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May 2011
The 20 articles with the most full-text downloads during the month, in descending order.
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Volume equalized constitutive equations for foamed polymer solutions J. Rheol. 36, 1033 (1992); http://dx.doi.org/10.1122/1.550300 (23 pages)
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In order to develop a constitutive equation for foamed polymer solutions their flow behavior was investigated in a large‐scale vertical tube. Starting from theoretical considerations, two new constitutive equations are proposed. A new variable−the specific volume expansion ratio−is introduced to characterize the relative gas content of the foam. With the new variable the proposed constitutive equations take simple forms and obey the principle of volume equalizing, i.e., the corresponding Reynolds numbers possess a certain invariance property. The proposed models are fitted to the experimental data. The principle of volume equalizing is checked in light of the current knowledge on foam flow behavior. |
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Local transient rheological behavior of concentrated suspensions J. Rheol. 55, 835 (2011); http://dx.doi.org/10.1122/1.3582848 (20 pages) Online Publication Date: 29 Apr 11
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This paper reports experiments on the shear transient response of concentrated non-Brownian suspensions. The shear viscosity of the suspensions is measured using a wide-gap Couette rheometer equipped with a particle image velocimetry device that allows measuring the velocity field. The suspensions made of PMMA particles (31 μm in diameter) suspended in a Newtonian index- and density-matched liquid are transparent enough to allow an accurate measurement of the local velocity for particle concentrations as high as 50%. In the wide-gap Couette cell, the shear induced particle migration is evidenced by the measurement of the time evolution of the flow profile. A peculiar radial zone in the gap is identified where the viscosity remains constant. At this special location, the local particle volume fraction is taken to be the mean particle concentration. The local shear transient response of the suspensions when the shear flow is reversed is measured at this point where the particle volume fraction is well defined. The local rheological measurements presented here confirm the macroscopic measurements of
Gadala-Maria and Acrivos [J. Rheol. 24, 799–814 (1980)]
. After shear reversal, the viscosity undergoes a steplike reduction, decreases slower, and passes through a minimum before increasing again to reach a plateau. Upon varying the particle concentration, we have been able to show that the minimum and the plateau viscosities do not obey the same scaling law with respect to the particle volume fraction. These experimental results are consistent with the scaling predicted by
Mills and Snabre [Eur. Phys. J. E 30(3), 309–316 (2009)]
and with the results of numerical simulation performed on random suspensions
[Sierou and Brady, J. Fluid Mech. 448, 115–146 (2001)]
. The minimum seems to be associated with the viscosity of an isotropic suspension or at least of a suspension whose particles do not interact through non-hydrodynamic forces, while the plateau value would correspond to the viscosity of a suspension structured by the shear where the non-hydrodynamic forces play a crucial role.
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Nonlinear rheology of colloidal gels with intermediate volume fraction J. Rheol. 55, 673 (2011); http://dx.doi.org/10.1122/1.3571554 (34 pages) Online Publication Date: 04 Apr 11
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The depletion attraction, induced upon addition of a nonadsorbing polymer to a colloidal solution, can lead to gel formation at sufficiently high polymer concentrations, which corresponds to strong attractive interactions. We have investigated the nonlinear rheological response, in particular the yielding, of colloidal gels with an intermediate volume fraction and variable interparticle attraction. Two distinct yielding processes are observed in both oscillatory experiments, namely, dynamic strain sweeps and transient experiments, here step rate, creep, and recovery tests. The first yielding process occurs at strains similar to the range of the interparticle potential and is interpreted as the breaking of bonds, which destroys the particle network and leads to individual clusters. The process of bond breaking is successfully modeled as the escape of a particle from the potential well of its nearest neighbor. The second yield point occurs at larger strains and is related to the deformation and fragmentation of clusters, consistent with the observed dependence of the yield strain on attraction. Both yield stresses exhibit a power-law dependence on attraction strength in agreement with observations of other systems and theoretical predictions. Furthermore, the observed two-step yielding reveals similarities, and also differences, to the rheology of attractive colloidal glasses.
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Oscillatory yielding of a colloidal star glass J. Rheol. 55, 733 (2011); http://dx.doi.org/10.1122/1.3579161 (20 pages) Online Publication Date: 12 Apr 11
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We investigate the response of a well-characterized colloidal star glass to large-amplitude oscillatory stress and strain fields. By combining these measurements with dynamic time sweeps we demonstrate the importance of probing both strain- and stress-induced nonlinear rheology of such complex fluids in order to elucidate the yielding and fluidization behavior. We also show that, due to the strong time dependence, it is essential to perform dynamic time sweeps at different strain and stress amplitudes, which result in different departures of the glass cage from its quiescent quasiequilibrium structure. This allows for steady-state responses to be reached and for nonlinear oscillatory responses to be treated properly while also suggesting that yielding is a gradual process. Further, we use a recently published framework for analyzing nonlinear responses to large-amplitude oscillatory shear [
Rogers et al., J. Rheol. 55, 435 (2011)
], based on the analysis of the whole stress waveforms as a sequence of physical processes, in order to measure the points of static and dynamic yielding. By doing so, we show that the stress-amplitude dependence of the dynamic yield stress can be linked to the strain-rate-amplitude dependence via the form of the steady-state flow curve.
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J. Rheol. 55, 713 (2011); http://dx.doi.org/10.1122/1.3571549 (19 pages) Online Publication Date: 12 Apr 11
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Reactive compatibilization, in which a compatibilizer is formed by an interfacial coupling between two reactive polymers, is commonly used when blending immiscible homopolymers. We consider reactive compatibilization using two multifunctional reactive polymers, which leads to a crosslinked copolymer at the interface. Experiments were conducted on model blends of polydimethylsiloxane (PDMS) and polyisoprene (PI). Compatibilizer was formed by a chemical reaction between amine-functional PDMS and maleic anhydride-functional PI. Droplet-matrix blends with a PI:PDMS ratio of 30:70 or 70:30 and reactive compatibilizer loadings from 0.1% to 3% were examined by optical microscopy and rheometry. Experiments reveal that the effects of interfacial crosslinking are highly asymmetric, with PI-continuous blends showing altogether different behaviors from PDMS-continuous blends. The PI-continuous blends show unusual features including drop clusters and nonspherical drops. In contrast, PDMS-continuous blends displayed a typical droplet-matrix morphology with round drops that do not appear to stick together. The rheological properties are also asymmetric: The PI-continuous blend showed gel-like behavior in oscillatory experiments, high viscosity, and viscosity overshoots during startup of shear flow, whereas PDMS-continuous blends showed liquidlike behavior that is qualitatively similar to that of compatibilizer-free blends. We speculate that the observed structural and rheological asymmetry is attributable to the asymmetry of the compatibilizer architecture on the two sides of the interface.
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Birefringence studies in die flows of an HDPE melt J. Rheol. 36, 1563 (1992); http://dx.doi.org/10.1122/1.550366 (21 pages)
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Flow studies of a high‐density polyethylene (HDPE) melt have been undertaken through planar slit dies with the purpose of establishing the birefringence pattern. Experimental results are compared with numerical solutions obtained by using an integral constitutive equation of the K‐BKZ type with a spectrum of relaxation times. The material parameters have been obtained by fitting viscosity and normal stress data as measured in shear, and elongational viscosity data available in the literature. The numerical simulations have been undertaken for a long (L/2H=2) and a short (L/2H=0.5) die at 180 °C. They show that as the flow rate increases, viscoelastic effects become important and manifest themselves in delayed relaxation of stresses along the slit and in stress overshoots at the die exit. This behavior is in close agreement with experimental birefringence patterns and in sharp contrast with purely viscous simulations which cannot predict such strong viscoelastic phenomena. Elastic recovery is also captured in an enhanced extrudate swell which is always higher for the short die. |
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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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New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear J. Rheol. 52, 1427 (2008); http://dx.doi.org/10.1122/1.2970095 (32 pages)
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Characterizing purely viscous or purely elastic rheological nonlinearities is straightforward using rheometric tests such as steady shear or step strains. However, a definitive framework does not exist to characterize materials which exhibit both viscous and elastic nonlinearities simultaneously. We define a robust and physically meaningful scheme to quantify such behavior, using an imposed large amplitude oscillatory shear (LAOS) strain. Our new framework includes new material measures and clearly defined terminology such as intra-/intercycle nonlinearities, strain-stiffening/softening, and shear-thinning/thickening. The method naturally lends a physical interpretation to the higher Fourier coefficients that are commonly reported to describe the nonlinear stress response. These nonlinear viscoelastic properties can be used to provide a “rheological fingerprint” in a Pipkin diagram that characterizes the material response as a function of both imposed frequency and strain amplitude. We illustrate our new framework by first examining prototypical nonlinear constitutive models (including purely elastic and purely viscous models, and the nonlinear viscoelastic constitutive equation proposed by Giesekus). In addition, we use this new framework to study experimentally two representative nonlinear soft materials, a biopolymer hydrogel and a wormlike micelle solution. These new material measures can be used to characterize the rheology of any complex fluid or soft solid and clearly reveal important nonlinear material properties which are typically obscured by conventional test protocols.
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Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers J. Rheol. 55, 495 (2011); http://dx.doi.org/10.1122/1.3553031 (22 pages) Online Publication Date: 09 Mar 11
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Studying the mechanical response of nearly monodisperse linear and comb polystyrene (PS) melts to medium amplitude oscillatory shear (MAOS),
Hyun and Wilhelm [Macromolecules 42, 411 (2009)]
identified two important scaling relations: (1) The relative intensity I3/1 of the third harmonic compared to the first harmonic scales with the strain amplitude according to γ02. Consequently, a new nonlinear coefficient Q ≡ I3/1/γ02 as well as the so-called intrinsic nonlinearity Q0 ≡ limγ0→0 Q was introduced. (2) In the terminal relaxation regime, the intrinsic nonlinearity Q0(ω) scales with ω2 and was found to be a very sensitive measure regarding molecular topology by identifying and separating relaxation processes in model branched polymers. A constitutive analysis based on a general single integral constitutive equation, which includes the Doi–Edwards model without (DE) and with (DE IA) independent alignment assumption as well as the molecular stress function (MSF) model, confirms both scaling relations. We show that the nonlinear viscoelastic moduli can be expressed as sums of their linear-viscolelastic counterparts at frequencies of ω, 2ω, and 3ω. The absolute value of Q0(ω) depends on the difference (α−β) between the third order orientational effect (parameter α) according to the DE or DE IA model and the second order isotropic stretching effect (parameter β) according to the MSF model. When comparing MAOS data to constitutive models, the apparent values of Q0(ω) measured in parallel-plate geometry have to be rescaled in order to take the non-uniform shear deformation into account. Both the DE and DE IA models fail to describe the experimental data. The data of four linear PS melts are quantitatively described by the MSF model with nonlinear parameters α = 5/21 (corresponding to the DE IA model) and β = 0.12 in the terminal relaxation regime. For the comb polymers, with the same orientational parameter of α = 5/21, stretch parameters of β = 0.14 for a polymer with unentangled branches and of β = 0.18 for two polymers with entangled branches are found. However, the model predicts a plateau at the level of the maximum of the experimental data, while the experimental values of Q0 decrease with increasing frequency. For the comb polymers with entangled branches, a minimum in Q0 is observed, and a second increase of Q0 at higher frequencies, which correspond to the terminal relaxation times of the branches. Surprisingly, these features can be modeled quantitatively if only the terminal relaxation modes of the backbone and, if present, the branches are assumed to deforming non-affinely and responding to the nonlinearity. The shorter modes seem to be deforming affinely and are excited only in the regime of finite linear viscoelasticity. We are presently not aware of any molecular mechanism that could explain this behavior.
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Large amplitude oscillatory shear flow of gluten dough: A model power-law gel J. Rheol. 55, 627 (2011); http://dx.doi.org/10.1122/1.3570340 (28 pages) Online Publication Date: 29 Mar 11
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In a previous paper [
T. S. K. Ng and G. H. McKinley, J. Rheol. 52(2), 417–449 (2008)
], we demonstrated that gluten gels can best be understood as a polymeric network with a power-law frequency response that reflects the fractal structure of the gluten network. Large deformation tests in both transient shear and extension show that in the absence of rigid starch fillers these networks are also time-strain factorizable up to very large strain amplitudes (γ∗>5). In the present work, we further explore the nonlinear rheological behavior of these critical gels by considering the material response obtained in large amplitude oscillatory shear over a wide range of strains and frequencies. We use a Lissajous representation to compare the measured material response with the predictions of a network theory that is consistent with the proposed molecular structure of gluten gels. In the linear viscoelastic regime, the Lissajous figures are elliptical as expected and can be quantitatively described by the same power-law relaxation parameters determined independently from earlier experiments. In the nonlinear regime, the Lissajous curves show two prominent additional features. First is a gradual softening of the network indicated by the rotation of the major axis of the stress ellipse. This feature is accounted for in the model by the inclusion of a simple nonlinear network destruction term that reflects the reduction in network connectivity as the polymer chains are increasingly stretched. Second, a distinct upturn in the viscoelastic stress is discernable at large strains. We show that this phenomenon can be modeled by considering the effects of finitely extensible segments in the elastic network. We use this model to quantitatively predict the material response in other large amplitude transient flows such as the start-up of steady shear and transient uniaxial extension up until the onset of strongly nonlinear unsteady phenomena such as edge fracture in shear and sample rupture during extension.
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Solution rheology of cellulose in 1-butyl-3-methyl imidazolium chloride J. Rheol. 55, 485 (2011); http://dx.doi.org/10.1122/1.3553032 (10 pages) Online Publication Date: 08 Mar 11
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Solution rheology of cellulose in 1-butyl-3-methyl imidazolium chloride ([BMIm]Cl) is reported using oscillatory and steady shear for cellulose concentrations from 0.1 to 10 wt %, spanning the dilute, semidilute unentangled, and entangled regimes. Although pure [BMIm]Cl is a crystalline solid at room temperature with a melting temperature of 65 °C, all solutions prepared at 75 °C are transparent and visually homogenous at 25 °C, and these supercooled solutions, with of order 0.1 wt % water, show no sign of crystallizing for months in either calorimetry or rheology measurements, allowing the potential for room temperature solution processing of native cellulose, such as fiber spinning. The overlap concentration of our cellulose in [BMIm]Cl is 0.5 wt % and the entanglement concentration is a factor of 4 larger (2 wt %). For semidilute unentangled solutions (between 0.5 and 2 wt %), the specific viscosity, relaxation time, and terminal modulus exhibit concentration dependences ηsp ∼ c2, τ ∼ c, and G ∼ c, respectively, while for entangled solutions (between 2 and 10 wt %) we find ηsp ∼ c14/3, τ ∼ c2.3, and G ∼ c2.3, consistent with scaling predictions for neutral polymers in a θ solvent. However, failure of the Cox–Merz rule with steady shear viscosity larger than complex viscosity and the observed internal mode structure of dilute and semidilute unentangled solutions suggest that cellulose in [BMIm]Cl is not simply a flexible polymer in a θ solvent.
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J. Rheol. 55, 753 (2011); http://dx.doi.org/10.1122/1.3574932 (27 pages) Online Publication Date: 13 Apr 11
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This paper is concerned with an investigation of the rheological performance of magnetorheological fluids under squeeze flow. Preliminary results on Newtonian fluids are first compared to Stefan’s equation. Then, unidirectional monotonic compression tests are carried out in the presence of uniaxial external magnetic fields at slow compression rates under constant volume operation. Results are compared to Bingham plastic, biviscous, and single chain micromechanical squeeze flow models. Measurements using combined deformation modes (compression+small-strain oscillatory shear) suggest a compression-induced shear strengthen effect up to strains of ∼ 0.5. Particle-level dynamic simulations are in qualitatively good agreement with experimental observations.
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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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Linear Viscoelasticity at the Gel Point of a Crosslinking PDMS with Imbalanced Stoichiometry J. Rheol. 31, 683 (1987); http://dx.doi.org/10.1122/1.549955 (15 pages)
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The evolution of linear viscoelasticity during cross‐linking of a stoichiometrically imbalanced polydimethylsiloxane (PDMS) was measured by small amplitude oscillatory shear. At the gel point (GP), stress relaxation was found to follow a power law, St−n, as described by the previously suggested gel equation. However, while stoichiometrically balanced gels (PDMS, polyurethanes) gave the specific exponent value of n=1∕2, a higher exponent value, 1∕2<n<1, was measured on a stoichiometrically imbalanced PDMS sample. Transformation of the data from the frequency to the time domain required the hypothesis that the power law behavior extends over the entire frequency range, 0<ω<∞. The imbalanced gel exhibited a higher loss than storage modulus, G″(ω)>Gv′(ω), and a higher rate of stress relaxation. GP was found to occur before the crossover point of the loss and storage moduli, G″(ω0,t), and G′(ω0,t), as measured during the cross‐linking reaction (reaction time, t) at constant frequency, ω0. This suggests new methods for localizing GP, for instance by the detection of a loss tangent independent of the frequency. All the experiments were performed with end‐linking networks far above the glass transition temperature. The network junctions were assumed to be due to chemical cross‐links only and not due to any other association phenomenon such as crystallization or phase separation. |
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The electrorheology of suspensions of Na-fluorohectorite clay in silicone oil J. Rheol. 55, 809 (2011); http://dx.doi.org/10.1122/1.3579189 (25 pages) Online Publication Date: 19 Apr 11
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Under application of an electric field E≳0.4 kV/mm, suspensions of the synthetic clay Na-fluorohectorite in a silicone oil aggregate into chain/columnlike structures parallel to E. This microstructuring results in a transition in the suspensions’ rheology, from Newtonian to a shear-thinning with a significant yield stress. We study this electrorheology (ER) as a function of E and of the particle volume fraction Φ on samples with a large clay particle polydispersity. The flow curves under fixed shear rate are well fitted by the Cho–Choi–Jhon model [
M. Cho et al., Polymer 46, 11484 (2005)
;
H. J. Choi and M. Jhon, Soft Matter 5, 1562 (2009)
]; proper scaling of E and of the measured shear stress provides a collapse of all flow curves onto a master curve. The corresponding dynamic yield stress scales as E1.93, while the static yield stress inferred from disruption tests behaves as E1.58. The bifurcation in the rheology when letting the flow evolve under constant shear stress is also characterized; the corresponding bifurcation yield stress scales as Eα with α ≃ 0.5–0.6. All measured yield stresses increase with Φ; for the static yield stress, a scaling law Φ0.54 is found. The three mutually consistent types of measurements are compared with previous measurements on laponite suspensions, and the rheologies of these two types of samples are discussed in light of existing theories of the ER effect.
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J. Rheol. 55, 435 (2011); http://dx.doi.org/10.1122/1.3544591 (24 pages) Online Publication Date: 07 Feb 11
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Recently, large-amplitude oscillatory shear has been studied in great detail with emphasis on its impact on the material response. Here we present a conceptually different, robust methodology based on viewing the stress waveforms as representing a sequence of physical processes. This novel approach provides the viscous and elastic contributions while overcoming the problems with infinite series encountered by Fourier transformation. Application to a soft colloidal star glass leads to the unambiguous determination and quantification of rate-dependent static and dynamic yield stresses, the rationalization of the response to strain sweeps and the post-yield regime by introducing the apparent cage modulus, and a connection to the steady-shear stress, all from a single-amplitude experiment. We propose that this approach is generic, but focus in this contribution only on a yield stress material which exhibits repeating cycles of (i) elastic extension, (ii) yielding, (iii) flow, and (iv) reformation. We show that this approach is qualitatively consistent with the Fourier–Chebyshev analysis.
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J. Rheol. 55, 581 (2011); http://dx.doi.org/10.1122/1.3569585 (46 pages) Online Publication Date: 28 Mar 11
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The orientation, microstructure, and rheology in non-Brownian shear flow were studied for suspensions of dicolloidal particles using a novel particle mesh Ewald Stokesian dynamics algorithm for anisotropic particles. Four different particle shapes were studied with dicolloids modeled as the union of two intersecting spheres. Dynamic simulations were conducted for periodic systems of 1000 particles for volume fractions ϕ = 0.05–0.55. The suspension microstructure was disordered for all particle shapes at 0 ≤ ϕ ≤ 0.50, with some systems showing ordered microstructure at ϕ = 0.55. The viscosity in the disordered state was similar for all particle shapes at equal volume fraction. Negative first and second normal-stress differences were found for ϕ ≤ 0.5, but positive values were observed for certain ordered systems at ϕ = 0.55. Complex orientation behavior was observed as a function of volume fraction and particle shape. All particles showed an orientation shift toward the vorticity axis for ϕ ≥ 0.10. Certain shapes showed a shift away from the vorticity axis for ϕ ≤ 0.10. The high ϕ orientation dynamics were consistent with predictions based on the mobility tensor MωS relating the angular velocity to particle stresslet. The orientation dynamics were dominated by the second normal-stress difference. The shift away from the vorticity axis for small ϕ was induced by migration away from orientations with large orientation fluctuations.
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The closed form t-T-P shifting (CFS) algorithm J. Rheol. 55, 1 (2011); http://dx.doi.org/10.1122/1.3503529 (16 pages) Online Publication Date: 03 Dec 10
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Time-dependent material functions of engineering plastics within the exploitation range of temperatures extend over several decades of time. For this reason material characterization is carried out at different temperatures and/or pressures within a certain experimental window. Using the time-temperature and/or time-pressure superposition principle, these response function segments can be shifted along the logarithmic time-scale to obtain a master curve at selected reference conditions. This shifting is commonly performed manually (“by hand”) and requires some experience. Unfortunately, manual shifting is not based on a commonly agreed mathematical procedure which would, for a given set of experimental data, yield always exactly the same master curve, independent of person who executes the shifting process. Thus, starting from the same set of experimental data two different researchers could, and very likely will, construct two different master curves. In this paper, we propose a closed form mathematical methodology (CFS) which completely removes ambiguity related to the manual shifting procedures. This paper presents the derivation of the shifting algorithm and its validation using several simulated- and real- experimental data. It has been shown that error caused by shifting performed with CFS is at least 10–50 times smaller then the underlying experimental error.
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Comparing tube models for predicting the linear rheology of branched polymer melts J. Rheol. 54, 223 (2010); http://dx.doi.org/10.1122/1.3301246 (38 pages) Online Publication Date: 17 Feb 10
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The hierarchical and “bob” (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent α and the factor p2 which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.
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Shear and extensional rheology of polypropylene melts: Experimental and modeling studies J. Rheol. 55, 95 (2011); http://dx.doi.org/10.1122/1.3523626 (32 pages) Online Publication Date: 15 Dec 10
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Non-linear correlations are found between the melt strength and fundamental shear flow properties such as low frequency loss tangent, crossover frequency, and zero-shear-rate viscosity for a series of polypropylene (PP) melts. The very good non-linear correlations suggest rheotens as a reliable rheological test to characterize extensional rheology relevant to fabrication, despite its non-homogeneous and non-isothermal flow kinematics. The rheotens model of
Doufas [J. Rheol. 50, 749–769 (2006)
] with a modified Giesekus (MG) viscoelastic constitutive equation is expanded to the case of PP melts. A single set of molecular parameters per material predicts the rheotens force curves very well over a wide range of processing conditions. The rheotens model is proposed as a tool for determination of rheological parameters of constitutive equations applicable to the simulation of complex polymer processes. Molecular considerations and predictions of the rheotens model are extensively discussed. A multi-mode MG model predicts the non-linear steady shear data (shear and first normal stresses) very favorably satisfying linear viscoelasticity. The oscillatory shear data and model predictions satisfy both the
Cox–Merz [J. Polym. Sci. 28, 619–621 (1958)]
and
Laun [J. Rheol. 30, 459–501 (1986)]
rules. The model exhibits stable numerical behavior without singularities or turning points in the prediction of steady shear viscosity even at quite high shear rates (e.g., on the order of 20 000 s−1), problems that have been reported for other constitutive equations.
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