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1.
Using the fact that for simple fluids the most general constitutive equation in constant stretch history flows for the extra
stress tensor τ is known in an explicit form, the Giesekus fluid model is cast into this (ω–D) form for two-dimensional flows. The three material functions needed to characterize τ are listed. The explicit results for
simple shear and planar elongation reveal that the parameter α should be restricted to values less than 0.5. It is demonstrated
that in this explicit form the constitutive equation is free from thermodynamic objections and can thus be used as a starting
point for numerical calculations of general, but steady, two-dimensional flows.
Received: 9 November 1998 Accepted: 20 May 1999 相似文献
2.
《ournal of non Newtonian Fluid Mechanics》2001,97(1):13-30
Numerical simulations have been undertaken for the creeping entry flow of a well-characterized polymer melt (IUPAC-LDPE) in a 4:1 axisymmetric and a 14:1 planar contraction. The fluid has been modeled using an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times (Papanastasiou–Scriven–Macosko or PSM model). Numerical values for the constants appearing in the equation have been obtained from fitting shear viscosity and normal stress data as measured in shear and elongational data from uniaxial elongation experiments. The numerical solutions show that in the axisymmetric contraction the vortex in the reservoir first increases with increasing flow rate (or apparent shear rate), goes through a maximum and then decreases following the behavior of the uniaxial elongational viscosity. For the planar contraction, the vortex diminishes monotonically with increasing flow rate following the planar extensional viscosity. This kinematic behavior is not in agreement with recent experiments. The PSM strain-memory function of the model is then modified to account for strain-hardening in planar extension. Then the vortex pattern shows an increase in both axisymmetric and planar flows. The results for planar flow are compared with recent experiments showing the correct trend. 相似文献
3.
The shear orientation of hexagonal and lamellar liquid crystalline phases of polymeric surfactants was investigated by rheo-optical
techniques (flow birefringence (Δn), small-angle light scattering) as well as by nuclear magnetic resonance and optical microscopy. The evolution of birefringence
in the hexagonal phase is discussed for simple and oscillatory shear, and an alignment of rodlike micelles along the flow
direction was found. A shear induced formation of vesicles (“onions”) is observed with the lamellar phase. They displayed
a characteristic four-lobe pattern in depolarized light scattering. Above a critical shear stress vesicles were degraded and
perpendicularly aligned lamellae (i.e. with their normal along the vorticity direction) were obtained. A comparison of experiments
performed at constant stress and constant rate revealed that the vesicle to planar lamellae transition occurred above a critical
shear stress. The behavior of the polysoap lyotropic mesophases under shear, i.e. the strain dependent alignment in the hexagonal
phase, the shear induced formation of vesicles, and a transition to planar lamellae in the lamellar phase, is very similar
to the behavior of lyotropic mesophases formed by low molar mass surfactants or amphiphilic block copolymers. The geometrical
constraints that are introduced when amphiphilic side groups are fixed to a polymer backbone do not significantly alter the
response of the mesophase to a shear deformation.
Received: 4 May 1999 /Accepted: 19 July 1999 相似文献
4.
A recently developed rheological technique known as continuous lubricated squeezing flow (CLSF) is adapted to perform constant stress, or creep, experiments in equibiaxial elongation flows of polymer melts. By modifying the CLSF technique, which was developed for constant strain rate deformations, we demonstrate that the technique can also be used to generate constant stress flows. Measured steady state viscosities are compared to constant rate elongation results for polymer melts having different molecular characteristics. Linear polymers show strain softening and compare well in constant stress and constant strain rate deformations. The branched polymer shows strain hardening and a viscosity that is slightly higher in constant stress for low rates. Limitations of the current version of the CLSF technique for creep flows are also briefly discussed. 相似文献
5.
The purpose of the present study is to compare numerical simulations of viscoelastic flows using the differential Oldroyd-B constitutive equations and two newly devised simplified algebraic explicit stress models (AES-models). The flows of a viscoelastic fluid in a 180° bent planar channel and in a 4:1 planar contraction are considered to illustrate and support the underlying theory. The flow in the bent channel is used to illustrate the frame-invariant property of the new models in a pure shear flow exhibiting strong streamline curvature. The flow in the 4:1 contraction serves as a benchmark test in a situation where strong elongation occurs. For both geometries, it is found that the predictions of the new AES-models are in good agreement with Oldroyd-B up to Deborah numbers of order 0.5, with a significant reduction in computational effort. 相似文献
6.
Enric Santanach Carreras Nadia El Kissi Jean-Michel Piau Fabrice Toussaint Sophie Nigen 《Rheologica Acta》2006,45(3):209-222
In the present work, the effects of pressure on the viscosity and flow stability of four commercial grade polyethylenes (PEs)
have been studied: linear-low-density polyethylene copolymer, high-density polyethylene, metallocene polyethylenes with short-chain
branches (mPE-SCB), and metallocene polyethylenes with long chain branching (mPE-LCB). The range of shear rates considered
covers both stable and unstable flow regimes. “Enhanced exit-pressure” experiments have been performed attaining pressures
of the order of 500×105 Pa at the die exit. The necessary experimental conditions have been clearly defined so that dissipative heating can be neglected
and pressure effects isolated. The results obtained show an exponential increase in both shear and entrance-flow pressure
drop with mean pressure when shear rate is fixed and as long as flow is stable. These pressure effects are described by two
pressure coefficients, βS under shear and, βE under elongation, that are calculated using time–pressure superposition and that are independent of mean pressure and flow
rate. For three out of four PE, pressure coefficient values can be considered equal under shear and under elongation. However,
for the mPE-LCB, the pressure coefficient under elongation is found to be about 30% lower than under shear. Flow instabilities
in the form of oscillating flows or of upstream instabilities appear at lower shear rates as mean pressure increases. Nevertheless,
the critical shear stress at which they are triggered remains independent of mean pressure. Moreover, it is found that the
βS values obtained for stable flows do not differ much from the values obtained during upstream instability regimes, and differ
really from pressure effects observed under oscillating flow and slip conditions. 相似文献
7.
Modification of near-wall turbulence structure in a shear-driven three-dimensional turbulent boundary layer 总被引:2,自引:0,他引:2
Most high Reynolds number flows of engineering interest are three-dimensional in nature. Key features of three-dimensional
turbulent boundary layers (3DTBLs) include: non-colateral shear stress and strain rate vectors, and decreasing ratio of the
shear stresses to the turbulent kinetic energy with increasing three-dimensionality. These are indicators that the skewing
has a significant effect on the structure of turbulence. In order to further investigate the flow physics and turbulence structure
of these complex flows, an innovative method for generating a planar shear-driven 3DTBL was developed. A specialized facility
incorporating a relatively simple geometry and allowing for varying strengths of crossflow was constructed to facilitate studies
where the skewing is decoupled from the confounding effects of streamwise pressure gradient and curvature. On-line planar
particle image velocimetry (PIV) measurements and flow visualization results indicate that the experimental configuration
generates the desired complex flow, which exhibits typical characteristics associated with 3DTBLs. Furthermore, spanwise shear
results in modification of the near-wall turbulence structure. Analysis of near-wall flow visualization photographs revealed
a reduction of mean streak length with increasing spanwise shear, while streak spacing remained relatively constant. In the
most strongly sheared case, where the belt velocity is twice that of the freestream velocity, the mean streak length was reduced
by approximately 50%.
Received: 28 October 1997/Accepted: 4 February 1998 相似文献
8.
Planar contraction flows of non-Newtonian fluids with integral constitutive models are studied to investigate the problem
of numerical breakdown at high Weissenberg or Debrorah numbers. Spurious shear stress extrema are found on the wall downstream
of the re-entrant corner for both sharp and rounded corners. Moreover, a non-monotonic relation between shear stress and strain
rate is found when the Deborah number limit is approached, which correlates with these shear extrema. This strongly suggests
that non-monotonicity between shear stress and strain rate may be responsible for the Deborah number limit problem in contraction
flow simulations. This non-monotonicity is caused by the inaccuracy of the quadrature, using constitutive equations that do
not have shear stress maxima when exactly evaluated. This conclusion agrees with recent analytical findings by others that
inaccuracy of the integration along the streamlines – either by numerical integration or asymptotic approximation – makes
the problem ill-conditioned, with spurious growth occurring on the wall downstream of the re-entrant corner.
Received: 5 March 1999/Accepted: 1 September 1999 相似文献
9.
In this paper a theory is presented in which the extra stress tensor is allowed to depend not only on the rate of strain tensor but also on the relative vorticity of the fluid, i.e. on the vorticity relative to the rate of rotation of the principal straining directions. This theory has
its origin in an expansion of in terms of kinematic tensors in the limit of stationarity in a material sense (constant stretch history flows). For two
dimensional flows of an incompressible fluid three tensors suffice to completely specify . The three material functions which appear can depend only on two invariants, namely the second invariant of and on . Using the predictions of an Oldroyd 8 constant fluid in a homogeneous planar flow of constant stretch history, the three
material functions are studied in detail. For the special case of a quasi-Newtonian fluid shear thinning and extension thickening
can directly be accounted for in the “viscosity” function.
Received: September 26, 1996 相似文献
10.
The extensional viscosity of some flexible chain polymers and a thermotropic liquid crystalline polymer was measured in uniaxial extensional flow at constant extension rate. Power law functions were found for the dependence of the extensional viscosity at constant accumulated strain on strain rate. The stress growth curves were compared with measurements in axisymmetric entry flow, where both elongation and shear occur. The comparison showed that the values of the extensional viscosity calculated from the measurements in the entry flow correspond to the ones calculated from the viscosity growth measured in uniaxial elongation and averaged over extensional strain equal to what is accumulated on the fluid as it flows from the barrel into the capillary. 相似文献
11.
The viscoelastic behavior of polymeric systems based upon the Leonov model has been examined for (i) the stress growth at constant strain rate, (ii) the stress growth at constant speed and (iii) the elastic recovery in elongational flow. The model parameters have been determined from the available rheological data obtained either in steady shear flow (shear viscosity and first normal-stress difference as a function of shear rate) or oscillatory flow (storage and loss moduli as a function of frequency in the linear region) or from extensional flow at very small strain rates (time-dependent elongation viscosity in the linear viscoelastic limit). In addition, the effect of the parameter characterizing the strain-hardening of the material during elongation has also been studied. The estimation of this parameter has been based upon the structural characteristics of the polymer chain which include the critical molecular weight and molecular weight of an independent segment. Five different polymer melts have been considered with varying number of modes (maximum four modes). Resulting predictions are in fair agreement with corresponding experimental data in the literature. 相似文献
12.
The shear orientation of viscoelastic clay-polymer solutions was investigated by means of rheology and flow birefringence
(Δn). The polymer chains are in dynamic adsorption/desorption equilibrium with the clay particles to form a “network”. The
elastic behavior of the network was characterized by constant stress, oscillatory shear, and stress relaxation experiments.
Constant stress experiments indicated a yield stress upon which shear flow started and no strain recovery could be observed.
Oscillatory shear experiments showed a broad elastic region followed by flow when a critical strain was reached. Stress relaxation
experiments showed several relaxation times when the same critical strain was reached. Experiments under steady flow characterized
the transient behavior of the network. With increasing steady shear rate a pronounced minimum in birefringence was observed
at a critical shear rate. The shear rate dependent viscosity showed near power law behavior and no corresponding critical
feature. While birefringence detects orientational effects on a microscopic length scale, rheology averages over macroscopic
changes in the sample. The same degree of orientation could be achieved under constant shear rate or constant stress conditions.
Received: 25 January 2001 Accepted: 22 May 2001 相似文献
13.
S. E. Stephenson 《Rheologica Acta》1986,25(1):62-65
Similarities between simple shear and pure shear or planar extension are exploited to derive equations relating stress in pure shear at constant extension rate to the stress in simple shear at constant shear rate. For the class of materials considered it follows that there are only two independent material functions required to describe simple shear. The relationships derived may also be used to estimate the ratio of first to second normal-stress differences in simple shear using experimental results from pure shear experiments. 相似文献
14.
R. G. Larson 《Rheologica Acta》1985,24(5):443-449
It is herein shown that for separable integral constitutive equations with power-law distributions of relaxation times, the streamlines in creeping flow are independent of flow rate.For planar flows of constant stretch history, the stress tensor is the sum of three terms, one proportional to the rate-of-deformation tensor, one to the square of this tensor, and the other to the Jaumann derivative of the rate-of-deformation tensor. The three tensors are the same as occur in the Criminale-Ericksen-Filbey Equation, but the coefficients of these tensors depend not only on the second invariant of the strain rate, but also on another invariant which is a measure of flow strength. With the power-law distribution of relaxation times, each coefficient is equal to the second invariant of the strain rate tensor raised to a power, times a function that depends only on strength of the flow. Axisymmetric flows of constant stretch history are more complicated than the planar flows, because three instead of two nonzero normal components appear in the velocity gradient tensor. For homogeneous axisymmetric flows of constant stretch history, the stress tensor is given by the sum of the same three terms. The coefficients of these terms again depend on the flow strength parameter, but in general the dependences are not the same as in planar flow. 相似文献
15.
16.
The spectral element method is applied on unstructured tetrahedral elements to solve the Navier–Stokes equations for fully developed laminar flow in pipes with two planar curvatures. Specific implementations of the spectral element method to double curved pipes and parallelization are described. Previous studies on flows in pipes focused on constant curvature or torsion geometries, as well as pipes with varying curvature. This study focuses on the periodic variation of both the curvature as well as torsion by analysing a pipe having two planar curvatures. The effects of the three parameters defining the pipe are studied to isolate the curvature and torsion effect on the magnitude and angle of the secondary flow. Furthermore, the geometric effects on the wall shear stress are studied, as it is an important fluid flow property, especially in blood flows. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
17.
The equations of linear and angular momentum for nematic liquid crystals have been described with Ericksen's transversely
isotropic fluid [TIF] model and solved for start-up of shear flow at constant rate and varying initial alignment conditions.
An analytical solution for the rotation provides predictions of the nematic director which closely agree with experimental
results of Boudreau et al. (1999), supporting the validity of Ericksen's TIF model. The solution is limited to flows where
the effects of director gradients are negligible.
Received: 13 September 1999/Accepted: 24 January 2000 相似文献
18.
J. L. Amundarain L. J. Castro M. R. Rojas S. Siquier N. Ramírez A. J. Müller A. E. Sáez 《Rheologica Acta》2009,48(5):491-498
Mixtures of xanthan and guar gum in aqueous solution were studied in two flow situations: simple shear and porous media. In
addition, solids transport in vertical annular flow of sand suspensions was explored. The zero shear rate viscosity of the
solutions displayed a pronounced synergy: the viscosity of the mixture is higher than that of the polymer solutions in a wide
range of relative concentrations of the two polymers, in agreement with previous literature. However, at relatively high shear
rates, the viscosity approaches the value of the more viscous xanthan gum solutions at mass fractions of xanthan gum between
0.1 and 0.15, and the degree of synergy substantially decreases. Stress relaxation experiments in simple shear indicate that
the polymer mixtures exhibit a well-defined yield stress after relaxation that is absent in solutions of pure polymers. In
porous media flow experiments, a synergistic behavior mimicking the shear flow results was obtained for the polymer mixtures
at low shear rates. However, at a critical shear rate, the apparent viscosity in porous media flows exceeds the shear viscosity
due to the elongational nature of flow in the pores. The solids transport capacity in annular flows is well-represented by
trends in shear viscosity and stress relaxation behavior. However, the lack of viscosity synergy at high shear rates limits
the applicability of the mixtures as a way to improve solids suspension capacity in annular flows. 相似文献
19.
20.
The liquid crystalline (LC) polymers are considered as anisotropic viscoelastic liquids with nonsymmetric stresses. A simple
constitutive equation for nematic polymers describing the coupled relaxation of symmetric and antisymmetric parts of the stress
tensor is formulated. For illustration of non-symmetric anisotropic viscoelasticity, the simplest viscometric flows of polymeric
nematics in the magnetic field are considered. The frequency and shear rate dependencies of extended set of Miesowicz viscosities
are predicted.
Received: 23 March 1999/Accepted: 13 December 1999 相似文献