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1.
V. K. Gupta 《Rheologica Acta》2012,51(1):51-70
Ghosh et al. (J Rheol 46:1057–1089, 2002) developed a new model for dilute polymer solutions in flows with strong extensional components. The model based on introducing
an adaptive length scale (ALS) as an internal variable was developed to reproduce the fine-scale physics of the Kramers chain.
The ALS model describes the polymer molecule as a set of identical segments in which each segment represents a fragment of
the polymer that is short enough so that it can sample its entire configuration space on the time scale of an imposed deformation
and therefore stretch reversibly. As the molecule unravels, the number of the segments decreases, but the maximum length of
each segment increases, so that the constant maximum contour length of the molecule is preserved. Though the single-segment-based
ALS model accounts for the orientability of the polymer molecules, it cannot describe the internal motions of the molecules
due to the lack of internal nodes. Hence, in this work we consider the more realistic chain (multi-segments) model composed
of N
seg springs connected linearly. The model presented in this work is an extension of the ALS model developed by Ghosh et al. (J
Rheol 46:1057–1089, 2002). We demonstrate that the ALS varies with the flow strength. Specifically, it is found that as the flow strength increases,
the ALS decreases. This implies that as the flow strength increases, the polymer molecule is required to divide into finer
and finer segments such that each segment can locally equilibrate with the imposed flow. However, there is a critical number
of such subdivisions beyond which further subdivision of the polymer molecule is not required to capture the polymer dynamics
for a given flow strength. Both shear viscosity and first normal stress coefficient predictions from ALS model show shear
thinning behavior with Weissenberg number. In weak flows, the ALS model and the finitely extensible non-linear elastic model
exhibit the same behavior. 相似文献
2.
Recently, the tube diameter relaxation time in the evolution equation of the molecular stress function (MSF) model (Wagner
et al., J Rheol 49: 1317–1327, 2005) with the interchain pressure effect (Marrucci and Ianniruberto, Macromolecules 37:3934–3942, 2004) included was shown to be equal to three times the Rouse time in the limit of small chain stretch. From this result, an advanced
version of the MSF model was proposed, allowing modeling of the transient and steady-state elongational viscosity data of
monodisperse polystyrene melts without using any nonlinear parameter, i.e., solely based on the linear viscoelastic characterization
of the melts (Wagner and Rolón-Garrido 2009a, b). In this work, the same approach is extended to model experimental data in shear flow. The shear viscosity of two polybutadiene
solutions (Ravindranath and Wang, J Rheol 52(3):681–695, 2008), of four styrene-butadiene random copolymer melts (Boukany et al., J Rheol 53(3):617–629, 2009), and of four polyisoprene melts (Auhl et al., J Rheol 52(3):801–835, 2008) as well as the shear viscosity and the first and second normal stress differences of a polystyrene melt (Schweizer et al.,
J Rheol 48(6):1345–1363, 2004), are analyzed. The capability of the MSF model with the interchain pressure effect included in the evolution equation of
the chain stretch to model shear rheology on the basis of linear viscoelastic data alone is confirmed. 相似文献
3.
The elongational viscosity data of model PS combs (Hepperle J, Einfluss der Molekularen Struktur auf Rheologische Eigenschaften
von Polystyrol- und Polycarbonatschmelzen. Doctoral Thesis, University Erlangen-Nürnberg, 2003) are reconsidered by including the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37:3934–3942, 2004] in the Molecular Stress Function model [Wagner et al., J Rheol 47(3):779–793, 2003, Wagner et al., J Rheol 49:1317–1327, 2005d]. Two nonlinear model parameters are needed to describe elongational flow, β and . The parameterβ determines the slope of the elongational viscosity after the inception of strain hardening. It is directly related to the
molecular structure of the polymer and represents the ratio of the molar mass of the (branched) polymer to the molar mass
of the backbone alone. β follows from the hypothesis of Wagner et al. [J Rheol 47(3):779–793, 2003] that side chains are compressed onto the backbone. We consider also the case that side chains are oriented by deformation,
but not stretched, and found little difference in the model predictions. The parameter represents the maximum strain energy stored in the polymeric system and determines the steady-state value of the viscosity
in extensional flows. The relation of this energy parameter to the molecular structure is discussed. Good correlations between
the energy parameter and different coil contraction ratios, as determined either experimentally or calculated theoretically
by considering the topology of the macromolecule, are found. The smaller the relative size of the polymer coil, the larger
is the energy parameter and the more strain energy can be stored in the polymeric system.
Presented at the 3rd Annual European Rheology Conference, AERC2006, Crete, Greece. 相似文献
4.
Saswati Pujari Leah Dougherty Christophe Mobuchon Pierre J. Carreau Marie-Claude Heuzey Wesley R. Burghardt 《Rheologica Acta》2011,50(1):3-16
We report steady and transient measurements of particle orientation in a clay dispersion subjected to shear flow. An organically
modified clay is dispersed in a Newtonian polymer matrix at a volume fraction of 0.02, using methods previously reported by
Mobuchon et al. (Rheol Acta 46: 1045, 2007). In accord with prior studies, mechanical rheometry shows yield stress-like behavior in steady shear, while time dependent
growth of modulus is observed following flow cessation. Measurements of flow-induced orientation in the flow-gradient plane
of simple shear flow using small-angle and wide-angle X-ray scattering (SAXS and WAXS) are reported. Both SAXS and WAXS reveal
increasing particle orientation as shear rate is increased. Partial relaxation of nanoparticle orientation upon flow cessation
is well correlated with time-dependent changes in complex modulus. SAXS and WAXS data provide qualitatively similar results;
however, some quantitative differences are attributed to differences in the length scales probed by these techniques. 相似文献
5.
Mohammad T. Islam 《Rheologica Acta》2006,45(6):1003-1009
We present a differential constitutive model of stress relaxation in polydisperse linear polymer melts and solutions that contains contributions from reptation, contour-length fluctuations, and chain stretching. The predictions of the model during fast start-up and steady shear flows of polymer melts are in accord with experimental observations. Moreover, in accordance with reported experimental literature (Osaki et al. in J Polym Sci B Polym Phys 38:2043–2050, 2000), the model predicts, for a range of shear rates, two overshoots in shear stress during start-up of steady shear flows of bidisperse polymer melts having components with widely separated molar masses. Two overshoots result only when the stretch or Rouse relaxation time of the higher molar mass component is longer than the terminal relaxation time of the lower molar mass component. The “first overshoot” is the first to appear with increasing shear rate and occurs as a result of the stretching of longer chains. Transient stretching of the short chains is responsible for the early time second overshoot. The model predictions in steady and transitional extensional flows are also remarkable for both monodisperse and bidisperse polymer solutions. The computationally efficient differential model can be used to predict rheology of commercial polydisperse polymer melts and solutions. 相似文献
6.
Mahmoud Rajabian Ghassem Naderi Charles Dubois Pierre G. Lafleur 《Rheologica Acta》2010,49(1):105-118
Transient elongational rheology of two commercial-grade polypropylene (PP) and the organoclay thermoplastic nanocomposites
is investigated. A specifically designed fixture consisting of two drums (SER Universal Testing Platform) mounted on a TA
Instruments ARES rotational rheometer was used to measure the transient uniaxial extensional viscosity of both polypropylene
and nanoclay/PP melts. The Hencky strain rate was varied from 0.001 to 2 s − 1, and the temperature was fixed at 180°C. The measurements show that the steady-state elongational viscosity was reached at
the measured Hencky strains for the polymer and for the nanocomposites. The addition of nanoclay particles to the polymer
melt was found to increase the elongation viscosity principally at low strain rates. For example, at a deformation rate of
0.3 s − 1, the steady-state elongation viscosity for polypropylene was 1.4 × 104 Pa s which was raised to 2.8 × 104 and 4.5 × 104 Pa s after addition of 0.5 and 1.5 vol.% nanoclay, respectively. A mesoscopic rheological model originally developed to predict
the motion of ellipsoid particles in viscoelastic media was modified based on the recent developments by Eslami and Grmela
(Rheol Acta 47:399–415, 2008) to take into account the polymer chain reptation. We show that the orientation states of the particles and the rheological
behavior of the layered particles/thermoplastic hybrids can be quantitatively explained by the proposed model. 相似文献
7.
This work examines the possibility that the previously observed elastic yielding, i.e., nonquiescent relaxation after a large
step shear (Ravindranath and Wang, Macromolecules 40:8031–8039, 2007) is due to an intrinsic experimental difficulty technically known as edge fracture. By redesigning the rheometric apparatus
to eliminate edge failure, we show by an example of a well-entangled polymer solution that elastic yielding still occurs in
the absence of any edge failure. We are also able to confirm that shear banding during large amplitude oscillatory shear (Ravindranath
and Wang, J Rheol 52:341–358, 2008a) is an inherent rheological characteristic related to internal yielding of the entanglement network. 相似文献
8.
We study the rheological response of monodomain ellipsoidal biaxial liquid crystal polymers (BLCP) as well as bent-core or
V-shaped liquid crystal polymers (VLCP) subject to steady and time-dependent small amplitude oscillatory shear in selected
regions of the model as well as flow parameter space. We adopt the two newly developed hydrodynamical kinetic theories for
ellipsoidal BLCPs and VLCPs, respectively (Sircar and Wang, PRE 78:061702, 2008, J Rheol 53:819–858, 2009; Sircar et al., Comm Math Sci (in press), 2010), in which a generalized Straley’s potential is used to represent the pairwise mean-field interaction of the mesoscopic system
in biaxial phases. Transient shear stresses and normal stress differences corresponding to steady and small amplitude oscillatory
shear are investigated; their variations with respect to the strength of the intermolecular potential, types of biaxial interaction,
and changes in the aspect ratios for ellipsoidal BLCPs and the bent angle for VLCPs are explored. 相似文献
9.
Mahdi Abbasi Nadereh Golshan Ebrahimi Mahdi Nadali Masood Khabazian Esfahani 《Rheologica Acta》2012,51(2):163-177
Molecular stress function theory with new strain energy function is used to analyze transient extensional viscosity data of
seven low-density polyethylene (LDPE) melts with various molecular structures as published by Stadler et al. (Rheol Acta 48:479–490,
2009) Pivokonsky et al. (J Non Newton Fluid Mech 135:58–67, 2006) and Wagner et al. (J Rheol 47(3):779–793, 2003). The new strain energy function has three nonlinear viscoelastic material parameters and assumes that the total stored energy
of a branched molecule is given by different backbone and side chains stretching. The model parameters have been fitted for
each LDPE in order to correlate with the supposed macromolecular structure expected from the type of synthesis. Most probable
molecular structures for these LDPEs are comb and Cayley tree structures for respectively low- and high-molecular weight parts. 相似文献
10.
Deformation and wobbling of a liquid drop immersed in a liquid matrix were studied under mild shear conditions for various
viscosity ratios. In situ visualization experiments were conducted on a homemade transparent Couette cell incorporated to
the Paar Physica MCR500 shear rheometer. The effect of drop or matrix elasticity was examined and was found to play a major
role in both deformation and wobbling processes. Experimental results were compared to Jackson and Tucker (J Rheol 47:659–682,
2003), Maffettone and Minale (J Non-Newton Fluid Mech 78:227–241, 1998) and Yu and Bousmina (J Rheol 47:1011–1039, 2003) ellipsoidal models. It was found that the agreement between the Newtonian models and the experimental results required an
increase in the drop viscosity. Such increment in viscosity was found to scale with the first normal stress difference. 相似文献
11.
Christian Carrot Jean-Charles Majesté Beatriz Olalla René Fulchiron 《Rheologica Acta》2010,49(5):513-527
The purpose of the presented work was to test the capability of the model proposed by Leonov (J Rheol 34:1039–1068, 1990) for the prediction of secondary plateaus on the storage and loss moduli during small-amplitude oscillatory shear flow experiments
on filled or heterogeneous polymer melts. Though the occurrence of a plateau on the storage modulus can be well explained
in the frame of a filler network, a plateau on the loss modulus can hardly be described with the classical models. In the
Leonov model, the continuum of dissipative processes is attributed to the rupture of flocs of particles. Experiments with
polyolefins filled with magnesium hydroxide show that there is a clear connection between the amount of agglomerates and the
occurrence of a plateau on the loss modulus. However, the value of the critical strain for floc rupture that can be calculated
from the experiment shows that the processes responsible for the low-frequency dissipation are rather changes of configuration
within the agglomerates than floc rupture. These processes are not described by the Leonov model, and the predicted strain
dependence of the plateau is not observed experimentally. 相似文献
12.
We revisit the classical problem of the viscoelastic response of nematic (liquid crystal) polymers to small amplitude oscillatory
shear. A multiple time scale perturbation analysis is applied to the Doi–Hess mesoscopic orientation tensor model to describe
key features observed of longtime experiments, both physical (Moldenaers and Mewis, J Rheol, 30:567–584, 1986; Larson and Mead, J Rheol, 33:1251–1281, 1989b) and numerical (herein). First, there is a very slow time scale drift in the envelope of oscillations of the major director;
we characterize the mean director angle and the envelope of oscillation. Second, there are bistable asymptotic orientational
states, distinguished in that they are precisely the zero-stress orientational distributions noted in Larson and Mead (J Rheol,
33:185–206, 1989a). Third, the drift dynamics and asymptotic mean director angle are determined by the initial orientation of the director,
not by material properties; we characterize the domain of attraction of each bistable state. Finally, the director drift leads
to a predicted longtime decrease in the storage and loss moduli, consistent with experimental observations.
相似文献
M. Gregory ForestEmail: |
13.
Strain recovery after the cessation of shear was studied in model immiscible blends composed of polyisobutylene drops (10–30%
by weight) in a polydimethylsiloxane matrix. Blends of viscosity ratio (viscosity of the drops relative to the matrix viscosity)
ranging from 0.3 to 1.7 were studied. Most of the strain recovery was attributable to interfacial tension, and could be well-described
by just two parameters: the ultimate recovery and a single retardation time. Both these parameters were found to increase
with the capillary number of the drops prior to cessation of shear. For blends that had reached steady shear conditions, the
ultimate recovery decreased with increasing viscosity ratio, whereas the retardation time increased with increasing viscosity
ratio. The retardation time was well-predicted, but the ultimate recovery was over-predicted by a linear viscoelastic model
developed previously by Vinckier et al. (Rheol Acta 38:65–72, 1999). 相似文献
14.
《ournal of non Newtonian Fluid Mechanics》2004,118(1):65-81
The steady-state and transient shear flow dynamics of polymer drops in a microchannel are investigated using the dissipative particle dynamics (DPD) method. The polymer drop is made up of 10% DPD solvent particles and 90% finite extensible non-linear elastic (FENE) bead spring chains, with each chain consisting of 16 beads. The channel’s upper and lower walls are made up of three layers of DPD particles, respectively, perpendicular to Z-axis, and moving in opposite directions to generate the shear flow field. Periodic boundary conditions are implemented in the X and Y directions. With FENE chains, shear thinning and normal stress difference effects are observed. The “colour” method is employed to model immiscible fluids according to Rothman–Keller method; the χ-parameters in Flory–Huggins-type models are also analysed accordingly. The interfacial tension is computed using the Irving–Kirkwood equation. For polymer drops in a steady-state shear field, the relationship between the deformation parameter (Ddef) and the capillary number (Ca) can be delineated into a linear and nonlinear regime, in qualitative agreement with experimental results of Guido et al. [J. Rheol. 42 (2) (1998) 395]. In the present study, Ca<0.22, in the linear regime. As the shear rate increases further, the drop elongates; a sufficiently deformed drop will break up; and a possible coalescence may occur for two neighbouring drops. Dynamical equilibrium between break-up and coalescence results in a steady-state average droplet-size distribution. In a shear reversal flow, an elongated and oriented polymer drop retracts towards a roughly spherical shape, with a decrease in the first normal stress difference. The polymer drop is found to undergo a tumbling mode at high Schmidt numbers. A stress analysis shows that the stress response is different from that of a suspension of solid spheres. An overshoot in the strain is observed for the polymer drop under extension due to the memory of the FENE chains. 相似文献
15.
We discuss the anisotropy of the thermal conductivity tensor in polymer flow in this paper. Isotactic polypropylene (iPP)
specimens were deformed by injection moulding at high shear rates and by steady shear at low shear rates, and were then quenched.
The thermal conductivities parallel and perpendicular to the shear direction were measured using modulated differential scanning
calorimetry (MDSC) in accordance with the ASTM E1952-01. The measured results showed that the thermal conductivity of the
sheared polymer was anisotropic with an increase in the shear direction. The thermal conductivity can be regarded as varying
either with the strain or the stress, as suggested by Van den Brule (1989). In addition to the Van den Brule mechanism, crystallization during flow also changes the thermal conductivity and this
effect may often be dominant. Suggestions for procedures in processing computations, based on both effects, are given. 相似文献
16.
Y. Renardy 《Rheologica Acta》2006,45(3):223-227
Direct numerical simulations are conducted for a Newtonian drop in a Newtonian matrix subjected to large amplitude oscillatory
shear flows. In the experimental study of Guido et al. (in Rheol Acta 43:575–583, 2004), the drop shape is found to oscillate at higher harmonics of the forcing frequency when the capillary number is increased.
Their phenomenological model requires a much smaller capillary number for predicting the harmonic nature of the experimental
data. In this paper, computational results on the evolution of drop length and inclination angle are obtained at the same
fluid and flow properties as the experiments, and are shown to reasonably reproduce the experimental data. In particular,
the computed velocity fields around the drop are shown to elucidate the over-rotation, which is a mechanism for the experimentally
observed harmonics. 相似文献
17.
18.
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
19.
In this article, we consider the dynamics of short chains in frozen polymer networks, at different degrees of swelling. The
crosslinked networks are bimodal, at monomer densities ranging from 0.51 in the dry state to 0.098 at the maximum degree of
swelling. The 3D bond-fluctuation method is used to simulate the polymers, and we use a Monte Carlo method for monomer moves
which has been presented in an earlier publication (Nedelcu and Sommer, J Chem Phys 130:204902, 2009). Crossover scaling functions for the terminal relaxation times τ
d
and diffusion coefficients D of the short chains are observed to approach de Gennes’ reptation predictions, similar to what has already been observed
for long chains diffusing in polymer melts. However, the mean square displacement of a middle monomer of a chain in high-density
networks shows only two regimes, first subdiffusive with a scaling exponent close to 1/4, followed by a smooth transition
to free diffusion at longer times. 相似文献
20.
Víctor Hugo Rolón-Garrido Radek Pivokonsky Petr Filip Martin Zatloukal Manfred H. Wagner 《Rheologica Acta》2009,48(6):691-697
Experimental data of two low-density polyethylene (LDPE) melts at 200°C for both shear flow (transient and steady shear viscosity
as well as transient and steady first normal stress coefficient) and elongational flow (transient and steady-state elongational
viscosity) as published by Pivokonsky et al. (J Non-Newtonian Fluid Mech 135:58–67, 2006) were analysed using the molecular stress function model for broadly distributed, randomly branched molecular structures.
For quantitative modelling of melt rheology in both types of flow and in a very wide range of deformation rates, only three
nonlinear viscoelastic material parameters are needed: Whilst the rotational parameter, a
2, and the structural parameter, β, are found to be equal for the two melts considered, the melts differ in the parameter describing maximum stretch of the polymer chains. 相似文献