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April 2013
The 20 articles with the most full-text downloads during the month, in descending order.
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Determination of shear rate and viscosity from batch mixer data J. Rheol. 43, 415 (1999); http://dx.doi.org/10.1122/1.551044 (19 pages)
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A general analysis allowing the determination of shear rate and viscosity from batch mixer rotor speed and torque data is presented. The batch mixer was represented by two effective adjacent sets of concentric cylinders exerting the same torque as that obtained from the batch mixer. The effective internal radius was determined through a general procedure for calibration using non-Newtonian fluid. The effective equivalent internal radius, Ri, was determined for different polymers and processing conditions. The results revealed that Ri is a universal quantity practically insensitive to the nature and to the rheological behavior of the fluid under mixing. In the case of small gaps, it was found that there is a special position in the gap where the effective internal radius, the shear rate and viscosity are independent of rheological characteristics of the fluid under mixing. This validates the Newtonian approximation previously used by Goodrich and Porter to extract the shear rate-viscosity dependence from batch mixer data. The technique was tested on seven different amorphous and semicrystalline polymers and the results were found to be in reasonable agreement with the data obtained independently with cone-and-plate and capillary rheometers. Contributions of both shear stress between the two cylinders and the stress generated at the wall were evaluated. The latter was found predominant. © 1999 Society of Rheology. |
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Nonlinear viscoelasticity of polymer nanocomposites under large amplitude oscillatory shear flow J. Rheol. 57, 767 (2013); http://dx.doi.org/10.1122/1.4795748 (23 pages) Online Publication Date: 01 Apr 13
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In this study, the nonlinear response of polymer nanocomposites under large amplitude oscillatory shear (LAOS) flow was investigated. We first investigated polycaprolactone (PCL)/multiwall nanotube (MWNT) composites under LAOS flow using different analyzing methods including Lissajous plot analysis, stress decomposition, and Fourier transform rheology (FT-rheology). The nonlinear parameter Q ( ≡ I3/1/γ02) was obtained from the FT-rheology as a function of strain amplitude, and the zero-strain nonlinearity Q0 ( ≡ limγ0→0Q) was also calculated. We compared the linear and nonlinear viscoelastic properties as we increase MWNT concentration (ϕ). It was found that the zero-strain nonlinearity (Q0) was more sensitive to detect the effect of MWNT concentration than the linear viscoelastic properties. We also investigated the effect of particle shape on nonlinear viscoelastic properties of the polymer composites containing particles of different shape, e.g., PCL/MWNT (one-dimensional thread shape), PCL/organomodified montmorillonite (two-dimensional plate shape), PCL/precipitated calcium carbonate (three-dimensional cubic shape). Furthermore, we introduced a new parameter, nonlinear–linear viscoelastic ratio, to compare linear and nonlinear viscoelasticity.
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J. Rheol. 57, 813 (2013); http://dx.doi.org/10.1122/1.4798626 (27 pages) Online Publication Date: 04 Apr 13
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The dynamic response of a viscoelastic suspension of spheres under small and large amplitude oscillatory shear is investigated by three-dimensional direct numerical simulations. A sliding triperiodic domain is implemented whereby the computational domain is regarded as the bulk of an infinite suspension. A fictitious domain method is used to manage the particle motion. After the stress field is computed, the bulk properties are recovered by an averaging procedure. The numerical method is validated by comparing the computed linear viscoelastic response of Newtonian and non-Newtonian suspensions with previous theories and simulations. The numerical predictions are in very good quantitative agreement with experimental data for the Newtonian case, whereas deviations are found with respect to some sets of experiments for semidilute and concentrated viscoelastic suspensions. To investigate on such discrepancies, the effect of aggregates in the bulk of the suspension is examined. The simulations show that the presence of structures significantly alters the loss modulus. Such an effect is more pronounced as the volume fraction increases. In this light, the above mentioned disagreement between simulations and data (and among experimental data themselves) can be rationalized, as its origin can be attributed to inhomogeneous particle configurations. For increasing strain amplitudes, both loss and storage moduli depart from the linear viscoelastic values. Although the deviations are qualitatively similar to the large amplitude response of the unfilled suspending matrix, our results for dilute and semidilute suspensions show that the decrease of the moduli is more and more pronounced as the volume fraction is higher. Furthermore, a higher concentration of solid particles reduces the value of strain amplitude such that the nonlinear behavior is observed. Simulations at higher frequencies also correctly capture the overshoot in the loss modulus for intermediate strain amplitudes. Finally, the effect of fluid elasticity on the particle motion is analyzed. The particles are found to move away from their starting positions and the average distance, computed at the beginning of each cycle with respect to the initial configuration, linearly increases with the number of cycles. The change in the microstructure is attributed to the long-range hydrodynamic interactions mediated by fluid viscoelasticity.
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J. Rheol. 57, 881 (2013); http://dx.doi.org/10.1122/1.4798559 (19 pages) Online Publication Date: 10 Apr 13
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The transient shear and extensional properties of ethylene vinyl acetate nanocomposites containing two geometrically different nanoparticles (spheres of CaCO3 and platelet of clay) were investigated experimentally and the data were compared to the rheological predictions of the modified molecular stress function (MSF) theory as recently proposed by Abbasi et al. [Rheol. Acta 51, 163–177 (2012)]. While good agreement was obtained for spherical particles, deviations were observed for platelet particles at concentrations higher than 2.5 wt. %. The limitation of MSF theory for such compositions was related to the domination of the linear rheological response by the presence of particle nanonetworks over polymeric chains' contribution. This particle network contribution was also found to increase nonlinearity under large deformation, a phenomenon which was quantified via Fourier transformed rheology on data obtained under large amplitude oscillatory shear.
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J. Rheol. 37, 695 (1993); http://dx.doi.org/10.1122/1.550391 (32 pages)
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The properties of aqueous solutions of model HEUR associative thickeners under dynamic and steady shear have been studied as a function of concentration, molecular weight, temperature, and hydrophobic end‐cap length. It is shown that solutions of AT behave as near perfect Maxwell fluids inasmuch that Cole–Cole plots of the dynamic moduli are almost exactly semi‐circular. An Arrhenius law temperature dependence of the static viscosity and relaxation time is also observed, providing confirmation of a single relaxation process. In certain other respects, AT solutions show more complex behavior, e.g., the Cox–Merz rule is not obeyed, with the steady shear viscosity showing a weaker dependence on shear rate than does the complex viscosity upon frequency. Furthermore, weak shear thickening is seen to precede shear thinning in steady shear. The above results are consistent with the predictions of a transient network theory presented recently by Tanaka and Edwards and Jenkins (generalized Green–Tobolsky theory). This does not however explain the strong effect of concentration on the various rheological coefficients. For example, the theory predicts a linear dependence of high‐frequency modulus and static viscosity on concentration, whereas in practice they are found to be more like quadratic and cubic, respectively, at low concentrations. In previous publications this strong dependence has been taken to mean that the network chains are entangled to the point where reptation dynamics determines the time scale of relaxation. This supposition has been tested by mixing solutions of AT with different relaxation times (achieved by means of different end‐cap lengths), on the basis that the mixed solutions should show an intermediate relaxation time if reptation is important. In practice, mixtures of two and three AT were found to show two or three sharp relaxation times, implying that the chains relax independently. It is shown that the true explanation of the strong concentration dependencies is connected with a different kind of change of network topology with concentration. An elementary statistical‐mechanical model, supported by Monte Carlo simulation, is used to argue for a gradual transition from, at low concentrations, micelles built predominantly from looped chains to, at high concentrations, a fully developed network comprising micelles linked by bridging chains. When the transient network theory is modified so as to take the presence of loops into account, it produces results in semiquantitative agreement with experiment. |
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J. Rheol. 57, 901 (2013); http://dx.doi.org/10.1122/1.4801757 (26 pages) Online Publication Date: 16 Apr 13
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We show that the addition of solid particles to droplet–matrix blends of immiscible polymers induces massive changes in the rheology and the flow-induced structure even at loadings as low as 0.1 vol. %. Experiments were conducted using blends of polyethylene oxide (PEO, dispersed phase), polyisobutylene (PIB, continuous phase), and 470 nm monodisperse silica particles with two different surface wettabilities. Rheological experiments were conducted under molten conditions, while the morphology was characterized at room temperature using scanning electron microscopy. We are able to image the morphology at both lengthscales: The >20 μm lengthscale of the dispersed phase, as well as the submicron lengthscale of the particles. Rheological experiments along different trajectories in the ternary particle/PEO/PIB composition diagram reveal that addition of ∼1 vol. % particles that are preferentially wetted by the PIB induces a large increase in steady shear viscosity, severe shear-thinning, and yield-like behavior. However if the particles are equally wetted by PEO and PIB, these effects are greatly diminished. Remarkably, addition of very low loadings (∼0.1 vol. %) of particles reduces the viscosity under some conditions regardless of wettability. These rheological changes are interpreted in terms of three observations from morphological studies: That particles greatly enhance coalescence at low volume loadings, that particles jam the interface at higher loadings, and that particles bridge across drops and glue them together into large clusters. The first two of these effects occur regardless of particle wettability, whereas the last occurs only with particles that are preferentially wetted by the continuous phase.
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Defining nonlinear rheological material functions for oscillatory shear J. Rheol. 57, 177 (2013); http://dx.doi.org/10.1122/1.4764498 (19 pages) Online Publication Date: 26 Nov 12
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Material functions underlie our understanding of rheology. They form the descriptive language of rheologists and require clear definitions. Here, it is shown that the definitions of oscillatory material functions depend on how the oscillating input is mathematically referenced, as a sine or cosine. Depending on this seemingly arbitrary trigonometric reference choice, the (3rd, 7th, 11th, etc.) Fourier coefficients of a nonlinear shear response change sign. Additionally, the even harmonic coefficients of a shear normal stress response are transposed. This impacts large-amplitude oscillatory shear (LAOS) characterization in both shear strain-control (LAOStrain) and shear stress-control (LAOStress) modes. It is important to resolve this issue, because it involves the leading-order nonlinearities and the signs of these higher harmonics convey important information. This paper provides a resolution, in two parts. First, it is shown that the deformation-domain Chebyshev coefficients are immune to the arbitrary trigonometric reference in the time domain, and therefore the Chebyshev-coefficient material functions can be used and interpreted without risk of inconsistency. Second, this paper proposes the convention of referencing to a sine input for strain-control tests (currently the typical convention) and using a cosine input for stress-control (where there is not currently a convention). Finally, clarity is brought to the practical issue of data processing a digital signal, which is required for numerical simulations and every instrument that performs oscillatory characterization.
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Theoretical study of wall effects on the rheology of dilute polymer solutions J. Rheol. 36, 175 (1992); http://dx.doi.org/10.1122/1.550360 (39 pages)
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The recently developed generalized bracket formulation of transport phenomena (a Helmholtz free energy‐based approach) is used to predict the rheological behavior of high molecular weight, dilute polymer solutions near planar, smooth, noninteracting solid surfaces. A boundary‐value problem (passage to a stochastic differential equation) is set up in order to estimate the entropy reduction caused by the presence of the solid barrier. Under flow, in addition to diffusional effects, such an entropy reduction results in different conformations of the macromolecules next to the wall, which in turn causes a different than the bulk rheological behavior. The resulting continuum equations account for wall effects under arbitrary flow conditions provided the confining flow boundary is smooth. For the steady‐state simple shear flow, two limiting cases, corresponding to a uniform and a nonuniform (fully developed) concentration profile, have been examined. In both cases, calculated apparent slip velocities are found to depend almost linearly on the wall shear stress, corresponding, however, to different proportionality (slip) coefficients. Moreover, both the chain conformation and the first normal stress are found to change appreciably near the wall in a fashion moderately dependent on the applied shear stress. Assuming fully developed concentration profiles, the corresponding depletion layer is found to decrease with increasing shear stress in agreement with the molecular simulation results of Duering and Rabin. |
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Analysis of Linear Viscoelasticity of a Crosslinking Polymer at the Gel Point J. Rheol. 30, 367 (1986); http://dx.doi.org/10.1122/1.549853 (16 pages)
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We suggest a very simple memory integral constitutive equation for the stress in crosslinking polymers at their transition from liquid to solid state (gel point). The equation allows for only a single (!) material parameter, the strength S[Pas1∕2], and it is able to describe every known viscoelastic phenomenon at the gel point. Measurements were performed on polydimethylsiloxane model networks with balanced stoichiometry for which the crosslinking reaction has been stopped at different degrees of conversion. At the gel point, the loss and storage moduli were found to be congruent and proportional to ω1∕2 over a wide range of temperature (−50°C to +180°C) and five decades of frequency ω. The hypothesis is made that this behavior is valid in the entire range 0<ω<∞. This congruence hypothesis is consistent with the Kramers‐Kronig relation and leads to a constitutive equation which shows that, for our polymer, congruent functions G′(ω)=G″(ω) are as much a rheological property at the gel point as are infinite viscosity and zero equilibrium modulus. This makes it now possible to measure exactly the instant of gelation of a crosslinking polymer without having to stop the crosslinking reaction. |
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Strong squeeze flows of yield-stress fluids: The effect of normal deviatoric stresses J. Rheol. 57, 719 (2013); http://dx.doi.org/10.1122/1.4794912 (24 pages) Online Publication Date: 13 Mar 13
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This work aims to study squeeze flows when the lubrication approximation does not necessarily hold. Strong squeeze flows are defined as the cases in which a sample is compressed by a disk with the initial speed of 40 cm/s, whereas weak squeeze flows are realized when the disk is softly released manually to avoid any impact of the sample at the beginning of compression. Strong and weak squeeze flows of yield-stress materials are studied experimentally and theoretically. In the experiments, disk-like constant-volume samples of Carbopol solutions and bentonite dispersions are compressed between two approaching disks being subjected to constant forces. In addition, experiments with shear flows in parallel-plate and vane viscometers are conducted. Using visualization through the transparent wall of the squeezing apparatus, it is demonstrated that the no-slip conditions hold. It is also demonstrated that during the fast stage of strong squeeze flows, the material response can be explained by deviatoric normal stresses, which elucidates the link of strong squeeze flows to elongational flows. The analysis of the data in the framework of the Newtonian and Herschel–Bulkley models shows that in the present case the nonlinearity of the rheological response at the fast stage of strong squeeze flows is not very significant, and a strain-rate-independent viscosity can be used as a reasonable approximation. On the other hand, at the final stage of squeeze flows, when samples spread significantly under the action of a constant squeezing force, the compressive stresses become small enough, and the dominant role is played by the yield stress. No significant signs of thixotrophy were observed. It is shown that strong squeeze flow in the squeezing apparatus is a convenient tool useful for the measurement of viscosity and the yield stress of complex soft materials.
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Molecular constitutive equations for a class of branched polymers: The pom-pom polymer J. Rheol. 42, 81 (1998); http://dx.doi.org/10.1122/1.550933 (30 pages)
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Polymer melts with long-chain side branches and more than one junction point, such as commercial low density polyethylene (LDPE), have extensional rheology characterized by extreme strain hardening, while the shear rheology is very shear thinning, much like that of unbranched polymers. Working with the tube model for entangled polymer melts, we propose a molecular constitutive equation for an idealized polymer architecture, which, like LDPE, has multiple branch points per molecule. The idealized molecule, called a “pom-pom,” has a single backbone with multiple branches emerging from each end. Because these branches are entangled with the surrounding molecules, the backbone can readily be stretched in an extensional flow, producing strain hardening. In start-up of shear, however, the backbone stretches only temporarily, and eventually collapses as the molecule is aligned, producing strain softening. Here we develop a differential/integral constitutive equation for this architecture, and show that it predicts rheology in both shear and extension that is qualitatively like that of LDPE, much more so than is possible with, for example, the K-BKZ integral constitutive equation. © 1998 Society of Rheology. |
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Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions J. Rheol. 56, 1175 (2012); http://dx.doi.org/10.1122/1.4722880 (34 pages) Online Publication Date: 20 Jun 12
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In active, nonlinear microrheology, a Brownian “probe” particle is driven through a complex fluid and its motion tracked in order to infer the mechanical properties of the embedding material. In the absence of external forcing, the probe and background particles form an equilibrium microstructure that fluctuates thermally. Probe motion through the medium distorts the microstructure; the character of this deformation, and hence its influence on probe motion, depends on the strength with which the probe is forced, Fext, compared to thermal forces, kT/b, defining a Péclet number, Pe = Fext/(kT/b), where kT is the thermal energy and b is the characteristic microstructural length scale. Recent studies showed that the mean probe speed can be interpreted as the effective material viscosity, whereas fluctuations in probe velocity give rise to an anisotropic force-induced diffusive spread of its trajectory. The viscosity and diffusivity can thus be obtained by two simple quantities—mean and mean-square displacement of the probe. The notion that diffusive flux is driven by stress gradients leads to the idea that the stress can be related directly to the microdiffusivity, and thus the anisotropy of the diffusion tensor reflects the presence of normal stress differences in nonlinear microrheology. In this study, a connection is made between diffusion and stress gradients, and a relation between the particle-phase stress and the diffusivity and viscosity is derived for a probe particle moving through a colloidal dispersion. This relation is shown to agree with two standard micromechanical definitions of the stress, suggesting that the normal stresses and normal stress differences can be measured in nonlinear microrheological experiments if both the mean and mean-square motion of the probe are monitored. Owing to the axisymmetry of the motion about a spherical probe, the second normal stress difference is zero, while the first normal stress difference is linear in Pe for Pe≫1 and vanishes as Pe4 for Pe≪1. The expression obtained for stress-induced migration can be viewed as a generalized nonequilibrium Stokes–Einstein relation. A final connection is made between the stress and an “effective temperature” of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a “nonequilibrium equation of state.”
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Uniaxial extensional rheology of well-characterized comb polymers J. Rheol. 57, 605 (2013); http://dx.doi.org/10.1122/1.4789443 (21 pages) Online Publication Date: 04 Feb 13
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We present a detailed systematic investigation of the transient uniaxial extensional response of a series of well-characterized, anionically synthesized comb polystyrenes and polyisoprenes. The comb architecture consists of a linear chain backbone with multiple branches of equal molar mass, and represents an excellent model branched polymer. The linear viscoelastic response has been studied already in great detail. Our results indicate that the strain hardening becomes more important as the Hencky strain rate is increased. In general, the larger the number of entanglements of the segments between branches and/or of the branches, the stronger the strain hardening and the smaller the characteristic rate for its onset. The key molecular parameter appears to be the number of entanglements per branch. By varying it, one can tailor the amount and onset of strain hardening. This can be rationalized by accounting for the combined effect of backbone tube dilation and extra friction, brought about by the branches. In fact, we define an effective “stretch time” of the comb as the timescale for stretch relaxation along the dilated backbone tube when accounting for the large friction that comes from the branches and suggest that extension hardening occurs at rates equal to or greater than its inverse. The good comparison of this prediction to experimental data is a promising guide toward a universal framework for understanding the effects of branches on extensional rheology, and hence providing some insight into the behavior of long-chain branched polyolefins.
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Wall slip and flow of concentrated hard-sphere colloidal suspensions J. Rheol. 56, 1005 (2012); http://dx.doi.org/10.1122/1.4719775 (33 pages) Online Publication Date: 19 Jun 12
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We present a comprehensive study of the slip and flow of concentrated colloidal suspensions using cone-plate rheometry and simultaneous confocal imaging. In the colloidal glass regime, for smooth, nonstick walls, the solid nature of the suspension causes a transition in the rheology from Herschel–Bulkley (HB) bulk flow behavior at large stress to a Bingham-like slip behavior at low stress, which is suppressed for sufficient colloid-wall attraction or colloid-scale wall roughness. Visualization shows how the slip-shear transition depends on gap size and the boundary conditions at both walls and that partial slip persist well above the yield stress. A phenomenological model, incorporating the Bingham slip law and HB bulk flow, fully accounts for the behavior. Microscopically, the Bingham law is related to a thin (subcolloidal) lubrication layer at the wall, giving rise to a characteristic dependence of slip parameters on particle size and concentration. We relate this to the suspension’s osmotic pressure and yield stress and also analyze the influence of van der Waals interaction. For the largest concentrations, we observe nonuniform flow around the yield stress, in line with recent work on bulk shear banding of concentrated pastes. We also describe residual slip in concentrated liquid suspensions, where the vanishing yield stress causes coexistence of (weak) slip and bulk shear flow for all measured rates.
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J. Rheol. 57, 841 (2013); http://dx.doi.org/10.1122/1.4797458 (16 pages) Online Publication Date: 09 Apr 13
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Edge fracture hampers the measurement of the two normal stress differences N1 and N2 in a cone-partitioned plate rheometer with two partitions (CPP2). A third nonmeasuring partition has therefore been added, solely to shield off edge fracture (CPP3). The partial normal forces on the inner two partitions are much better balanced than on the CPP2. The new partitioned plate rheometer cell has been downsized to fit an MCR300. Potentially, N1 and N2 can now be obtained for all rheometric tests that can be performed with that rheometer. This publication reports on the technical features of the CPP3 cell. Step shear-rate tests in the range 0.1 < Wi < 3 and a strain of γ = 40 have been performed with a poly(dimethyl siloxane) (PDMS) standard to proof the rheometric functionality. The characteristic relaxation time of the PDMS is comparable to the axial response time, in spite of a cone angle of 0.15 rad. This means that transient normal force data are affected by instrument compliance. Steady state N1 and N2 however are measured correctly. N1 compares with data from a CPP2 and the MCR300, but can be determined with much less polymer. The scattering of the steady state second normal stress difference N2 is substantially reduced compared to the CPP2. A critical evaluation of the pros and cons of the CPP3 is given, based on the results of this study.
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J. Rheol. 57, 27 (2013); http://dx.doi.org/10.1122/1.4754023 (44 pages) Online Publication Date: 04 Oct 12
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Large amplitude oscillatory shear (LAOS) is used as a tool to probe the nonlinear rheological response of a model elasto-viscoplastic material (a Carbopol microgel). In contrast to most recent studies, these large amplitude measurements are carried out in a stress-controlled manner. We outline a descriptive framework of characterization measures for nonlinear rheology under stress-controlled LAOS, and this is contrasted experimentally to the strain-controlled framework that is more commonly used. We show that this stress-controlled methodology allows for a physically intuitive interpretation of the yielding behavior of elasto-viscoplastic materials. The insight gained into the material behavior through these nonlinear measures is then used to develop two constitutive models that prescribe the rheological response of the Carbopol microgel. We show that these two successively more sophisticated constitutive models, which are based on the idea of strain decomposition, capture in a compact manner the important features of the nonlinear rheology of the microgel. The second constitutive model, which incorporates the concept of kinematic hardening, embodies all of the essential behaviors exhibited by Carbopol. These include elasto-viscoplastic creep and time-dependent viscosity plateaus below a critical stress, a viscosity bifurcation at the critical stress, and Herschel–Bulkley flow behavior at large stresses.
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J. Rheol. 43, 1437 (1999); http://dx.doi.org/10.1122/1.551054 (23 pages)
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High molecular weight paraffins are known to form gels of complex morphology at low temperatures due to the low solubility of these compounds in aromatic or naphthene-base oil solvents. The characteristics of these gels are strong functions of the shear and thermal histories of these samples. A model system of wax and oil was used to understand the gelation process of these mixtures. A significant depression in the gel point of a wax-oil sample was observed by either decreasing the cooling rate or increasing the steady shear stress. The wax-oil sample separates into two layers of different characteristics, a gel-like layer and a liquid-like layer, when sheared with a controlled-stress rheometer at high steady shear stresses and low cooling rates. The phase diagram of the model wax-oil system, obtained using a controlled-stress rheometer, was verified by analyzing the wax content of the incipient gel deposits formed on the wall of a flow loop. Based on the rheological measurements, a law has been suggested for the prediction of the wax content of the gel deposit on the laboratory flow loop walls. The wax content of the incipient gel formed on the wall of a field subsea pipeline was predicted to be much higher than that for the flow loop at similar operating conditions. This variation in the gel deposit characteristics is due to the significant differences in the cooling histories in the two cases. © 1999 Society of Rheology. |
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Rheological and morphological study of cocontinuous polymer blends during coarsening J. Rheol. 56, 1315 (2012); http://dx.doi.org/10.1122/1.4739067 (20 pages) Online Publication Date: 30 Jul 12
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One of the challenges in the study of cocontinuous blends is to relate their rheological behavior with their morphology. This is due to the inherent instability of cocontinuous structures. We have studied the morphological and rheological time evolution of cocontinuous blends with different interfacial tension and viscosity ratio during annealing. In general, the presence of an interface generates an extra contribution to the elastic modulus, G′int. We have found that both the initial value of G′int and its rate of evolution during coarsening are proportional to the ratio between interfacial tension and blend viscosity. We have related time evolution of the elastic modulus to that of the interfacial area via a simplification of Doi–Ohta model for the case of small amplitude oscillatory shear flow. This simplification is based on the experimental evidence that the degree of anisotropy generated during small amplitude oscillations is negligible [López-Barrón and Macosko, Langmuir 26, 14284–14293 (2010b)]. The simplification gives a linear relation between the characteristic size and time and an asymptotic decrease of the elastic modulus with a limit behavior at long times: G′|t→∞∝t−1. This behavior was observed on blends with low interfacial tension. However, blends with high interfacial tension underwent a transition toward a decrease in the rate of coarsening, which is accompanied by a slower decrease of the elastic modulus. Doi–Ohta model is not sensitive to this transition and fails in predicting the time evolution of the characteristic length and elasticity of high interfacial tension blends.
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The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites J. Rheol. 31, 751 (1987); http://dx.doi.org/10.1122/1.549945 (34 pages)
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The properties of a set of even‐order tensors, used to describe the probability distribution function of fiber orientation in suspensions and composites containing short rigid fibers, are reviewed. These tensors are related to the coefficients of a Fourier series expansion of the probability distribution function. If an n‐th‐order tensor property of a composite can be found from a linear average of a transversely isotropic tensor over the distribution function, then predicting that property only requires knowledge of the n‐th‐order orientation tensor. Equations of change for the second‐ and fourth‐order tensors are derived; these can be used to predict the orientation of fibers by flow during processing. A closure approximation is required in the equations of change. A hybrid closure approximation, combining previous linear and quadratic forms, performs best in the equations of change for planar orientation. The accuracy of closure approximations is also explored by calculating the mechanical properties of solid composites with three‐dimensional fiber orientation. Again the hybrid closure works best over the full range of orientation states. Tensors offer considerable advantage for numerical computation because they are a compact description of the fiber orientation state. |
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Studying the origin of “strain hardening”: Basic difference between extension and shear J. Rheol. 57, 89 (2013); http://dx.doi.org/10.1122/1.4763568 (16 pages) Online Publication Date: 30 Oct 12
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This work studies the origin of the so called "strain hardening" observed when comparing the transient stress response of entangled melts to uniaxial extension with that to simple shear. Strain hardening occurs when the transient extensional viscosity measured from a startup uniaxial extension of finite rate deviates upward from the zero-rate transient viscosity. Our theoretical analysis shows that polymer melts would always exhibit strain hardening at sufficient high Hencky rates because the entanglement network can be effectively strengthened during extension and can only be weakened during shear for linear chains. The kinematic difference between simple shear and uniaxial extension has two effects: (a) The force resulting from the startup deformation is measured from an increasingly shrinking area in uniaxial extension instead of a constant area as in simple shear; and (b) the tendency of the entanglement network to yield, i.e., to undergo chain disentanglement is partially suppressed during startup extension at high Hencky rates. In short, the phenomenon of strain hardening reflects the reality that entangled melts are not fluids but temporary solids and that the conventional description of their uniaxial extension in terms of the Cauchy stress contains a geometric condensation factor.
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