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1.
Tensile stress and flow-induced birefringence have been measured during uniaxial elongation at a constant strain rate of two polystyrene melts with narrow molecular weight distribution. For both melts, the stress- optical rule (SOR) is found to be fulfilled upto a critical stress of 2.7 MPa, independent of strain rate and temperature. Estimation of the Rouse times of the melts, from both the zero-shear viscosity and the dynamic-shear moduli at high frequency, shows that the violation of the SOR occurs when the strain rate multiplied by the Rouse time of the melt exceeds by approximately 3. The presented results indicate that in contrast to current predictions of molecular theories, the regime of extensional thinning observed by Bach et al. (2003) extends well beyond the onset of failure of the SOR, and therefore the onset of chain stretch in the non-Gaussian regime.
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Clarisse LuapEmail: Phone: +41-1-632-68-89Fax: +41-1-632-1076 |
2.
Summary Investigation of time dependent behaviour of a polystyrene melt is carried out with the aid of a new apparatus for biaxial extension. Use is made of the method of two impinging fluid streams guided by lubricated trumpet shaped metal walls. The flow birefringence is measured in the plane of symmetry and, at the same time, the force is measured which tends to separate the trumpets. The linear stress-optical relation turns out to be valid in this new flow geometry. An accurate value for the stress-optical coefficient can be determined from the relaxation experiments. The stress build-up as calculated from the optical measurements, is compared with the pertinent result of the theory of linear viscoelasticity. For the desired interconversion of dynamic moduli use is made of the approximation by Schwarzl and Struik. The steady state measurements are checked by the results of the non-linear model of Acierno et al.With 16 figures and 2 tables 相似文献
3.
Creep and creep recovery experiments in elongation were performed with melts of anionically polymerized polystyrenes (PS) and with their blends at a temperature of 150 °C. For stresses
0 < 10 000 N/m2 the samples with narrow molecular weight distribution show linear viscoelastic behavior up to the maximum Hencky strain = 3.5, achievable in a newly developed elongational rheometer for polymer melts. The compliances,D (t), of the blends are linear-viscoelastic only up to a strain limit
L
. For strains beyond
L
the compliance of each blend depends on the stress
0. For a series of binary blends, prepared from the same components of narrow MWD, the linear-viscoelastic limit
L
seems to be independent of the mixing ratio and stress.
L
seems to be a function only of the molecular weights of the original components, the blends investigated were made from.Paper presented at the Annual Conference of the German Society of Rheology at Ulm, March 7–10, 1983. 相似文献
4.
5.
The deformation of an isolated drop in an immiscible liquid undergoing oscillatory shear flow is experimentally investigated
as a function of frequency and up to moderate amplitudes. Oscillatory shear flow is generated by using a parallel plate apparatus.
Drop shape is observed by video light microscopy along the vorticity direction of the shear flow. The two principal axes and
the orientation of the drop in the plane of shear are measured by image analysis. In the small amplitude range, the time dependence
of the axes is also harmonic, but not in phase with the applied strain, the phase difference being a decreasing function of
the imposed frequency. The linear range (where the major axis is proportional to the amplitude) extends up to strains of 0.5.
Good quantitative agreement was found with the Palierne linear viscoelastic model (Palierne, J. F., Linear rheology of viscoelastic
emulsions with interfacial tension, Rheol. Acta, 29, 204–214, 1990), thus providing a further example of the good agreement
between experiments and small deformation theory. 相似文献
6.
Rheological and fracture properties of optimally mixed flour doughs from three wheat cultivars which perform differently in cereal products were studied in uniaxial and biaxial extension. Doughs were also tested in small angle sinusoidal oscillation. In accordance with previously published results the linear region was found to be very small. The rheological properties at small deformations hardly depended on the cultivar. A higher water content of the dough resulted in a lower value for the storage modulus and a slightly higher value for tan . For both uniaxial and biaxial extension a more than proportional increase in stress was found with increasing strain, a phenomenon called strain hardening. In uniaxial extension (i) stresses at a certain strain were higher and (ii) the stress was less dependent on the strain rate than in biaxial extension. This indicates that in elongational flow orientational effects are of large importance for the mechanical properties of flour dough. This conclusion is consistent with published data on birefringence of stretched gluten. Fracture stress and strain increased with increasing deformation rate. The observed time-dependency of fracture properties can best be explained by inefficient transport of energy to the crack tip. Presumably, this is caused by energy dissipation due to inhomogeneous deformation because of friction between structural elements, e.g. between dispersed particles and the network. Differences in the rheological properties at large deformations between the cultivars were observed with respect to (i) stress, (ii) strain hardening, (iii) strain rate dependency of the stress, (iv) fracture properties and (v) the stress difference between uniaxial and biaxial extension. 相似文献
7.
The results of a numerical study of the viscous oscillating flow past four circular cylinders, for a constant frequency parameter equal to 50 and KC ranging between 0.2 and 10, are presented. The cylinders were placed on the vertices of a square, two sides of which were perpendicular and two parallel to the oncoming flow, for pitch ratios, P/D, ranging between 2 and 5. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables, whereas the pressure distribution throughout the computational domain was obtained from the solution of Poisson’s equation. When the Keulegan-Carpenter number is lower than 4, the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution domain and periodic at consecutive cycles. As KC increases to 4, the flow becomes aperiodic in different cycles, although symmetry with respect to the horizontal central line of the domain is preserved. For KC equal to 5, asymmetries appear intermittently in the flow, which are eventually amplified as KC increases still further. These asymmetries, in association with the aperiodicity of flow in different cycles, lead to an almost chaotic configuration as KC grows larger. For characteristic cases the flow pattern and the time histories of the in-line and transverse forces exerted on the cylinders are presented. The mean transverse forces acting on the cylinders, the r.m.s. values of the in-line and transverse forces, together with the drag and inertia coefficients of the in-line force, were evaluated for each pitch ratio in the range of Keulegan-Carpenter numbers examined and are presented in diagrams. 相似文献
8.
Birefringence in liquid polymers offers the possibility of obtaining information about stress in complex flows. In this work,
this is done for extensional flows of polyisobutylene in a “breathing bubble” rheometer. In this type of rheometer, a bubble
consisting of an incompressible, low-viscosity fluid (usually water) is injected into the sample with a nozzle. Expanding
or collapsing the bubble by adding or removing water induces biaxial or uniaxial extension in the surrounding sample. The
pressure difference between the bubble and the surroundings can be measured and compared to the predictions of constitutive
equations. This measurement only gives one integral value for a complex flow history.
In this paper, the birefringence around the bubble is measured in order to learn more about the flow. This is done by comparing
pressure and birefringence results to those of standard constitutive equations for a polyisobutylene sample. A good agreement
between the pressure and optical measurements and the theory is found with a single value of the stress-optical constant.
Received: 25 June 1997 Accepted: 12 November 1997 相似文献
9.
10.
Glutens were isolated from flour of three European wheat cultivars which perform differently in cereal products. The rheological and fracture properties of gluten-water doughs were determined in uniaxial and biaxial extension at large deformations and small angle sinusoidal oscillation tests and compared with the mechanical properties of the parental flour doughs. At 25 °C the linear region was in the same range as that of flour dough, while at a higher temperature (45 °C) the linear region was more than an order of magnitude higher. At 45 °C the storage modulus and tan were lower than at 25 °C. Variation in moduli between cultivars was much more pronounced for gluten than for flour doughs.Similarly to flour dough in both uniaxial and biaxial extension the stress () increased more than proportionally with the strain, a phenomenon called strain hardening. The stress at a set strain and strain hardening depended much more strongly on the type of deformation for gluten than for flour dough: was higher in biaxial extension for gluten than for flour dough, but was much higher in uniaxial extension. This indicates that orientational effects in elongational flow are of even larger importance for the mechanical properties of gluten than of flour dough. It is likely that it is the glutenin fraction that, because of its large size, confers these direction dependent properties to gluten and flour doughs. Fracture stresses were much higher for gluten than for flour dough, while fracture strains were in the same range or higher. For gluten dough fracture strains increased less strongly with increasing strain rate than for flour dough. Glutens exhibiting a higher stress at a certain strain had a smaller fracture strain.Our findings confirm the conviction that the large deformation properties of flour dough are mainly governed by the gluten fraction. However, there are also differences. Compared to flour dough gluten dough exhibits (i) a stronger strain hardening, (ii) a larger difference in between uniaxial and biaxial extension and (iii) a smaller strain rate dependency of the fracture strain. 相似文献
11.
This paper presents numerical results for laminar, incompressible and non-isothermal polymer melt flow in sudden expansions. The mathematical model includes the mass, momentum and energy conservation laws within the framework of a generalized Newtonian formulation. Two constitutive relations are adopted to describe the non-Newtonian behavior of the flow, namely Cross and Modified Arrhenius Power-Law models. The governing equations are discretized using the finite difference method based on central, second-order accurate formulas for both convective and diffusive terms. The pressure–velocity coupling is treated by solving a Poisson equation for pressure. The results are presented for two commercial polymers and demonstrate that important flow parameters, such as pressure drop and viscosity distribution, are strongly affected by heat transfer features. 相似文献
12.
This paper looks at the magnetohydrodynamic (MHD) analysis for transient flow of an Oldroyd-B fluid in a porous medium. The presented analysis takes into account the modified Darcy's law. The flow is induced due to constantly accelerated and oscillating plate. Expressions for the corresponding velocity field and the adequate tangential stress are determined by means of the Fourier sine transform. The influence of various parameters of interest on the velocity and tangential stress has been shown and discussed. A comparison for different kinds of fluids is also provided. 相似文献
13.
Homogeneous shearing is required in sliding plate flow experiments with one plate fixed and the other oscillating. However,
when fluid inertia becomes significant, the velocity gradient and the stress will not be uniform. MacDonald et al. (1969)
and Schrag (1977) investigated this effect for a linear viscoelastic fluid. However, linear viscoelasticity does not describe
the behavior of melts in large amplitude oscillatory shear (LAOS). Jeyaseelan et al. (1993) have shown that the Berkeley kinetic
network model does accurately describe the LAOS behavior of polymer melts. In this work, the Berkeley model is solved for
LAOS in sliding plate flow with fluid inertia, by numerical integration of spatially discretized forms of the governing equations.
Nonlinear viscoelasticity is predicted to aggravate the effects of fluid inertia in LAOS and experiments confirm this. Specifically,
fluid inertia amplifies the first harmonic and produces no even harmonics. Operating limits are presented graphically for
minimizing inertial effects in LAOS experiments.
Received: 2 January 1998 Accepted: 27 April 1998 相似文献
14.
Jonathan S. Schulze Timothy P. Lodge Christopher W. Macosko Jens Hepperle Helmut Münstedt Heike Bastian Dino Ferri David J. Groves Yong Hoon Kim Mike Lyon Thomas Schweizer Terry Virkler Erik Wassner Wim Zoetelief 《Rheologica Acta》2001,40(5):457-466
The transient uniaxial extensional viscosity η
e
of linear low density polyethylene (LLDPE) has been measured using the commercial Rheometric Scientific RME and the Münstedt
Tensile Rheometer in an effort to compare the performance of available extensional rheometers. The RME indicated a significant
strain hardening of the LLDPE, especially at a strain rate of 1 s−1. In contrast, the Münstedt rheometer showed the LLDPE to be only slightly strain hardening. This artificial strain hardening
effect in the RME resulted from the strain rate applied to the sample, determined from the sample deformation, being up to
20% less than the set strain rate. These results initiated a round-robin experiment in which the same LLDPE was tested on
several RMEs in various locations around the world. All but one of the RMEs indicated a deviation between set and applied
strain rates of at least 10%, especially at strain rates above 0.1 s−1. The strain rate deviation was found to depend strongly on the value of the basis length L
0
, and may result from the upper pair of belts not properly gripping the sample during extension. Thus visual inspection of
the sample deformation is necessary to determine the applied strain rate. The most accurate measurements of η
e
with respect to the strain rate deviation were obtained when the correct L
0
value and belt arrangement were used. A list of recommendations for running an RME test is provided. Future work focusing
on the fluid mechanics during the test may identify fully the cause of the strain rate deviation, but from a practical point
of view the problem can be corrected for in the determination of η
e
.
Received: 27 September 2000/Accepted: 5 February 2001 相似文献
15.
We present the first direct comparisons of rheological data from the lubricated squeezing flow (LSF) technique and the MultiAxiales
Dehnrheometer (MAD) instrument developed by Meissner and coworkers (J Rheol 47:989–1010, 2003). Comparisons of transient equibiaxial elongational viscosity are carried out at strain rates well into the nonlinear regime
on low-density polyethylene and polystyrene melts. We find data obtained using LSF deviate from the MAD data when the Hencky
strain reaches a value of approximately 1, which we interpret as a failure of the LSF technique. The strain at which the LSF
technique fails is relatively insensitive to experimental parameters including strain rate. For Hencky strains larger than
1, LSF data display behavior that could easily be mistaken for the phenomenon of strain hardening. 相似文献
16.
Start up of plane Couette flow and large amplitude oscillatory shear flow of single and multimode Maxwell fluids as well as Oldroyd-B fluids have been analyzed by analytical or semi-analytical procedures. The result of our analysis indicates that if a single or a multimode Maxwell fluid has a relaxation time comparable or smaller than the rate of change of force imparted on the fluid, then the fluid response is not singular as Elasticity Number (E ). However, if this is not the case, as E , perturbations of single and multimode Maxwell fluids give rise to highly oscillatory velocity and stress fields. Hence, their behavior is singular in this limit. Moreover, we have observed that transients in velocity and stresses that are caused by propagation of shear waves in Maxwell fluids are damped much more quickly in the presence of faster and faster relaxing modes. In addition, we have shown that the Oldroyd-B model gives rise to results quantitatively similar to multimode Maxwell fluids at times larger than the fastest relaxation time of the multimode Maxwell fluid. This suggests that the effect of fast relaxing modes is equivalent to viscous effects at times larger than the fastest relaxation time of the fluid. Moreover, the analysis of shear wave propagation in multimode Maxwell fluids clearly show that the dynamics of wave propagation are governed by an effective relaxation and viscosity spectra. Finally, no quasi-periodic or chaotic flows were observed as a result of interaction of shear waves in large amplitude oscillatory shear flows for any combination of frequency and amplitudes. 相似文献
17.
The deformation of linear low-density and low-density polyethylene particles dispersed in a polystyrene matrix was studied during defined uniaxial elongational flow conditions for different capillarity numbers and different temperatures. The morphology of the elongated samples was analysed by quenching the specimens in liquid nitrogen directly after the deformation. Furthermore, morphology development after recovery was investigated. By measuring the transient elongational viscosity of the blend matrix the true hydrodynamic stress during the flow process was calculated. Using a modified critical capillarity number, the fibril formation of the dispersed phase could be described at all test conditions. Virtually no break-up processes were observed. This finding could be explained by calculating the characteristic time of fibril break-up due to Rayleigh instabilities. By annealing the elongated samples a spherical shape of the dispersed droplets was regained. Compared with the initial sample morphology a pronounced increase of the particle sizes due to coalescence processes during elongation was observed. 相似文献
18.
We use a modified filament stretching rheometer to quantify the influence of a known controlled pre-shear history on the transient
extensional viscosity of a dilute polymer solution. Two different types of pre-deformation are explored; both influence the
subsequent stretching significantly, albeit in opposite ways. Small-amplitude oscillatory straining parallel to the direction
of stretching enhances strain hardening and accelerates the tensile stress growth toward the steady-state value. Conversely,
steady torsional shearing orthogonal to the direction of stretching retards strain hardening and results in a delayed approach
to steady-state elongational flow. In both cases, the final steady-state extensional viscosity is the same as that observed
with no pre-shearing. Calculations using a finitely extensible nonlinear elastic Peterlin dumbbell model qualitatively capture
the trends observed in experiments, enabling interpretation of these observations in terms of the degree of polymer chain
stretching imposed by the flow before extensional stretching. 相似文献
19.
We investigate the rheological behavior of the polymer blends with fibril morphology, with special focus on the effect of fibril morphology on the extensional properties under uniaxial extension. We add a small amount of the dispersed phase to the matrix, and control the blend morphology by changing the viscosity ratio. When the fibril morphology is maintained, the blend shows not only a significant increase of the extensional viscosity but the strain hardening behavior. The extensional viscosity increases depending on the aspect ratio of the fibers, while the strain hardening behavior originates from the restricted stretching of deformable fibers, which has been confirmed theoretically by introducing the concept of rigidity of the fiber. It suggests a way to induce the strain hardening behavior by introducing deformable fibrils into the matrix, that is, by the design of polymer blends with a small amount of dispersed phase such that the fibril structure is maintained. 相似文献
20.
Kyu Hyun Jung Gun Nam Manfred Wilhellm Kyung Hyun Ahn Seung Jong Lee 《Rheologica Acta》2006,45(3):239-249
Rheological properties of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer
solution in both linear and nonlinear regions have been investigated. PEO-PPO-PEO triblock copolymer solution shows a dramatic
change in mechanical properties as temperature changes. PEO-PPO-PEO triblock copolymer undergoes a transition from sol to
gel with increase of temperature. During this transition the copolymer solution passes through three different stages, namely
sol, soft gel, and hard gel. In our previous research (Hyun et al. in J Non-Newtonian Fluid Mech 55:51–65, 2002), large amplitude oscillatory shear (LAOS) behavior was found to be very sensitive to the generated microstructures. In this
study, we investigated the relationship between the LAOS type and the microdomain structure. Newtonian behavior is observed
in sol region, while there appear two kinds of LAOS types in the soft gel region. One is type I (G′, G′′ decreasing) and the other is a combination of type I and type IV (G′, G′′ increasing followed by decreasing). Type III (G′ decreasing, G′′ increasing followed by decreasing) is observed in the hard gel region. We compared the shape of stress curves, Lissajous
pattern, and Fourier transform (FT) rheology of hard gel and soft gel under LAOS, and tried to relate the complex LAOS behavior
with the microstructural change. From these investigations, it was found that the LAOS behavior and the stress pattern at
large strain are closely related to the microdomain structure of PEO-PPO-PEO triblock copolymer, and provide a lot of useful
information on the microstructures induced by large deformation. 相似文献