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- The Rayleigh Approach to the Rheology of Compressible Granular
Flow
- Tommaso Astarita, Raffaella Ocone, and Gianni Astarita
- The Continuous Chain Model for the Elastic Extensionof Polymer
Fibres in the Glassy State
- J.J.M. Baltussen, M.G. Northolt, and R. van der Hout
- The Elastic Extension of Polymer Fibres in the Glassy State:
Experimental Results
- J.J.M. Baltussen and M.G. Northolt
- Yield Stress in MR and ER Fluids: A Comparison Between Microscopic
and Macroscopic Structural Models
- G. Bossis, E. Lemaire, O. Volkova, and H. Clercx
- Shear Induced Gelation of Colloidal Dispersions
- B. Cabane, K. Wong, P. Lindner, and F. Lafuma
- Flow of RX-08-FK High-Energy Paste in a Capillary Rheometer
- J. F. Carley, E. von Holtz, and G. L. Flowers
- Migration of Particles Undergoing Pressure Driven Flow in a
Circular Conduit
- R. E. Hampton, A. A. Mammoli, A. L. Graham, N. Tetlow, and S. A. Altobelli
- Viscoelastic Material Functions of Noncolloidal Suspensions with
Spherical Particles
- Birnur K. Aral and Dilhan M. Kalyon
- Reentrant Corner Flows of Newtonian and Non-Newtonian Fluids
- Joel Koplik and Jayanth R. Banavar
- Extensional Rheometry of Polymer Multilayers: A Sensitive Probe of
Interfaces
- Leon Levitt, Christopher W. Macosko, Thomas Schweizer, and Joachim Meissner
- The Two-Way Interaction Between Anisotropic Flow and Fiber
Orientation in Squeeze Flow
- K. A. Ericsson, S. Toll, and J.-A. E. Månson
- Viscosity Equation for Concentrated Suspensions of Charged
Colloidal Particles
- A. Ogawa, H. Yamada, S. Matsuda, K. Okajima, and M. Doi
- Transient Rheological Response and Morphology Evolution of
Immiscible Polymer Blends
- I. Vinckier, P. Moldenaers, and J. Mewis
- Molecular-Level Modeling of the Viscoelasticity of Crosslinked
Polymers - Effect of Time and Temperature
- Philip P. Simon and Harry J. Ploehn
- A Recursive Model for Rheotens Tests
- V. Rauschenberger and H. M. Laun
- Rheology and Phase Separation in a Model UCST Polymer Blend
- D. Vlassopoulos, A. Koumoutsakos, S. H. Anastasiadis, S. G. Hatzikiriakos, and P.
Englezos
- Accurate Simulation of Linear Viscoelastic Properties by Variance
Reduction Through the Use of Control Variates
- Norman J. Wagner and Hans Christian Öttinger
The Rayleigh Approach to the Rheology of
Compressible Granular Flow
Tommaso Astarita1, Raffaella Ocone2, and Gianni
Astarita3
1 Department of Energetics, Thermofluodynamics and Environmental Control
3 Department of Materials and Production Engineering
Universita' di Napoli "Federico II"
Piazzale Tecchio 80, 80125 Napoli, Italy
2Department of Chemical Engineering
University of Nottingham
University Park, Nottingham NG7 2RD, England
Abstract
We develop a Rayleigh-type approach to the analysis of compressible granular flow. In
this approach, a (possibly negative) influx of energy from the walls is taken into
account. This is greatly advantageous in granular flow rheology, since such influx of
energy arises spontaneously as soon as the balance between the energy influx (due to
whatever mechanism keeps the unperturbed system in a thermalized state) and the
dissipation rate is violated. We show that standing waves, although waves of a rather
peculiar type, may well exist, and that such waves have thicknesses of several hundreds
particle diameters. We also give an analysis of the stability of compressible granular
flow, which exhibits some peculiar characteristics.
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The Continuous Chain Model for the Elastic
Extension
of Polymer Fibres in the Glassy State
J.J.M. Baltussen1*, M.G. Northolt2, and R. van der
Hout2
1AKZO Nobel Central Research
Zutphenseweg 10, P.O. Box 10
7400 AA Deventer, The Netherlands
2AKZO Nobel Central Research
Velperweg 76, P.O. Box 9300
6800 SB Arnhem, The Netherlands
*Corresponding author
Abstract
Fibres of linear polymers below the glass transition show a strong nonlinear
deformation behaviour even at small strains. The elastic modulus is a fast increasing
function of the strain. A new model for the description of the deformation of these fibres
is presented. It is assumed that the fibre consists of long and continuous polymer
chains which do not break during the extension of the fibre. The deformation of the fibre
is calculated for finite strains and arbitrary values of the orientation parameter.
Equations for the elastic stress versus strain curve and modulus versus strain curve have
been derived. The model can be used for the calculation of the modulus of isotropic and
sheets with uniplanar orientation as well.
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The Elastic Extension of Polymer Fibres in
the Glassy State:
Experimental Results
J.J.M. Baltussen1* and M.G. Northolt2
1AKZO Nobel Central Research
Zutphenseweg 10, P.O. Box 10
7400 AA Deventer, The Netherlands
2AKZO Nobel Central Research
Velperweg 76, P.O. Box 9300
6800 SB Arnhem, The Netherlands
*Corresponding author
Abstract
The results of the continuous chain model for the elastic deformation of
polymer fibres in the glassy state, which has been presented in the previous paper, is
compared to the results from experiments on PpPTA, PET, cellulose and PE fibres, and PpPTA
ant PET sheets. The calculated elastic stress versus strain curve is compared to the
experimental curve of PpPTA fibres. The predicted relation between the elastic modulus
versus strain curve and the orientation of the fibre during extension are compared to the
results obtained by X-ray diffraction. The effect of plastic deformation on the
experimental modulus versus strain curve is considered, and a new method for the
experimental determination of the shear modulus g from the elastic modulus versus
strain curve is presented. The calculated elastic modulus versus strain curves are
compared to the experimental curves of PpPTA, PET, cellulose and PE fibres with widely
divergent values for their orientation parameter. The shear moduli for these fibres have
been determined and are compared with literature values, the relation between the
experimentally determined shear modulus and the structure of the fibre is
discussed. The shear moduli of a series of PET fibres are compared to the values obtained
by birefringence. The modulus of PpPTA and PET sheets are compared to the calculated
values. Good agreement between the experimental and calculated results has been obtained.
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Yield Stress in MR and ER Fluids:
A Comparison Between Microscopic and Macroscopic Structural Models
G. Bossis, E. Lemaire, O. Volkova
Laboratoire de Physique de la Matière Condensée
Parc Valrose, 06108 Nice Cedex 02, France
H. Clercx
Department of Physics, Eindhoven University of Technology
P.O. Box 513, 5600 MB Eindhoven , The Netherlands
Abstract
The yield stress of a magnetorheological suspension is calculated from two different
approaches. The first one is based on a mesoscopic description of the structure taking
only into account the shape anisotropy of the strained aggregates. The second one is based
on a microscopic approach where the interparticle forces, due to the application of the
field, are calculated numerically by taking into account the magnetostatics between the
particles inside the aggregates. We show that the macroscopic description well applies to
suspensions of non magnetic particles in a ferrofluid and that a layered structure,
consisting of parallel slabs of magnetizable materials should have a yield stress much
higher than a structure made of cylindrical aggregates. On the other hand the microscopic
approach is appropriated for the description of suspensions of particles of high
permeability. In this case, the yield stress is mainly determined by the rupture between
pairs of particles and, consequently, it strongly increases with the angle between
the line of centers of the pair undergoing the rupture and the field.
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Shear Induced Gelation of Colloidal Dispersions
B. Cabane1, K. Wong2, P. Lindner3, F.
Lafuma4
1Equipe Mixte CEA-RP, Service de Chimie Moléculaire
CEA-Saclay, 91191 Gif sur Yvette, France
2Rhone-Poulenc, 93308 Aubervilliers, France
3Institut Laue Langevin, B.P. 156
38042 Grenoble Cedex 9, France
4Physico-chimie Macromoléculaire, ESPCI
10 rue Vauquelin, 75231 Paris, France
Abstract
Nanometric silica particles, dispersed in water, have been bridged into long necklaces
by adsorbing rnacromolecules of poly(ethylene oxide). At high coverage of particles by
macromolecules the necklaces repel each other and the dispersions are homogeneous
solutions; at low coverage the necklaces bind to each other and a concentrated phase
separates from excess water. It is reported here that shear induced gelation and shear
induced flocculation are observed near the boundary of the phase separation region. The
structures of these dispersions under shear have been observed through small angle neutron
scattering. It has been found that, above a critical shear rate, the necklaces connect to
each other to form thread-like objects which align along the velocity. At higher shear
these objects associate sideways to form 3-dimensional flocs.
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Flow of RX-08-FK High-Energy Paste in a
Capillary Rheometer
J. F. Carley* and E. von Holtz
Lawrence Livermore National Laboratory
P. O. Box 808, Livermore, CA 94551
G. L. Flowers
Mason & Hanger - Silas Mason Co., Inc.
Pantex Plant, Amarillo, TX 79177
*Address correspondence to JFC at 579 Ruby Rd, Livermore, CA 94550
Abstract
The flow of RX-08-FK, a mostly organic, high-energy, paste-extrudable explosive (PEX)
containing about 75% suspended solids, was experimentally studied. The paste was forced
through long capillary tubes in a specially designed, double-piston rheometer at
temperatures ranging from -54 to +74°C, and at nominal shear rates at the tube
walls from 50 to 40,000 s-1. Paste was preconditioned for many hours to achieve
the desired experimental temperature and the rheometer itself was enclosed in a
preconditioned temperature-controlled chamber. We found the paste to be pseudoplastic with
significant yield stress and entrance effects. The results of 176 runs at temperatures of
-35°C and higher were fitted by an empirical model much like the original model
suggested by Herschel and Bulkley, modified to include a factor correcting the stress for
the substantial entrance loss experienced with this paste. The observed stresses at -54°
were substantially higher and less shear-dependent than those extrapolated from the above
model; these differences may relate to the fact that the glass-transition temperature of
RX-08-FK is approximately -60°C.
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Migration of Particles Undergoing Pressure
Driven Flow in a Circular Conduit
R. E. Hampton, A. A. Mammoli, A. L. Graham*,
and N. Tetlow
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
S. A. Altobelli
The Lovelace Institutes, Albuquerque, NM 87108, USA
*Corresponding author
Abstract
This study focuses on the demixing of neutrally buoyant suspensions of spheres during
slow, pressure driven flows in circular conduits. Distributions of the solid fraction of
particles, f, and the suspension velocity, v, are
measured at different lengths from a static in-line mixer. Experiments were conducted over
a range of volume average solids fractions, fbulk,
(0.10 £ f £ 0.50) and at two different ratios of the particle radius, a,
to the radius of the circular conduit, R (a/R = 0.0256 and a/R = 0.0625).
At fbulk³ 0.20, the
particles rapidly migrate to the low-shear-rate region in the center of the conduit. This
migration results in a blunting of the v profile, relative to the parabolic
profile observed in homogeneous Newtonian fluids. For the flow geometry with the smaller
ratio of a/R the f profile builds to a sharp maximum or
cusp in the center. Particle structures are observed in the experiments with the higher a/R.
The entrance lengths for the development of the f and v
fields, Lf and Lv
respectively, are strong functions of a/R and fbulk.
Lf and Lv rapidly
decrease as f and a/R increase. Over the range of our
data, the v profiles are observed to develop more rapidly than the f profiles.
The experimental results are compared with fully developed flow predictions from the
shear-induced migration (SIM) model and the suspension balance (SB) model. At the smaller a/R
the SIM model more accurately predicts the experimental results. At larger a/R,
some qualitative features of the experimental results are better predicted by the SB
model, however neither model provides good quantitative predictions, especially at low fbulk.
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Viscoelastic Material Functions of Noncolloidal
Suspensions with Spherical Particles
Birnur K. Aral* and Dilhan M. Kalyon
Highly Filled Materials Institute
Chemical Sciences and Engineering Department
Stevens Institute of Technology
Castle Point on the Hudson, Hoboken, NJ 07030
*Currently with Rheometric Scientific at Piscataway, NJ
Abstract
We have characterized various steady and time-dependent material functions of
suspensions of a non-Newtonian binder, poly(dimethyl siloxane), incorporated with ten to
sixty percent by volume of hollow and spherical glass beads. The material functions
included storage and the loss moduli, shear stress and first normal stress difference
growth and relaxation, relaxation modulus upon step strain and creep and recovery
behavior. Both constant shear stress and shear rate experiments were carried-out using
multiple rheometers over a broad temperature range (-35 to 40°C) while
following sample fracture and wall slip effects. With increasing volume fraction, f, of the noncolloidal particles, the strain range, over which linear
viscoelastic behavior is observed, became narrower and the relaxation time of the
suspension increased. Increasing solid content gave rise to the development of the yield
stress and the dependence of large amplitude oscillatory shear properties on time and
deformation history. The yield stress values increased with f,
but were not sensitive to temperature. For f ³ 0.3 the first normal stress difference values reached reproducible
and steady negative values (with tensile force positive). Larger negative values of the
first normal stress difference were observed with increasing deformation rate and solid
concentration. The manifestations of the material functions resulting from the
incorporation of the solids into the non-Newtonian binder included the suppression of the
extrudate swell and the dipping of the free surface in the Weissenberg experiment.
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Reentrant Corner Flows of Newtonian and
Non-Newtonian Fluids
Joel Koplik
Benjamin Levich Institute and Department of Physics
City College of the City University of New York
New York, NY 10031
Jayanth R. Banavar
Department of Physics and Center for Materials Physics
Pennsylvania State University, University Park, PA 16802
Abstract
Computations of the flow of non-Newtonian fluids in the presence of a
reentrant corner have a long history of convergence problems, which are believed to
originate from a non-square-integrable stress singularity. Local flow analyses near such a
corner have been inconclusive, due to the non-linearity and the model-dependence of the
governing equations. We have used molecular dynamics simulations to compute the flow of
both a Newtonian liquid and a model polymer melt through a channel with a reentrant
corner, providing an unbiased and convergent calculation. The fluids interact via
Lennard-Jones potentials, and for the polymer case we employ FENE chains of length
up to 30. For the Newtonian fluid, the shear stress near the corner is found to agree with
the Stokes flow prediction of Moffatt. In the non-Newtonian case, the shear stress has a
stronger apparent divergence, increasing with velocity but not with chain length, which
appears to saturate at an integrable value of approximately 0.8. The molecular origin of
the stress enhancement is the additional elongation and rotation of the molecules near the
reentrant corner.
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Extensional Rheometry of Polymer Multilayers: A
Sensitive Probe of Interfaces
Leon Levitt and Christopher W. Macosko
Department of Chemical Engineering and Materials Science
University of Minnesota, Minneapolis, MN 55455
Thomas Schweizer and Joachim Meissner
Swiss Federal Institute of Technology Zurich
Institute fur Polymere, Polymerphysik
Sonneggstrasse 3, CH-8092 Zurich
Abstract
When an alternating stack of molten polymer sheets is pulled in uniaxial tension parallel
to the layers, interfacial area per unit volume increases, amplifying interfacial effects.
Multilayers of several polymer pairs were prepared by lamination (up to 100 layers). Pairs
with low and high interfacial tension, G, and pairs with
functional groups which could react were selected. These were stretched at 220°C at
various constant extension rates in a rotating clamp extensional rheometer. At low rates
the extra measured stress could be related to G and the number
of interfaces. This method for measuring interfacial tension can be applied to opaque
samples and does not require knowing sample density or viscosity. For the reactive pairs
there was pronounced strain hardening caused by coupled and even cross linked chains al
each interface. The contribution of the cross linked interface was shown to follow rubber
elasticity theory. As the result of the reaction the measured stress was two orders of
magnitude higher than for the non-reactive case. Extra stress due to the grafting reaction
was also measured. It increased with extension rate, presumably due to entanglements of
the grafts across the interface.
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The Two-Way Interaction Between Anisotropic
Flow and Fiber Orientation in Squeeze Flow
K. A. Ericsson*, S. Toll†, and J.-A. E.
Månson‡
Laboratoire de Technologie des Composites et Polymères
Ecole Polytechnique Fédérale de Lausanne
CH-1015 Lausanne, Switzerland
*Present address: ABB High Voltage Cables, Box 546, S-371 23 Karlskrona,
Sweden
†Present address: Chalmers University of Technology, S-412 96 Gothenburg,
Sweden
‡To whom correspondence should be addressed.
Abstract
The rheology of a discontinuous fiber filled polypropylene in squeeze flow between
parallel plates is studied. The material has an initial anisotropic fiber orientation
distribution and therefore displays a strongly anisotropic inplane flow behavior with
predominant flow transverse to the axis of principal orientation. The kinematic field is
computed using a linear, orthotropic constitutive model, where the fibers are assumed to
move affinely with the surrounding fluid. The fiber orientation distribution is updated in
each timestep thus coupling orientation and flow. Two different orientation descriptions
are evaluated: orientation tensors with closure approximations, and a technique based on
direct solution of the orientation of a set of test fibers. The two methods are first
compared to exact solutions of the orientation distribution function in simple shear and
pure extension; the direct solution is exact within numerical error whereas the methods
based on orientation tensors and quadratic and hybrid closure fail to correctly describe
any transient fiber orientation evolution. Finally, the orientation representations are
implemented in the kinematic model and compared to the experimental data; the direct
solution method is found to give a very accurate prediction of the observed flow
kinematics, whereas the other techniques result in substantial errors.
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Viscosity Equation for Concentrated
Suspensions of Charged Colloidal Particles
A. Ogawa*, H. Yamada, S. Matsuda, and K. Okajima
Fundamental Research Laboratory of Natural & Synthetic Polymers
Asahi Chemical Industry Co., Ltd
11-7 Hacchonawate, Takatsuki, Osaka 569, Japan
M. Doi
Department of Applied Physics, Faculty of Engineering
University of Nagoya
Furo-cho, Chikusa, Nagoya 464, Japan
*Corresponding author
Abstract
Concentrated suspensions of charged stabilized colloidal particles exhibit very large
viscosity at low shear rate, and a strong shear-thinning behavior at intermediate shear
rate, and a constant second Newtonian viscosity at high shear rate. This type of
non-Newtonian behaviour is affected by many factors such as the particle volume fraction f, the particle diameter, the surface electric potential y0, and salt concentration etc. Generalized equation for
the viscosity h of this system is proposed by applying Eyring's
transition state theory. The surface electric potential y0
and the thickness of the electric double layer k-l
are determined by applying the theory to experimental data. Systematic experiments of h of the model colloidal dispersion systems are carried out as the
function of f and g and the results
are satisfactorily reproduced by the present theory. The effects of hydrodynamic diameter dh
and y0 of the colloidal particle on h are also quantitatively explained.
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Transient Rheological Response and Morphology
Evolution of Immiscible Polymer Blends
I. Vinckier, P. Moldenaers, and J. Mewis
Department of Chemical Engineering
K.U. Leuven, 3001 Leuven, Belgiurn
Abstract
The response of semi-concentrated model blends (10% disperse phase), consisting of
slightly viscoelastic polymers, on a stepwise increase in shear rate is investigated.
During the initial stage of the response droplets deform into fibrils. The shear and
normal stress transients during the deformation process are modeled by combining the
approach of Doi and Ohta with the affine deformation theory for single droplet behaviour.
In the proposed equations the sealing relations of Doi and Ohta for transient stresses are
preserved. They do not contain any fitting parameter. First, the model predictions are
compared with experimental results on model blends. A good agreement is found under
conditions for which affine deformation is expected. Secondly, the applicability of the
scaling relations of the Doi-Ohta theory is verified experimentally. Although the scaling
laws should only apply for 50:50 mixtures of Newtonian liquids with equal viscosity, the
experiments show that they hold as well for semi-concentrated systems containing slightly
viscoelastic components with viscosity ratios deviating from unity.
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Molecular-Level Modeling of the Viscoelasticity
of Crosslinked Polymers - Effect of Time and Temperature
Philip P. Simon and Harry J. Ploehn
Department of Chemical Engineering, University of South Carolina
Swearingen Engineering Center, Columbia, SC 29208
Abstract
We present a new molecular-level picture of chain dynamics for describing the
viscoelasticity of crosslinked polymers. The associated mathematical model consists of a
time-dependent momentum balance on a representative polymer segment in the crosslinked
network, plus phenomenological expressions for forces acting on the segments. These
include a cohesive force that accounts for intermolecular attraction, an entropic force
describing the thermodynamics governing chain conformations, and a frictional force that
captures the temperature dependence of relative chain motion. We treat the case of
oscillatory uniaxial deformation. Solution of the model equations in the frequency domain
yields the dynamic moduli as functions of temperature and frequency. The model reproduces
all of the qualitative features of experimental dynamic modulus data across the complete
spectrum of time and temperature, spanning the glassy zone, the b-transition,
the dynamic glass transition, and the rubbery zone. All of the model parameters can be
evaluated through the use of independent experimental data. Comparison of model
predictions with experimental data yields good quantitative agreement outside of the glass
transition region.
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V. Rauschenberger and H. M. Laun
BASF Aktiengesellschaft, Polymer Research Division
Polymer and Solid State Physics, ZKM - G201
D-67056 Ludwigshafen/Rhein, Germany
Abstract
An iterative model is described to predict isothermal and nonisothermal elongation of
an extruded filament at a given force. The principle of the model allows a quite simple
description of Rheotens tests with much flexibility regarding the shape of the
elongational viscosity function, including true viscoelastic flow and thermal boundary
conditions. The algorithm is compact and computing time on a PC is short. The application
of an integral K-BKZ constitutive equation to predict Rheotens curves of the well
characterized LDPE Melt I is demonstrated and the influence of the slope of the transient
viscosity in the strain-hardening regime is discussed. A simple approximation to take into
account the prehistory of the material in the die based on purely elongational strains is
proposed which includes the irreversibility assumption of the damping function (Wagner
model). Predicted Rheotens curves are compared with experimental results.
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Rheology and Phase Separation in a Model
UCST Polymer Blend
D. Vlassopoulosl, A. Koumoutsakos2, S. H.
Anastasiadis3
Foundation for Research and Technology-Hellas (FO.R.T.H.)
Institute of Electronic Structure & Laser
P.O. Box 1527, Heraklion 71110, Crete, Greece
S. G. Hatzikiriakos, and P. Englezos
Department of Chemical Engineering
The University of British Columbia
Vancouver, B.C. V6T 1Z4, Canada
lCorresponding author. E-mail: dvlasso@iesl.forth.gr
2Permanent address: Department of Chemical Engineering
The University of British Columbia, Vancouver, B.C. V6T 1Z4, Canada
3Also at the Physics Department, University of Crete
Heraklion 71110, Crete, Greece
Abstract
The viscoelastic properties of a model binary polymer blend exhibiting an Upper
Critical Solution Temperature (UCST) phase diagram were investigated by utilizing small
amplitude oscillatory and steady shear measurements. A mixture of unentangled monodisperse
polystyrene and poly(phenyl methyl siloxane), exhibiting Newtonian shear viscosity, was
used, and its phase diagram was established by turbidity and dynamic light scattering
measurements. In the miscible region, the concentration dependence of the viscosity was
adequately described by a mixing rule accounting for the surface fractions instead of
volume fractions. Near the phase separation temperature and far from the glass transition,
critical concentration fluctuations dominated the linear viscoelastic response and were
responsible for the observed thermorheological complexity. An appropriate quantitative
account of these fluctuations resulted in the accurate rheological determination of both
the binodal and spinodal temperatures, extending thus the applicability of the relevant
procedure earlier applied to lower critical solution temperature blends involving higher
molecular weight entangled polymers. In the phase separated regime, the normal stress of
the dispersed phase undergoing spinodal decomposition followed a recent scaling proposed
for molecular mixtures with large viscosity difference.
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Accurate Simulation of Linear Viscoelastic
Properties by Variance Reduction Through the Use of Control Variates
Norman J. Wagner * and Hans Christian Öttinger
ETH Zürich, Department of Materials, Institute of Polymers and Swiss F.I.T. Rheocenter
CH-8092 Zürich, Switzerland
*Permanent Address: Center for Molecular and Engineering Thermodynamics,
Chemical Engineering, University of Delaware, Newark, DE 19716
Abstract
An algorithm is demonstrated to yield accurate linear viscoelastic properties in a
nonequilibrium stochastic simulation by variance reduction. For non-interacting polymer
dumbbells, multiple orders of magnitude improvements in computational accuracy for
nonequilibrium viscoelastic properties are easily realized. This simple and robust control
variate scheme uses control variables defined as the viscoelastic properties obtained from
a parallel, equilibrium simulation. Results for strongly-interacting colloidal particles
demonstrate some advantages as well as limitations of the method.
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