom number, curvature ratio, and aspect ratio is conducted. The results indicate that a drag reduction is caused in the flow field by increasing the Hedstrom number. It is shown that unlike the Newtonian creeping Dean flow, the critical aspect ratio (an aspect ratio in which the flow resistance ratio is independent from curvature ratio) does not exist at large enough Hedstrom numbers. Analytical solution also indicated that as Hedstrom number is increased, the value of Poiseuille number is enhanced, and unlike the Newtonian flows, the value of Poiseuille number is not zero at edges of cross section.

In this work, a chain extender (CE) was added to polylactide (PLA) to improve its foamability. The steady and transient rheological properties of neat PLA and CE-treated PLA revealed that the introduction of the CE profoundly affected the melt viscosity and elasticity. The linear viscoelastic properties of CE-enriched PLA suggested that a long-chain branching (LCB) structure was formed from the reaction with the CE. LCB-PLA exhibited an increased viscosity, more shear sensitivity, and longer relaxation time in comparison with the linear PLA. The LCB structure was also found to affect the transient shear stress growth and elongational flow behavior. LCB-PLA exhibited a pronounced strain hardening, whereas no strain hardening was observed for the linear PLA. Batch foaming of the linear and LCB-PLAs was also examined at foaming temperatures of 130, 140, and 155 °C. The LCB structure significantly increased the integrity of the cells, cell density, and void fraction.

We present a model for the shear viscosity of non-colloidal suspensions with Newtonian matrix fluids. The model is based on the original idea first presented by Brinkman (Applied Sci Research A1:27-34. 1947) for the viscous force exerted by a flowing fluid on a dense swarm of spherical particles. In particular, we consider an inertialess suspension in which the mean flow is driven by a pressure difference, and simultaneously, the suspension is subject to simple shear. Assuming steady state, incompressibility and taking into account a resistance force which is generated due to the presence of the particles in the flow, the three-dimensional governing equations for the mean flow around a single spherical particle are solved analytically. Self-consistency of the model provides a relationship between the resistance parameter and the volume fraction of the solid phase. A volume, or an ensemble, averaging of the total stress gives the bulk properties and an expression for the relative (bulk) viscosity of the suspension. The viscosity expression reduces to the Einstein limit for dilute suspensions and agrees well with empirical formulas from the literature in the semi-dilute and concentrated regimes. Since the model is based on a single particle and its average interaction with the other particles is isotropic, no normal stress differences can be predicted. A possible method of addressing this problem is provided in the paper.