Steady-state Viscosity Research Articles

Hemorheological risk factors of acute chest syndrome and painful vaso-occlusive crisis in children with sickle cell disease

Little is known about the effects of blood rheology on the occurrence of acute chest syndrome and painful vaso-occlusive crises in children with sickle cell anemia and hemoglobin SC disease. To address this issue, steady-state hemorheological profiles (blood viscosity, red blood cell deformability, aggregation properties) and hematologic parameters were assessed in 44 children with sickle cell anemia and 49 children with hemoglobin SC disease (8-16 years old) followed since birth. Clinical charts were retrospectively reviewed to determine prior acute chest syndrome or vaso-occlusive episodes, and rates of these complications were calculated. Multivariate analysis revealed that: 1) a higher steady-state blood viscosity was associated with a higher rate of vaso-occlusive crises in children with sickle cell anemia, but not in children with hemoglobin SC disease; 2) a higher steady-state red blood cell disaggregation threshold was associated with previous history of acute chest syndrome in children with hemoglobin SC disease and boys with sickle cell anemia. Our results indicate for the first time that the red blood cell aggregation properties may play a role in the pathophysiology of acute chest syndrome in children with hemoglobin SC disease and boys with sickle cell anemia. In addition, whereas greater blood viscosity is associated with a higher rate of vaso-occlusive crises in children with sickle cell anemia, no association was found in children with hemoglobin SC disease, underscoring differences in the etiology of vaso-occlusive crises between sickle cell anemia and hemoglobin SC disease.

Spherical‐Earth finite element model of short‐term postseismic deformation following the 2004 Sumatra earthquake

Decadal‐scale postseismic deformation of subduction earthquakes has been widely modeled using a Maxwell viscoelastic Earth with a mantle‐wedge viscosity of about 1019 Pa s. Short‐term postseismic deformation within a few years after the earthquake remains a more challenging problem because of the predominance of afterslip of the megathrust and the potentially more complex mantle rheology. Questions include the necessity of invoking the transient rheology and the relative importance of contributions from afterslip and viscoelastic relaxation. In this work, we address these questions by developing a spherical‐Earth viscoelastic finite element model for the short‐term postseismic deformation following the magnitude 9.2 Sumatra earthquake of 2004. The model consists of elastic overriding and subducting plates and a viscoelastic mantle of bi‐viscous Burgers rheology, with the continental mantle (mantle wedge) being less viscous than the oceanic mantle by a factor of ten. Primary observational constraints for the short‐term postseismic deformation include ∼1 year net displacements of nine near‐field GPS sites and ∼3 year time series from three far‐field sites several hundred kilometers from the 2004 rupture zone. Model results indicate that the afterslip of the fault must be at work within the first few years after the earthquake. The observed deformation is best explained with a model that includes both the afterslip and transient rheology. In the preferred model, the transient and steady state viscosities of the mantle wedge are 5 × 1017 Pa s and 1019 Pa s, respectively.

Investigation of shear thinning behavior and microstructures of MWCNT/epoxy and CNF/epoxy suspensions under steady shear conditions

This report investigates the steady-state viscosities of multiwall carbon nanotube (MWCNT)/epoxy and carbon nanofiber (CNF)/epoxy suspensions with varying filler concentrations under different shear rates at various temperatures. In situ observation of filler networks suggests the build-up of shear induced MWCNT and CNF agglomerates at low shear rates, which correlates with the measured shear thinning behavior. The agglomeration process in MWCNT/epoxy suspensions is enhanced at lower shear rates in the case of higher temperatures, whereas, at high shear rates, both nano-fillers show good dispersion. Shear thinning behavior is observed for both types of fillers, and shear thinning exponential parameters are evaluated as a function of filler content. The shear thinning exponent increases in conjunction with increase in filler content, but it is found to saturate at a specific value, independently of filler material. Finally, the micromechanical elasticity-based analogy model is applied to the prediction of steady state shear viscosity of suspensions at higher shear rates with the assumption of complete dispersion and alignment of individual nano-fillers in suspensions. The predicted viscosities and the experimental data at higher shear rates are compared. The results conclude that fairly good agreement can be seen for the cases of CNF/epoxy suspensions at lower temperatures, whereas MWCNT/epoxy suspensions and CNF/epoxy suspensions at higher temperatures show discrepancy between the prediction and the experimental data.

Differences in the osteoarthritic synovial fluid composition and rheology between patients with or without flare-up. A pilot study

Purpose: To study the influence of the inflammatory status (flare or not) on hyaluronic acid (HA) and protein composition and on the intrinsic viscosity of the synoviol fluid (SF) from patients with knee osteoarthritis (KOA) Patients and Methods: Patients with KOA were classified as having flare (F+) when they fulfilled the 4 following clinical criteria: 1) sudden aggravation of knee pain, 2) whose beginning was identifiable, 3) causing nocturnal awakenings 4) with clinical evidence of knee effusion. Patients were classified F- (no flare) if they do not fulfill any of the 3 first criteria. 44 SF were obtained by arthrocentesis and assayed using Steric Exclusion Chromatography, which allows HA to be separated from the proteins and to determine both molecular weight (Mw) and and concentration (C) of both HA and proteins. SF rheology was determined using a rheometer at 25° C using a cone and plate geometry. Steady-state viscosity was determined in Pa.s, as a function of the shear rate at 1s-1. Correlations between Steady-state viscosity(Pa.s) and HA and Pr (Mw, C and Mw x C) were calculated. Results: Among the 44 assayed SF, 25 were classified F- and 19 F+. There were statistically significant differences between F- and F+ for most of the studied variables: HA concentration and Mw (p=0.01 and 0.001 respectively), protein concentration and Mw (p 0.02 and 0.001 respectively), product Mw x C of the proteins (p<0.0001) and viscosity(p=0.0005). The product [(Mw xC) HA x (MwxC) proteins] was highly discriminating between F+ and F- (p<0.0001). The steady state viscosity was highly related to HA concentration (p= 0.0002) and HA Mw (p=0.01) and was negatively correlated with (Mw x C) proteins (p=0.0005), protein concentration (p=0.0007) and protein Mw (p=0.03). Conclusion This pilot study shows significant differences of SF composition in patients having a flare-up compared to that of patients who do not have flare. These differences relate to both protein and HA composition and suggest that SF analysis makes possible to distinguish patients with and without flare.

Nonlinear Rheology of Telechelic Associative Polymer Networks: Shear Thickening and Thinning Behavior of Hydrophobically Modified Ethoxylated Urethane (HEUR) in Aqueous Solution

Flow behavior was examined for a 1.0 wt % aqueous solution of hydrophobically modified ethoxylated urethane (HEUR; Mw = 4.6 × 104). In the linear viscoelastic regime, the solution exhibited single-Maxwellian behavior attributable to thermal reorganization of the transient network composed of strings of HEUR flower micelles. Under shear flow at intermediate shear rates γ just above the equilibrium relaxation frequency 1/τ, the solution exhibited thickening characterized by monotonic increase of the viscosity growth function η+(t;γ) with time t above the linear η+(t) and by the steady-state viscosity η(γ) larger than the zero-shear viscosity η0. However, at those γ, the first normal stress coefficient growth function Ψ1+(t;γ) and its steady-state value Ψ1(γ) remained very close to the linear Ψ1+(t) and Ψ1,0 and exhibited no nonlinearity. In addition, the relaxation times of the viscosity and normal stress coefficient decay functions η–(t;γ) and Ψ1–(t;γ) measured after cessation of steady flow agreed...

Influence of water on cellulose-EMIMAc solution properties: a viscometric study

The influence of water on cellulose dissolved in 1-ethyl-3-methylimidazolium acetate (EMIMAc) is analysed by measuring steady state viscosity of dilute solutions. The goal is to determine: (a) the maximal water content allowing keeping cellulose dissolved (in dilute regime) and (b) the influence of water on solution flow and cellulose hydrodynamic properties. Mixing EMIMAc and water is exothermal and EMIMAc-water viscosity does not obey a logarithmic mixing rule suggesting strong interactions between the components. Newtonian flow of cellulose-EMIMAc-water solutions was recorded at water concentrations below 15 wt% and a shear thinning was observed for higher water content. It was suggested that above 15 wt% water cellulose is not completely dissolved: swollen aggregates form a sort of a “suspension” which is structuring under shear. Cellulose intrinsic viscosity showed a peak at 10 wt% water-90 wt% EMIMAc. It was hypothesised that the addition of water leads to the formation of large cellulose aggregates due to the preferential cellulose–cellulose interactions.

Relationships between rheological properties, texture and structure of apple (Granny Smith var.) affected by blanching and/or osmotic dehydration

The objective of this work was to evaluate and correlate rheological properties (small-scale dynamic oscillatory and creep/recovery measurements and large-scale compression force-deformation testing), texture (sensory evaluation by trained panel) and structure (optical and transmission electronic microscopy observations) of apples osmotically dehydrated to water activity (aw) 0.97 with glucose, with or without previous blanching. All apple samples showed a solid behavior (G′ > G″) dominating the viscoelastic response, but both dynamic moduli were reduced due to processing. The instantaneous elastic compliance (J0) and the retarded compliances (J1 and J2) increased for treated tissues and the steady-state viscosity (ηN) was approximately 15% to 29% of the value of fresh apple. In general, compression parameters decreased for all treated tissues. Changes in structural features were mainly evidenced in heated samples. Partial least squares regression analysis regression models revealed that texture could be well predicted by rheological properties (compression and creep parameters). Juiciness, crispness and sensory hardness were negatively correlated to J0, J1 and J2, and ηN was negatively correlated to sensory fracturability. Some mechanical parameters (fracturability, hardness 2, area 2, modulus of deformability and cohesiveness) were positively related to sensory fracturability, crispness and sensory hardness; and juiciness was negatively correlated to hardness. Compression and creep parameters showed ability to evidence structure differences (rupture of membranes, swelling of cells and degradation of cell walls) and to explain texture of treated apples.

Lower crustal relaxation beneath the Tibetan Plateau and Qaidam Basin following the 2001 Kokoxili earthquake

SUMMARY In 2001 November a magnitude 7.8 earthquake ruptured a 400 km long portion of the Kunlun fault, northeastern Tibet. In this study, we analyse over five years of post-seismic geodetic data and interpret the observed surface deformation in terms of stress relaxation in the thick Tibetan lower crust. We model GPS time-series (first year) and InSAR line of sight measurements (years two to five) and infer that the most likely mechanism of post-seismic stress relaxation is time-dependent distributed creep of viscoelastic material in the lower crust. Since a single relaxation time is not sufficient to model the observed deformation, viscous flow is modelled by a lower crustal Burgers rheology, which has two material relaxation times. The optimum model has a transient viscosity 9 × 1017 Pa s, steady-state viscosity 1 × 1019 Pa s and a ratio of long term to Maxwell shear modulus of 2:3. This model gives a good fit to GPS stations south of the Kunlun Fault, while displacements at stations north of the fault are over-predicted. We attribute this asymmetry in the GPS residual to lateral heterogeneity in rheological structure across the southern margin of the Qaidam Basin, with thinner crust/higher viscosities beneath the basin than beneath the Tibetan Plateau. Deep afterslip localized in a shear zone beneath the fault rupture gives a reasonable match to the observed InSAR data, but the slip model does not fit the earlier GPS data well. We conclude that while some localized afterslip likely occurred during the early post-seismic phase, the bulk of the observed deformation signal is due to viscous flow in the lower crust. To investigate regional variability in rheological structure, we also analyse post-seismic displacements following the 1997 Manyi earthquake that occurred 250 km west of the Kokoxili rupture. We find that viscoelastic properties are the same as for the Kokoxili area except for the transient viscosity, which is 5 × 1017 Pa s. The viscosities estimated for the Manyi and Kokoxili areas are consistent with constraints obtained from other earthquakes in the northwest and south central parts of the Tibetan Plateau.

Experimental study of attenuation and dispersion over a broad frequency range: 2. The universal scaling of polycrystalline materials

attenuation QE1 were measured accurately over a broad frequency range (10 −4 ≤ f (Hz) ≤ 2.15) and at low strain amplitude (10 −5 –10 −6 ). Creep experiments were performed with the same apparatus to measure the steady state viscosity. Anelasticity and viscosity were measured at high homologous temperatures (T =2 2 –48°C; T/Tm = 0.61–0.67) and various grain sizes (3–22 mm), the growth of which was controlled by annealing. Using the measured viscosities h and the unrelaxed modulus EU determined from ultrasonic experiments, the frequency of the entire data set was normalized by the Maxwell frequency fM = EU/h, resulting in E and Q −1 master curves. The Q −1 data from previous studies on olivine‐dominated samples also collapse onto the same curve when scaled by fM,, demonstrating the universality of anelasticity for polycrystalline materials. The similitude by the Maxwell frequency scaling indicates that the dominant mechanism for the anelasticity observed in this study and in previous studies is diffusionally accommodated grain boundary sliding. A generalized formulation for this similitude is provided to extrapolate the experimental data to velocity and attenuation of seismic shear waves.

Experimental study of attenuation and dispersion over a broad frequency range: 1. The apparatus

[1] We have developed a new experimental method to investigate the anelasticity of a polycrystalline solid at high homologous temperature (T/Tm = 0.6–0.7). By using a rock analogue (borneol polycrystals) and a partially molten rock analogue (borneol + melt) having low melting and eutectic temperatures (Tm = 204.5°C, Te = 43°C), respectively, testing high homologous temperature can occur near room temperature. An apparatus is described for cyclic compressive, Young's modulus type attenuation experiments over a wide range of frequencies (10–10−4 Hz) and at small strain amplitudes (10−6–10−5). Creep tests to measure steady state viscosity can also be performed. Details of the apparatus, including its piezoelectric actuator, dual laser displacement meters and trio of load cells, are discussed. Attenuation spectra and modulus dispersion measured for aluminum, acrylic plastic, and a rock analogue are presented to illustrate the accuracy of the method.

The Steady State Rheological Behavior of Semisolid AlSi6Mg2 Alloy

In the present work, basing on the rheological model of Chen and Fan (CF) [1] of semisolid metal slurries (SSMS), the rheological behavior at steady state of AlSi6Mg2 alloy is investigated. Experimental results on steady state viscosity of the present system in the literature are used to determine the parameters of the CF model by fitting. It has been shown that the steady state viscosity and the average agglomerate size increase with increasing the solid volume fraction and decreasing the shear rate. The theoretical prediction of the CF model is in good agreement with the experimental results in the literatures quantitatively. The importance of the effective solid volume fraction is shown by explaining the strong coupling between the viscosity and the microstructure. Specifically, the external flow conditions such as shear rate influences the viscosity by changing the agglomeration degree of the solid particles, that is, the effective solid volume fraction and then changing the viscosity.

Cross-slot extensional rheometry and the steady-state extensional response of long chain branched polymer melts

Stress-optical measurements at a flow stagnation point in confined geometries such as the cross-slot provide an elegant way to perform extensional testing for polymer melts. This technique is especially useful for samples which have a steady-state that cannot be reached (easily) in standard elongational rheometry, for example, highly branched polymers which show a non-homogeneous deformation that occurs in stretching experiments for Hencky strains above 4. In contrast to filament stretching, the cross-slot provides one point at which steady-state extensional flow may be sustained indefinitely. In this study, a Cambridge multi-pass rheometer [Coventry, K. D., and M. R. Mackley, J. Rheol. 52, 401–415 (2008)] is used to generate planar elongational flow in a cross-slot geometry for different polyethylene melts. The experimental results are compared to finite element flow simulations using the multi-mode Pompom constitutive equations. The steady-state elongational viscosity at the stagnation point is computed...

The extensional viscosity properties of long-chain branched fluorothermoplastics and correlations to molecular structure

The uniaxial extensional rheology behaviour of tailor-made long-chain branched TFE39/HFP11/ VDF50 terpolymers, LCB-THVs, is investigated at 265°C using the extensional viscosity fixture (TA Instruments). Within the window of applied extension rates (0.03 s − 1 ≤ e ∙ ≤ 30 s − 1) the model polymer fluids show weak to marked strain-hardening behaviour depending on their level of branching. A straightforward data filtering and evaluation procedure capable to extrapolate for quasi steady-state conditions from the similarity of the data sets is presented. Flexible approximation functions for the nominal transient elongational viscosity curves \(\eta _{\text{E}}^{+} (t,\varepsilon^{\bullet})\) and for quasi steady-state elongational viscosity curves \(\eta_E^{\text{\ddag}} (\varepsilon^{\bullet})\) are proposed. In the latter case, there are three adjustable parameters employed which have the physical meaning of: the elongational stress response time τ controlling the location of the maximum in the \(\eta_E^{\ddag} (\varepsilon^{\bullet})\) function, the polydispersity ξ of a unimodal LCB population, and its effective amount. An approximation function is also proposed for bimodal LCB distributions, which applies very well for the LDPE IUPAC A standard resin. Empirically, τ is found to depend on the size dimension of branching λ, derived from molecular characterization, by the relationship τ∼λ3.3.

Prediction of steady-state viscous and elastic properties of polyolefin melts in shear and elongation

The linear and nonlinear steady-state viscosities and elastic compliances were measured in shear and elongational flows for two low-density polyethylenes, a linear polypropylene, and two metallocene catalyzed polyethylenes (one linear and one long-chain branched) by Wolff et al. (Rheol Acta 49:95–103, 2010) and Resch (dissertation, 2010). Comprehensive data of this type are rarely found in the literature, and comprehensive modeling of both viscous and elastic effects is even rarer. In this contribution, the reliability of a modeling approach proposed by Laun (J Rheol 30(3):459–501, 1986) and based on the damping function concept is tested. The strain hardening seen for the long-chain branched polymers and its absence in the case of the linear polymer, the stronger decrease of the tensile compliance in comparison to the shear compliance with increasing stress, as well as the extended linear-viscoelastic regime of the shear viscosity in contrast to the shear compliance are correctly modeled. While the modeling of the nonlinear response in shear can be achieved with only one material parameter for most of the polymers considered here, the nonlinear modeling in elongation is achieved with two parameters. The same parameter values are shown to describe viscous as well as elastic properties of the melts, and thus the relations of Laun can be used to test the consistency of viscosity and compliance measurements.

The effect of dynamic tube dilation on chain stretch in nonlinear polymer melt rheology

The pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic (Doi and Edwards [10]). At deformation rates larger than the inverse Rouse time of the polymer chain, chains are stretched and their confining tubes become increasingly anisotropic. In a tube model with variable tube diameter, this leads to an interchain tube pressure term in the lateral direction of the tube (Marrucci and Ianniruberto [15]), which limits chain stretch. Here we assume that chain stretch is balanced by two restoring tensions with weights of 1/3 in the longitudinal direction of the tube, due to a linear entropic spring force, and 2/3 in the lateral direction, due to a nonlinear interchain tube pressure, both of which are characterized by the Rouse stretch relaxation time τ R . This approach is in quantitative agreement with the time-dependent and steady-state elongational viscosity of two monodisperse polystyrene melts with molar masses of 390,000 and 200,000 kg/mol as investigated by Bach et al. [2] and Hassager [12]. In bidisperse polymer blends, the interchain pressure is reduced in accordance with dynamic dilation of the tube. Implementation of the dilation effect into the evolution equation of the stretch leads to a quantitative description of the elongational behavior of bidisperse polystyrene blends consisting of a long and a short chain component as investigated by Nielsen et al. [22]. Due to the effect of chain ends, dynamic tube dilation is also of importance for monodisperse polymer melts with low molar masses having few entanglements, as demonstrated for two polystyrene melts with molar masses of M w = 102,800 and 51,700 g/mol. If dynamic tube dilation is taken into account, quantitative agreement between highly nonlinear viscoelastic experiments and predictions can be obtained based exclusively on the linear-viscoelastic characterization of polymer melts.

A Steady State Model for the Rheological Behavior of Semisolid Al-6.5wt%Si Alloy

In the present work, The Chen and Fan (CF) model [1] of semisolid metal slurries (SSMS) is improved by modifying the expression of the packing parameter, of the solid particles and then the modified CF (MCF) model is obtained. Subsequently, the MCF model is applied to the Al-6.5wt%Si alloy to investigate its rheological behavior at steady state. The factors which affect the steady state behavior have been studied. It has been shown that the steady state viscosity and the average agglomerate size increase with increasing the solid volume fraction and decreasing the shear rate. The prediction of the model is in good agreement with the experimental results in the literatures qualitatively. The importance of the effective solid volume fraction is shown by explaining the strong coupling between the viscosity and the microstructure. The external flow conditions such as shear rate etc change the agglomeration degree, that is, the effective solid volume fraction and then the viscosity

Influence of gellan gum concentration on the dynamic viscoelasticity and transient flow of fluid gels

Start-up at the inception of shear and flow interrupted experiments were carried out to illustrate the transient flow properties and thixotropic recovery of low-acyl gellan gum fluid gels prepared by a low-energy mechanical treatment. Small amplitude oscillatory shear tests were conducted to illustrate the rheological response under non-destructive conditions. Confocal laser scanning microscopy revealed the occurrence of a dispersion of gel-like domains in a continuous phase. Rheological methods were used to check that the samples characterised were free of thermo-mechanical history effects prior starting the transient flow tests. Start-up shear flow experiments at 10 s −1 resulted in a nearly instantaneous sharp rise of viscosity until a peak value was reached before it dropped following a sum of two first-order kinetic equations. The kinetic coefficients as well as the relative fall in viscosity were found to increase with gellan concentration. The equilibrium modulus as well as the peak and steady-state viscosities scaled with the gellan concentration following a power law equation with a characteristic exponent of about 2.0. Conversely, the degree of thixotropic recovery after a rest time of 10 s went down as gellan concentration increased, emphasising the need to balance both effects when formulating gellan fluid gels as stabilisers. The results obtained do a better job of highlighting the importance of peak viscosity than steady-state viscosity when data for pump selection and calculation are required.

Influence of molecular parameters on the stress dependence of viscous and elastic properties of polypropylene melts in shear

The stress dependencies of the steady-state viscosity η and, particularly, that of the steady-state elastic compliance J e of various linear isotactic polypropylenes (PP) and one long-chain branched PP are investigated using creep-recovery tests. The creep stresses applied range from 2 to 10,000 Pa. In order to discuss the stress-dependent viscosity η and elastic compliance J e with respect to the influence of the weight average molar mass M w and the polydispersity factor M w/M n the PP are characterized by SEC–MALLS. For the linear PP, linear steady-state elastic compliances \(J_{\rm e}^0 \) in the range of 10 − 5–10 − 3 Pa − 1 are obtained depending on the molar mass distribution. \(J_{\rm e}^0 \) of the LCB-PP is distinctly higher and comes to lie at around 10 − 2 Pa − 1. \(J_{\rm e}^0 \) is found to be independent of M w but strongly dependent on polydispersity. η and J e decrease with increasing stress. For the linear PP, J e as a function of the stress τ is temperature independent. The higher M w/M n the stronger is the shear thinning of η and the more pronounced is the stress dependence of J e. For the LCB-PP, the strongest stress dependence of η and J e is observed. Furthermore, for all PP J e reacts more sensitively to an increasing stress than η. A qualitative explanation for the stronger stress dependence of J e compared to η is given by analyzing the contribution of long relaxation times to the viscosity and elasticity.

The Great Myths of Rheology, Part II: Transient and Steady-State Melt Deformation: The Question of Melt Entanglement Stability

One of the most difficult problems to solve in rheology is prediction of the deformation of the melt during its “transient” conditions, i.e., before it reaches steady-state deformation. Most of our present understanding concerns the steady state when properties, e.g., viscosity or modulus, no longer depend on time and remain invariant. This article is concerned with the transient states obtained under non-linear conditions and asks why it sometimes takes a long time for the viscosity to reach steady state, when its terminal time τo calculated from the steady-state viscosity at that temperature, or from the crossover of G′ and G″ (τo = 1/ωx) indicates that the melt should relax in much shorter times. In pure viscometry (at constant shear rate), a transient behavior is expected before the melt reaches its steady state. Questions regarding the origin of this transient are experimentally and theoretically investigated and debated for a linear low-density polyethylene (M/M e ∼200). We show that the steady-state stability is a function of the melt's previous thermomechanical history. In order to study the instability of the melt under conditions that separate the effects of strain and strain rate, we investigate the triggering of time dependence of the moduli by strain in dynamic experiments performed in the non-linear range. We study, for linear polycarbonate and polystyrene, the effects of various parameters affecting the stability of entanglements under dynamic non-linear conditions, i.e., frequency, strain amplitude, and temperature. In all these experimental tests, we observe the same phenomenon: as strain is increased beyond a certain critical value (a function of frequency and temperature), the melt starts to become transient, e.g., its viscosity changes with time until it reaches a steady-state value. We review and rule out (for our results) the challenging interpretations based on melt edge fracture and melt surface decohesion. For transient and steady states obtained by pure viscometry or by dynamic shear oscillation, we compare the rheological properties [G′ (ω) and G″ (ω)] of the unsheared melt, before the transient, and of the “sheared melt,” after the transient, by performing a frequency sweep in the linear range. The results display large differences in G′ (ω) and G″ (ω) and in the value of the terminal time. In our proposed explanation we point to the limitation, as we enter the non-linear range, of the basic assumption of rheology regarding the scalability of the rheological parameters (stress and deformation tensors) in terms of viscosity, strain, and strain rate to describe the effect of the gap thickness. The definition of viscosity (ratio of stress and strain rate) and of strain rate (gradient of the velocity profile across the gap) requires a homogeneous melt, or, as we further propose, a homogeneous, unstructured entanglement network, which is a valid and justified concept only for certain conditions of deformation, e.g., in the linear viscoelastic range. A melt can be brought out of equilibrium with respect to its entanglement state. The return to equilibrium explains the transient properties. New entanglement states can be made quasistable, even at high temperature in the melt, by coupling entropic and enthalpic effects produced under specific conditions of melt processing. The currently accepted descriptions of rheology, we suggest, only apply to a stable entanglement state, which is not general enough and even becomes a severe limitation in the exploration of new frontier research in the application of rheology to processing of polymer melts. A supplemental table of contents is available for this article. Go to the publisher's online edition of the Journal of Macromolecular Science, Part B: Physics to view the free table of contents.

On the resolution of shallow mantle viscosity structure using postearthquake relaxation data: Application to the 1999 Hector Mine, California, earthquake

Most models of lower crust/mantle viscosity inferred from postearthquake relaxation assume one or two uniform‐viscosity layers. A few existing models possess apparently significant radially variable viscosity structure in the shallow mantle (e.g., the upper 200 km), but the resolution of such variations is not clear. We use a geophysical inverse procedure to address the resolving power of inferred shallow mantle viscosity structure using postearthquake relaxation data. We apply this methodology to 9 years of GPS‐constrained crustal motions after the 16 October 1999 M = 7.1 Hector Mine earthquake. After application of a differencing method to isolate the postearthquake signal from the “background” crustal velocity field, we find that surface velocities diminish from ∼20 mm/yr in the first few months to ≲2 mm/yr after 2 years. Viscoelastic relaxation of the mantle, with a time‐dependent effective viscosity prescribed by a Burgers body, provides a good explanation for the postseismic crustal deformation, capturing both the spatial and temporal pattern. In the context of the Burgers body model (which involves a transient viscosity and steady state viscosity), a resolution analysis based on the singular value decomposition reveals that at most, two constraints on depth‐dependent steady state mantle viscosity are provided by the present data set. Uppermost mantle viscosity (depth ≲ 60 km) is moderately resolved, but deeper viscosity structure is poorly resolved. The simplest model that explains the data better than that of uniform steady state mantle viscosity involves a linear gradient in logarithmic viscosity with depth, with a small increase from the Moho to 220 km depth. However, the viscosity increase is not statistically significant. This suggests that the depth‐dependent steady state viscosity is not resolvably different from uniformity in the uppermost mantle.