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1.
We describe experimental results on the extensional viscosity of mobile polymer solutions obtained from two instruments, the first being a commercial Spin Line Rheometer and the second a custom-built lubricated-die Converging Flow Rheometer. The interpretation of data in terms of Trouton ratios is facilitated by a simple analysis for the Generalized Newtonian Fluid model.Agreement between data from the two rheometers is satisfactory and we show that polymer solutions can be either tension stiffening or tension thinning. However, the Trouton ratios in both cases are greater than the Newtonian values and we anticipate that this will always be the case for polymer solutions.Invited paper, presented at the 2nd Conference of European Rheologists, Prague, June 17–20, 1986 相似文献
2.
D. Kivotides V.V. Mitkin T.G. Theofanous 《ournal of non Newtonian Fluid Mechanics》2009,161(1-3):69-85
We take a step towards accessing the physics of viscoelastic liquid breakup in high speed, high strain rate flows by performing Brownian dynamics computations of dilute uniaxial, equibiaxial, and ellipsoidal polymeric extensional flows. Our computational implementation of the bead-spring model, when tailored to the DNA molecule, consistently with recent works of Larson and co-workers, is shown: (a) to predict a coil-stretch transition at Deborah number De≈0.5, and (b) to reproduce the experimental longest relaxation time. Furthermore, after adapting the model parameters to represent the polyethylene oxide (PEO) chain (for M=106 Da), we find it possible to reproduce our own experimental data of the longest relaxation time, the transient extensional viscosity of dilute solutions at small Deborah numbers, and a coil-stretch transition at Deborah number De≈0.5. Extended to large Deborah numbers, the model predicts that polymer stretching is controlled by: (a) the randomness of the initial conditions that, in combination with rapid kinematically imposed compression, lead to the formation of initially frozen chain-folds, and (b) the speed with which thermo-kinematic processes relax these folds. The slowest fold relaxation occurs during uniaxial extension. As expected, the introduction of stretching along a second direction enhances the efficiency of fold relaxation mechanisms. Even for Deborah numbers (based on the chain longest relaxation time) of the order of one thousand, there is a large variation in the time a polymer needs in order to extend fully, and the effects of Brownian motion cannot be ignored. The computed Trouton ratios and polymer contributions to the total stress as functions of Hencky strain provide information about the relative importance of elastic effects during polymeric liquid stretching. At high strain rates, the steady state elastic stresses increase linearly with the Deborah number, resembling at that stage an anisotropic Newtonian fluid (constant extensional viscosity). 相似文献
3.
On the eddy viscosity model of periodic turbulent shear flows 总被引:4,自引:0,他引:4
Physical argument shows that eddy viscosity is essentially different from molecular viscosity. By direct numerical simulation,
it was shown that for periodic turbulent flows, there is phase difference between Reynolds stress and rate of strain. This
finding posed great challenge to turbulence modeling, because most turbulence modeling, which use the idea of eddy viscosity,
do not take this effect into account.
The project supported by the National Natural Science Foundation of China (19732005) and Liu Hui Center for Applied Mathematics
of Nankai & Tianjin University 相似文献
4.
Dilip Rajagopalan 《Rheologica Acta》2000,39(2):138-151
Recent computational analysis of entrance flows (Mitsoulis et al. 1998) suggests that the entrance pressure drop is insensitive
to large changes in steady extensional viscosity-a result that directly contradicts a large body of experimental work in this
area. A re-examination of entrance flows using numerical simulations is presented in this work which shows that entrance pressure
drops do depend on the steady extensional viscosity, provided the extension rate in the entrance flow is large enough. Numerical
simulations are presented using both the strain thinning and thickening versions of the Phan-Thien–Tanner (PTT) constitutive
model. Several techniques for extracting extensional viscosity from entrance pressure are applied to the results of these
simulations. The resulting predictions of extensional viscosity are compared to the steady extensional viscosity curves predicted
by the PTT constitutive model used to generate the simulated pressure drop curves. The analytical techniques examined here
are shown to provide reasonably accurate estimates of the steady extensional viscosity. This work also clearly demonstrates
the advantage of using variable power-law coefficients for the rheological properties, used as inputs to the analyses, to
capture the extensional behavior at deformation rates below the power law region more accurately.
Received: 23 July 1999/Accepted: 24 November 1999 相似文献
5.
Polymer melt viscoelastic fluids often exhibit in elongational flows a significant increase in the elongational viscosity known as strain hardening. This phenomenon could be related to polydispersity, e.g. the presence of a small fraction of very high molecular weight chains whose time frame relaxation spectrum is different from the small chains one. In the present work, we present a fully objective constitutive equation (CE) to primarily model extensional strain hardening based on the new concept of multiple configuration materials. Next, we analyze the CE stability properties with respect to small perturbations about the rest state. 相似文献
6.
Stephen E. Bechtel Nivine T. Youssef M. Gregory Forest Hong Zhou Kurt W. Koelling 《Rheologica Acta》2001,40(4):373-383
A model for oscillating free surface jet flow of a fluid from an elliptical orifice, together with experimental measurements,
can be exploited to characterize the elongational viscosity of non-Newtonian inelastic fluids. The oscillating jet flow is
predominantly elongational, with a small strain that oscillates rapidly between large and zero strain rates. We find that
to reproduce the experimentally observed steady oscillating jet flow in model simulations, the assumed form of the non-Newtonian
viscosity as a function of strain rate must have zero gradient, i.e., be Newtonian, at zero strain rate (a behavior exhibited,
in general, by real inelastic fluids). We demonstrate that the Cross, Carreau, Prandtl-Eyring, and Powell-Eyring forms, although
they have finite viscosity at zero strain rate, have either nonzero or even unbounded gradient at zero, and hence are unable
to model oscillating jet behavior. We propose a new non-Newtonian viscous form which has all of the desirable features of
existing forms (high and low strain rate plateaus, with adjustable location and steepness of the transition) and the additional
feature of Newtonian behavior at low strain rates.
Received: 7 February 2000 Accepted: 31 October 2000 相似文献
7.
8.
A study is undertaken to ascertain non-Newtonian effects in steady flows of elastic fluids due to an infinite rotating disk when there is suction across its surface. The fluids considered are of a class for which the similarity-type solution of von Kármán is an exact solution. It is shown that the presence of elasticity (of the type considered) does not result in flow reversal, the disk acting as a centrifugal fan as in Newtonian flow. 相似文献
9.
Based on elasticity theory, various two-dimensional (2D) equations and solutions for extensional deformation have been deduced
systematically and directly from the three-dimensional (3D) theory of thick rectangular plates by using the Papkovich–Neuber
solution and the Lur’e method without ad hoc assumptions. These equations and solutions can be used to construct a refined
theory of thick plates for extensional deformation. It is shown that the displacements and stresses of the plate can be represented
by the displacements and transverse normal strain of the midplane. In the case of homogeneous boundary conditions, the exact
solutions for the plate are derived, and the exact equations consist of three governing differential equations: the biharmonic
equation, the shear equation, and the transcendental equation. With the present theory a solution of these can satisfy all
the fundamental equations of 3D elasticity. Moreover, the refined theory of thick plate for bending deformation constructed
by Cheng is improved, and some physical or mathematical explanations and proof are provided to support our justification.
It is important to note that the refined theory is consistent with the decomposition theorem by Gregory. In the case of nonhomogeneous
boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order
terms with respect to plate thickness. The correctness of the stress assumptions in the classic plane-stress problems is revised.
In an example it is shown that the exact or accurate solutions may be obtained by applying the refined theory deduced herein. 相似文献
10.
11.
J. W. Banks 《国际流体数值方法杂志》2011,65(5):602-608
In this short note we describe a simple extension to the multi‐material shock‐capturing algorithm presented in (J. Comput. Phys. 2007; 223 :262–297) that can be used to maintain sharp material interfaces. The method takes the form of an artificial compression which is designed so that the material indicator jumps across only a few cells but which does not excite physical instabilities in the flow. The advantages of the approach include its simplicity and flexibility in that it provides a parameter that effectively determines the captured interface thickness. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
12.
Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS (URANS). Some typical linear and nonlinear eddy viscosity turbulence models (LEVM and NLEVM) and a quadratic explicit algebraic stress model (EASM) are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding. 相似文献
13.
An algorithm is derived for calculating flow-induced birefringence using a bead-spring model with and without excluded volume
effects. The simulation results for the bead-spring model compare well with experimental results for stress and birefringence
in extensional flows of dilute solutions of polystyrene molecular weight 2 million in a filament-stretching device in both
“theta” and “good” solvents (Orr and Sridhar 1999; Sridhar et al. 2000). In a “good” solvent, both stress and birefringence
rise much more rapidly with strain than in a “theta” solvent, making extensional rheology a very sensitive indicator of solvent
quality.
Received: 7 December 1999 Accepted: 23 May 2000 相似文献
14.
Abdelaziz Mestadi Magdeleine Normandin Dr. Jean-Robert Clermont Pierre Attané 《Rheologica Acta》1996,35(4):337-346
In this paper, we propose a numerical simulation of axisymmetric extensional experiments on a viscoelastic polydimethylsiloxane (PDMS) material, using a falling-weight extensional rheometer. The polymer behaviour is represented by a K-BKZ memory-integral constitutive equation, involving a damping function of the Wagner type. Under the assumption of a homogeneous flow zone in the sample, a numerical model is set up, using the stream-tube method and approximating functions. The governing equations of the problem, associated to a limited number of unknowns, are solved by means of the Levenberg-Marquardt optimization algorithm. The numerical results are found to be consistent with the experimental data and reveal the importance of the non-homogeneous flow zone, in relation to the estimation of the extensional strain rate. The calculations involve the sensitivity of the model on the fluid parameters and those concerning the size of the initial column of fluid. The limited computing (CPU) time of the code is also to be underlined. 相似文献
15.
J. R. Jones 《Rheologica Acta》1975,14(5):397-401
Summary An analysis is presented of steady (isothermal) co-current laminar flows of two immiscible elasticoviscous liquids in cylindrical channels to include (i) unidirectional stratified flow with ripple-free, plane liquid interface, and (ii) concentric-layered swirling flow with ripple-free cylindrical liquid interface. The general conditions are derived for such two-phase channel flows to be physically realizable. It is shown that, whereas (under certain circumstances)single-phase laminar flows are physically possible,two-phase flows, on the other hand, of liquids of the same class may not be. But liquids of theRoberts type (Roberts 1953), with a normal stress difference equivalent to an extra simple tension along the streamlines in simple shearing, are capable of steady unidirectional flowin all circumstances (whether in single or two-phase flow), though they are not in a privileged position so far astwo-phase swirling flows are concerned. 相似文献
16.
We consider the potential energy of the equlibrium configuration under gravity and prescribed vertical forces or displacement of a vertical bar which is composed of a mixture of two elastic materials. It is supposed that in each horizontal cross section the mixture has an effective Young's modulus which depends only on the ratio of the two materials in that cross section, and that the dependence satisfies the bound of Paul [2].It is shown that among all arrangements of the constituents with a given volume fraction, the smallest potential energy is attained when one of the materials is segregated in a single horizontal layer. This result suggests that when a composite cylinder is kept in such a state of strain, its constituent material will eventually diffuse into this segregated state.
Sommario Si considerano le possibili configurazioni di equilibrio di una sbarra composta da una miscela solida di due materiali elastici, posta in posizione verticale e soggetta, oltre al campo gravitazionale, ad una azione, forza o spostamento applicato, in corrispondenza di una estremità. Si suppone che, in ogni sezione trasversale, il modulo di Young della sbarra dipenda solo dal rapporto locale fra i due componenti della miscela in quella sezione e che questa dipendenza soddisfi la diseguaglianza di Paul [2].Viene mostrato che fra tutte le possibili disposizioni dei due materiali base presenti all'interno del corpo in quantità assegnata, quella che corrisponde ad un minimo per l'energia potenziale prevede che uno dei due componenti si separi dall'altro, concentrandosi in un singolo strato orizzontale. Questo risultato suggerisce che quando un cilindro composito è sottoposto a queste sollecitazioni, i suoi materiali costituenti tenderanno a diffondersi e, alla fine, a separarsi.相似文献
17.
In this study, three EVAs (ethylene-vinyl acetate co-polymers) with different vinyl contents (VA) ranging from 9 wt% to 28 wt% (EVA9, EVA18 and EVA28) were melt blended with organo-clay to obtain polymer layered silicate nanocomposites. Filler intercalation and exfoliation were evidenced by X-ray diffraction. The melt state viscoelastic properties of EVA nanocomposites were studied to examine the influence of clay in altering the flow properties of these polymeric nanocomposites. The EVA18 and EVA28 nanocomposites exhibited remarkable difference in dynamic and steady shear properties compared to neat polymers. On the other hand, EVA9-5% nanocomposite did not exfoliate and exhibited rheological behaviour very similar to that of the neat polymer. Furthermore, the first normal stress difference was found to be dependent on the silicate loadings when measured at low shear stresses. The uniaxial extensional viscosity measurement indicated that the strain hardening was weaker in EVA nanocomposites compared to neat polymers. Environmental scanning electron (ESE)-microscopy elucidated a possible reason for reduced strain hardening in these systems. 相似文献
18.
The Larson-Doi (LD) polydomain model is used to simulate orientation development along the centerline of slit-expansion and
slit-contraction flows of liquid crystalline polymers (LCPs). Orientation is computed using the LD structural evolution equations,
subject to an imposed velocity field that accounts for the spatial variation of both shear and extension rates characteristic
of this class of flows. Computed axial distributions of orientation averaged through the sample thickness are qualitatively
similar to birefringence and X-ray scattering measurements of molecular orientation in similar flows of lyotropic and thermotropic
LCPs. In slit-expansion flows, the simulations predict a 90∘ flip in orientation direction near the midplane due to transverse stretching in the expansion region. Far away from the midplane
where shear gradients dominate, orientation remains primarily along the flow direction. Within the LD model, tumbling and
flow aligning materials respond in a qualitatively similar manner to mixed shear and extension, although tumbling materials
are systematically more susceptible to the effects of extension.
Received: 22 October 1999/Accepted: 13 January 2000 相似文献
19.
Over the last decade several international programmes have been developed around different standard fluids, one of which
is the so-called S1 fluid. This is a solution of polyisobutylene in a mixed solvent and the aim of the programme has been
to study the rheology of polymer solutions from the dilute solution to the melt. The focus of this paper will be on the flow
visualisation of contraction flows of S1 through orifice dies and on the estimation of some of its extensional properties.
The contraction ratios range from 24.4:1 and 124.3:1. The measured entry pressure drops will be correlated with contraction
ratio and apparent wall shear rate. Experimental evidence will show that, when regarded as a function of wall shear rate,
the entry pressure drops are independent of the contraction ratios. The flow fields for different contraction ratios, at any
constant apparent wall shear rate, however, differ substantially. The evolution of the flow fields is monitored and it is
shown that an initial increase in vortex size is followed by a slower decrease, this happening at a constant Weissenberg number.
At the same Weissenberg number, small scale instabilities start occurring near the office. As the shear rate is increased
further, these instabilities grow in size until, eventually, the flow structure is destroyed. An extensional viscosity is
evaluated using a modified form of the Binding analysis for contraction flows and we show that the results are not only in
qualitative agreement with those from other groups, but also that the analysis is able to predict exactly the onset of the
aforementioned flow instabilities.
Received: 20 March 1997 Accepted: 18 September 1997 相似文献
20.
Manfred H. Wagner Heike Bastian Peter Hachmann Joachim Meissner Stefan Kurzbeck H. Münstedt F. Langouche 《Rheologica Acta》2000,39(2):97-109
By generalizing the Doi-Edwards model to the Molecular Stress Function theory of Wagner and Schaeffer, the extensional viscosities
of polyolefin melts in uniaxial, equibiaxial and planar constant strain-rate experiments starting from the isotropic state
can be described quantitatively. While the strain hardening of four linear polymer melts (two high-density polyethylenes,
a polystyrene and a polypropylene) can be accounted for by a tube diameter that decreases affinely with the average stretch,
the two long-chain-branched polymer melts considered (a low-density polyethylene and a long-chain branched polypropylene)
show enhanced strain hardening in extensional flows due to the presence of long-chain branches. This can be quantified by
a molecular stress function, the square of which is quadratic in the average stretch and which follows from the junction fluctuation
theory of Flory. The ultimate magnitude of the strain-hardening effect is governed by a maximum value of the molecular stress,
which is specific to the polymer melt considered and which is the only free non-linear parameter of the theory.
Received: 1 June 1999/Accepted: 24 November 1999 相似文献