- NMR Imaging of Particle Migration in Suspensions Undergoing
Extrusion
- S. A. Altobelli, E. Fukushima, and L. A. Mondy
- Influence of Shear on a Lamellar Triblock Copolymer Near the
Order-Disorder Transition
- T. Tepe, D.A. Hajduk, M.A. Hillmyer, P.A. Weimann, M. Tirrell, F.S. Bates, K. Almdal,
and K. Mortensen
- Influence of Elastic Properties on Drop Deformation in
Elongational Flow
- F. Mighri, A. Ajji, and P. J. Carreau
- From Dynamic Moduli to MWD: A Study of Various Polydisperse Linear
Polymers
- Christian Carrot and Jacques Guillet
- Multiaxial Linear Viscoelastic Behavior of a Soda-lime-silica
Glass Based on a Generalized Maxwell Model
- L. Duffrène, R. Gy, H. Burlet, and R. Piques
- A New Method to Determine Wall Shear Stress Distribution
- F.J.H. Gijsen, A. Goijaerts, F.N. van de Vosse, and J.D. Janssen
- Rheological Properties and Fiber Orientations of Short
Fiber-Reinforced Plastics
- Jin Kon Kim and Ju Ho Song
- Rheological Properties and Domain Structures of Immiscible Polymer
Blends under Steady and Oscillatory Shear Flows
- Shinichi Kitade, Akihiro Ichikawa, Naotomo Imura, Yoshiaki Takahashi, and Ichiro Noda
- Three Dimensional Constitutive Viscoelastic Laws with Fractional
Order Time Derivatives
- Nicos Makris
- Prediction of the Sub-yield Extension and Compression Responses of
Glassy Polycarbonate from Torsional Measurements
- Jean-Jacques Pesce and Gregory B. McKenna
- Numerical Simulation of the Spinning Flow of Liquid Crystalline
Polymers
- N. Mori, Y. Hamaguchi, and K. Nakamura
- Structure and Linear Viscoelastic Behaviour of Main-chain
Thermotropic Liquid Crystalline Polymers
- A. Romo-Uribe, T. J. Lemmon, and A. H. Windle
- A Technique for Direct Observation of Particle Motion under Shear
in a Langmuir Monolayer
- M. Levent Kurnaz and Daniel K. Schwartz
- Rheology of Reconstituted Type I Collagen Gel in Confined
Compression
- David M. Knapp, Victor H. Barocas, Alice G. Moon, Kyeongah Yoo, Linda R. Petzold, and
Robert T. Tranquillo
- A Note on the Melt Strength of Liquid Crystalline Polymer
- M.H. Wagner, Th. Ixner, and K. Geiger
- Biaxial Steady States and Their Stability in Shear Flows of Liquid
Crystal Polymers
- Qi Wang
NMR Imaging of Particle Migration in
Suspensions Undergoing Extrusion
S. A. Altobelli and E. Fukushima
The Lovelace Institutes
Albuquerque, New Mexico 87108
L. A. Mondy
Sandia National Laboratories
Albuquerque, New Mexico 87185-0834
Abstract
Nuclear magnetic resonance (NMR) imaging was used to measure fluid velocity and fluid
fraction in suspensions flowing into an abrupt four-to-one contraction in pipe diameter,
through a section of smaller diameter pipe, and out of an abrupt expansion back to the
original pipe size. Suspensions of 50% by volume of particles in a Newtonian liquid were
forced to flow by a plunger moving at a constant, slow velocity. Two sizes (100 and 675 mm diameter) of suspended spheres were studied. Conditions were such
that buoyant, inertial, Brownian, and surface forces could be assumed to be negligibly
small. Little change in particle concentration was seen in the region of the contraction
until the plunger was within about one pipe diameter of the contraction. The particles in
the small diameter section of pipe migrated toward the pipe axis, the region of lowest
shear rate. Particle concentration varied downstream of the pipe expansion, especially in
a suspension of the larger particles. Over time, particles were partially swept out of the
region immediately downstream of the expansion joint. Although Reynolds numbers based on
average suspension properties were identical in the two suspensions, the velocity fields
in the expansion region differed, showing that demixing may markedly influence the
downstream flow field in systems with complex geometry.
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T. Tepe, D.A. Hajduk, M.A. Hillmyer, P.A. Weimann, M. Tirrell*, and F.S.
Bates*
Department of Chemical Engineering and Materials Science
University of Minnesota, Minneapolis, Minnesota 55455, USA
K. Almdal and K. Mortensen
Risø National Laboratory
DK-4000 Roskilde, Denmark
* to whom correspondence should be addressed
Abstract
The effects of a large strain (600%) reciprocating steady shear on the lamellar
orientation and the order-disorder transition of a nearly symmetric poly(ethylene
propylene)-poly(ethylethylene)-poly(ethylene propylene) (PEP-PEE-PEP) triblock copolymer
have been studied using small-angle neutron scattering and rheological measurements.
Shearing in the ordered state produced parallel lamellae under all steady-state conditions
investigated, and the lamellar-to-disorder transition temperature decreased dramatically
with increasing shear rate. Both phenomena are qualitatively different from the
documented behavior of PEP-PEE diblock copolymers. However, cooling the disordered
material while shearing at a relatively low deformation rate initially induces
perpendicular lamellae, analogous to the diblock response. These observations are
considered in the context of theory and other experimental studies.
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F. Mighri, A. Ajji**, and P. J. Carreau*
Centre de Recherche Appliquée sur les Polymères, CRASP
Ecole Polytechnique of Montreal, C. P. 6079, Stn. Centre-Ville
Montreal, Qc, H3C 3A7 Canada
** Industrial Materials Institute, National Research Council Canada
75 Bd. de Mortagne, Boucherville, Qc, J4B 6Y4 Canada
*To whom correspondence should be addressed.
Abstract
We report experimental results on the deformation of a single drop
suspended in a medium under uniaxial elongational flow along the central axis of a
converging conical channel made of Plexiglas. Both the drop and the continuous phases
consist of constant viscosity elastic fluids, so-called Boger fluids. This study reveals
several interesting features about the role played by both the drop and matrix
elasticities on the drop deformability. In a given matrix fluid, the drop deformation
decreases as its elasticity increases. For a given drop fluid, the matrix elasticity has
the opposite effect: the drop deformation increases with increasing matrix elasticity. An
empirical relation between the drop and matrix deformations is established as a function
of the drop and matrix characteristic elastic times.
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Christian Carrot, Jacques Guillet
Laboratoire de Rhéologie des Matières Plastiques
Faculté de Sciences et Techniques
Université Jean Monnet
23, Rue du Docteur Paul Michelon
42023 Saint-Etienne Cedex 2, France
Abstract
The linear viscoelastic behavior of various polydisperse linear polymers in the melt is
used to predict their average molecular weights and polydispersity index. The method is
based on simplified molecular dynamics and has been previously shown to enable a
correct description of the dynamic moduli of polypropylenes from the knowledge of their
molecular weight distribution (MWD). This so-called forward calculation only requires a
few parameters, namely the scaling law for the zero-shear viscosity of narrow fractions h0 f(M), the plateau modulus G0N,
and the value of the molecular weight between entanglements Me.
The main goal of the present work is to find a solution to the "inverse"
problem. To avoid the problem to become ill-posed, the shape of the MWD has to be
prescribed. Using the assumption of a typical logarithmic bell-shaped Wesslau MWD, the
method has been proved to be successful for the recovery of the weight average molecular
weight and of the polydispersity index of many linear polymers in a large range of
molecular weights and polydispersity indices. Rough estimates of MZ have been
obtained for well characterized polypropylenes by the use of a generalized exponential
distribution (GEX).
Attention has also been focused on some requirements for the frequency window which is
necessary to get reasonable accuracy on the values of the parameters Mw and Ip.
It was found that, because of tube renewal and constraint release, three or four decades
are generally a sufficiently wide range which can be easily achieved with routine
rheological dynamic measurements.
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L. Duffrène
Saint-Gobain Recherche, Aubervilliers, France and
Centre des Matériaux - Ecole des Mines de Paris, URA CNRS 866, Evry, France
R. Gy
Saint-Gobain Recherche, Aubervilliers, France
H. Burlet and R. Piques
Centre des Matériaux - Ecole des Mines de Paris, URA CNRS 866, Evry, France
Abstract
The multiaxial linear viscoelastic behavior of a soda-lime-silica glass has been
investigated in the transition range using shear and uniaxial creep-recovery experiments.
The shear and uniaxial viscoelastic constants and retardation functions have been
precisely measured. The no-stress and the no-temperature dependence of the viscoelastic
constants show respectively linear viscoelastic and simple thermorheological behaviors of
the glass. The deviatoric part of the viscoelastic behavior is first investigated from the
shear experimental data. A generalized Maxwell model with one set of parameters is shown
to correctly simulate the shear creep-recovery experiments. Using the deviatoric part of
the model, the spheric part of the viscoelastic behavior is deduced from the uniaxial
experimental data. In particular, we show the first experimental measurements of the bulk
equilibrium modulus and the temperature dependence of the hydrostatic pressure
viscoelastic behavior for a soda-lime silica glass. A second set of parameters of the
generalized Maxwell model is determined for the hydrostatic pressure viscoelastic
behavior.
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F.J.H. Gijsen, A. Goijaerts, F.N. van de Vosse, and J.D. Janssen
Department of Mechanical Engineering
Eindhoven University of Technology
P.O. Box 513, 5600 MB Eindhoven
The Netherlands
Abstract
The absence of a model to predict near wall viscosity of complex
suspensions instigated an investigation for a new method to determine the wall shear
stress. If the inner wall of a flow model is covered with a highly flexible gel layer, the
local wall shear stress will deform this gel layer. Through the known properties of the
gel layer, the measured deformation can be transformed to the wall shear stress. To
measure the deformation of the gel layer, Speckle Pattern Interferometry was applied. The
performance of the developed speckle apparatus was evaluated using a well
controlled benchmark experiment and a resolution of 50 nm was achieved. The
deformation of a gel layer was measured in a 2D rectangular duct, using a Newtonian
and a non-Newtonian measuring fluid. The wall shear stresses were measured as a function
of the flow rate and compared to theoretical predictions and the results
demonstrated the potential of the method.
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Jin Kon Kim* and Ju Ho Song
Department of Chemical Engineering
Pohang University of Science and Technology
Pohang, Kyungbuk 790-784, Korea
* Corresponding author
Abstract
The effect of fiber orientation on the rheological properties of short glass
fiber-reinforced composites was investigated by dynamic oscillatory shearing with parallel
plate fixtures. As an oscillatory shear amplitude and frequency applied to
fiber-reinforced composites increased, more fibers in the composites were aligned to the
flow direction, thus the complex viscosity gradually decreased. This phenomenon was
confirmed by observing the fiber orientations using optical photographs.
The complex viscosity depended upon the strain amplitude, and pre-oscillatory shearing
frequency and shearing time. Experimental results for fiber orientations and complex
viscosity were compared with predictions available in the present time. The predictions of
the dependence of fiber orientation upon strain amplitudes and fiber volume fractions are
in qualitative agreement with experimental data. However, the effects of the magnitude of
frequency and oscillatory shearing time on fiber orientation, thus, complex viscosity,
cannot be predicted successfully although these effects were clearly demonstrated by
experiment.
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Shinichi Kitade, Akihiro Ichikawa, Naotomo Imura,
Yoshiaki Takahashi, and Ichiro Noda
Department of Applied Chemistry, Graduate School of Engineering
Nagoya University, Nagoya 464-01, Japan
Abstract
Rheological properties of three immiscible polyisoprene (PI)/polydimethylsiloxane
(PDMS) blends (PI:PDMS=1:9 by weight) having viscosity ratios hd/hm = 0.155, 0.826 and 4.02, where hd
and hm are the viscosities of the droplet and
matrix, were investigated by directly measuring the droplet size distributions with a
video-microscope. Steady state measurements were performed by sequentially stepping up the
shear rate g (step-up) and step decrease (step-down) of the
shear rate. Dynamic frequency sweep measurements were also performed immediately following
cessation of steady shear flow. In the step-up measurements for blends with hd/hm = 0.155 and
0.826, stresses were proportional to g and the droplet sizes
were well regulated by the flow and inversely proportional to g
for g ³ 0.553 s-l, in good agreement with Doi-Ohta
model [J. Chem. Phys. 95, 1242-1248 (1991)] . The results of step-down
measurements were consistent with dynamic moduli measurements, because the droplet sizes
were almost unchanged during these measurements. The results are in accord with Palierne's
model [Rheol. Acta 29, 204-214 (1990)]. For the hd/hm = 4.02 blend, however, the droplet sizes were
insensitive to g, resulting in worse agreement between the
experimental and theoretical results than for the other blends.
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Nicos Makris
Department of Civil and Environmental Engineering, SEMM
University of California, Berkeley, CA 94720
Abstract
In this paper the three-dimensional behavior of constitutive models containing
fractional order time derivatives in their strain and stress operators is investigated.
Assuming isotropic viscoelastic behavior it is shown that when the material is incompressible,
then the one-dimensional constitutive law calibrated either from shear or elongation
tests can be directly extended in three dimensions, and the order of fractional
differentiation is the same in all deformation patterns. When the material is viscoelastically
compressible, the constitutive law in elongation involves additional orders of
fractional differentiation that do not appear in the constitutive law in shear. In the
special case where the material is elastically compressible, the constitutive laws
during elongation and shear are different; however the order of fractional differentiation
remains the same. It is shown that for an elastically compressible material, the
four-parameter fractional solid model (RTG model) which has been used extensively to
approximate the elongation behavior of various polymers, can be constructed from
the three-parameter fractional Kelvin model (RT model) in shear and the elastic
bulk modulus of the material. Some of the analytical results obtained herein with
operational calculus are in agreement with experimental observations reported in the
literature. Results on the viscoelastic Poisson behavior of materials described with the
fractional solid model are presented and it is shown that at early times the Poisson
function reaches negative values.
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Jean-Jacques Pesce and Gregory B. McKenna
Polymers Division
National Institute of Standards and Technology
Gaithersburg, MD 20899
Abstract
Modeling of the response of solid-like polymers is often difficult not only due to the
highly nonlinear behavior of the materials but also because of the difficulty of obtaining
relevant material data in the laboratory. Here we examine the possibility of using
concepts from finite elasticity theory to describe the isochronal single step stress
relaxation response for a polymer glass (polycarbonate) far below its glass transition.
Torque and normal force measurements from torsional stress relaxation experiments are used
to obtain isochoric values for the derivatives W1 and W2 of the
strain energy density function in terms of the deformation invariants at specific time
values (isochrones). The values of W1 and W2 are then used to
determine isochronal values of the Valanis-Landel [1967] (VL) function derivatives w'(l) and to predict the tension and compression responses for different
deformations l below yield. It is found that, for the
conditions examined, the experimentally obtained tension and compression responses are
well described within the VL framework despite the fact that polycarbonate is a
compressible material. This success suggests that the set of experiments required to
describe the nonlinear behavior of glassy materials may be smaller than previously
thought. Also, volumetric measurements in the uniaxial deformations indicate a
densification of the glass at large deformations and long relaxation times which is
consistent with concepts in the literature which invoke mechanically accelerated aging to
describe mechanical and structural interactions in the physical aging of glassy polymers.
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N. Mori*, Y. Hamaguchi, and K. Nakamura
Department of Mechanical Engineering
Osaka University, Suita, Osaka 565 Japan
* Corresponding author: Noriyasu Mori
Department of Mechanophysics Engineering
Graduate School of Engineering, Osaka University
211 Yamadaoka Suita, Osaka 565 Japan
Abstract
The spinning flow of liquid crystalline polymers is numerically calculated
using a modified Doi model. The flow dealt with is an axisymmetric spinning flow for the
examination of velocity and molecular orientation developments inside a filament and is
solved with a finite difference method. The velocity profile varies from a convex profile
to a uniform one through a concave one that is peculiar to the liquid crystalline
polymers. The distribution of the molecular orientation near the nozzle exit is found to
cause the generation of the concave profile. Furthermore, the results of the simulation
suggest the requirement of a long spinline for the attainment of a uniform profile of the
molecular orientation inside a fiber.
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A. Romo-Uribe*, T. J. Lemmon, and A. H. Windle
Department of Materials Science and Metallurgy
University of Cambridge
Pembroke Street, Cambridge, CB2 3QZ England
*Present address: USAF Wright Laboratory, Materials Directorate
WL/MLBP Bldg. 654, 2941 P Street, Ste 1
Wright-Patterson Air Force Base, OH 45433-7750
Abstract
The influence of molecular weight on the ordering processes and linear viscoelastic
properties of a series of thermotropic main-chain liquid crystalline polymers has been
investigated. The polymers are wholly aromatic copolyesters based on random units of 75
mol% 1,4-hydroxybenzoic acid (B) and 25 mol% 2,6-hydroxynaphthoic acid (N). The thermal
characterisation, performed between -50°C and 360°C, showed that annealing below 290°C
gives rise to a secondary endotherm. However, only one endotherm is observed when
annealing is carried out above 290°C, showing that all
transitions are completed by 310°C. Hot-stage wide-angle X-ray
scattering demonstrates that the second endotherm is associated with a solid-solid
transformation from pseudo hexagonal to orthorhombic. The orthorhombic phase, found on
slow heating or annealing below the melting point, has a higher melting point than the
pseudo hexagonal phase. The increase in melting point which can result from such thermal
treatments is avoided in all the experiments reported here by comparatively rapid heating
of the specimens into the melt. In-situ optical microscopy and X-ray scattering
measurements show that the 'as-moulded' samples for rheological experiments exhibit
preferred orientation, which is associated with their mechanical history. However, holding
the sample in the molten state over periods of time leads to a relaxation of the degree of
orientation, until a macroscopically unoriented (textured) state is obtained. This
reduction of degree of orientation is correlated with an increase of the complex
viscosity, where a plateau value is reached in the final unoriented state. The rheological
characterisation, on textured samples, show that B-N copolyesters exhibit a linear
viscoelastic (LVE) regime similar to that observed in common flexible chain polymers.
However, it is also found that this linearity extends only up to strains of about 10%, and
is independent of the molecular weight. Dynamic oscillatory experiments in the LVE regime
reveal a rubber-like region (minimum in delta loss angle), suggesting that the B-N
thermotropic copolyesters behave like lightly cross-linked materials, adding thus support
to the elastic network hypothesis.
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M. Levent Kurnaz and Daniel K. Schwartz*
Department of Chemistry, Tulane University, New Orleans, LA
*To whom correspondence should be addressed
Tel: 504/862-3562
FAX: 504/865-5596
E-mail: dks @ mailhost.tcs.tulane.edu
Abstract
We have used fluorescence microscopy to observe the effect of shear on rigid
two-dimensional structures residing in a Langmuir monolayer. Monolayers of 12-NBD stearic
acid undergo a two-dimensional liquid to solid transition on the water surface. The
domains of solid phase that form in the coexistence region are elongated (needle-shaped)
crystallites. We observe the effect of shear within the monolayer in two geometries:
two-dimensional Poiseuille flow and simple shear flow created by moving bands. The
technique allows us to determine the average orientational order parameter as well as the
details of the rotational kinematics, which are, as expected, well-described by a Jeffery
orbit. We propose that this technique of direct observation in Langmuir monolayers will be
a useful method for the study of systems of rigid particles under flow.
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David M. Knapp, Victor H. Barocas, Alice G. Moon,
Kyeongah Yoo+, Linda R. Petzold+, and Robert T. Tranquillo*
Department of Chemical Engineering and Materials Science
+Department of Computer Science
University of Minnesota, Minneapolis, MN 55455
* Corresponding author (Tel: 612-625-6868; Fax: 612-626-7246)
Abstract
Collagen gels are used extensively for studying cell-matrix mechanical interactions and
for making tissue-equivalents, where these interactions lead to bulk deformation of the
sparse network of long, highly-entangled collagen fibrils and syneresis of the
interstitial aqueous solution. We have used the confined compression test in conjunction
with a biphasic theory to characterize collagen gel mechanics.
An FEM model based on our biphasic theory was used to analyze the experimental results.
The results are qualitatively consistent with a viscoelastic collagen network, an inviscid
interstitial solution, and significant frictional drag. Using DASOPT, a novel differential
algebraic equation solver coupled with an optimizing algorithm, the aggregate modulus for
the collagen gel was estimated as 6.32 Pa, its viscosity as 6.6 × 104 Pa s,
and its interphase drag coefficient as 6.4 × 109 Pa s m-2 in
long-time (5 hr) creep. Analysis of short-time (2 min) constant strain rate tests gave a
much higher modulus (318.3 Pa), indicating processes that generate high resistance at
short time but relax too quickly to be significant on a longer time scale. This indication
of a relaxation spectrum in compression is consistent with that characterized in shear
based on creep and dynamic testing. While Maxwell fluid behavior of the collagen network
is exhibited in shear as in compression, the modulus measured in shear was larger. This is
hypothesized to be due to microstructural properties of the network. Furthermore,
parameter estimates based on the constant strain rate data were used to predict accurately
the stress response to sinusoidal strain up to 15% strain, defining the linear
viscoelastic limit in compression.
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M.H. Wagner, Th. Ixner, and K. Geiger
Institut für Kunststofftechnologie, Universität Stuttgart,
Böblingerstr. 70, D-70199 Stuttgart, Germany
Abstract
Results of Rheotens experiments on a commercial liquid crystalline polymer
(LCP) melt are reported. In non-isothermal extension of extruded filaments under the
action of constant tensile force, we find a maximum melt tension at break or melt fracture
stress of about sB = 7 MPa, rather independent of
extrusion speed or melt temperature.
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Qi Wang
Department of Mathematical Sciences
Indiana University-Purdue University Indianapolis
Indianapolis, IN 46202
Abstract
We study the biaxiality of the steady state solutions and their stability to
out-of-plane disturbances in shear flows of spatially homogeneous liquid crystal polymers
using two approximate BMAB models, BMAB-Doi and BMAB-HLl, which are derived from the
BMAB kinetic theory using the Doi and the first Hinch-Leal closure approximation. By
casting the models in a novel biaxial representation of the orientation tensor with two
built-in order parameters and a triad of directors, we show explicitly that the steady
states of the BMAB models exhibit biaxial symmetry except for some uniaxial degeneracy at
isolated Peclet numbers and polymer concentration values. Moreover, we obtain all the
steady states in which two directors are confined to the shearing plane and analyze their
stability with respect to both in-plane and out-of-plane disturbances. We find that
(1) flow-aligning family is the unique stable solution family in the BMAB-Doi
model, where two order parameters are of opposite signs; (2) the flow-aligning family in
the BMAB-HL1 model is stable only in a finite range of polymer concentration 0 <
N £ 10 and the log-rolling family is born unstable and
attains stability through an instability to stability transition at a sufficiently
high polymer concentration value, N > 10, which grows with respect to the Peclet
number; (3) the loss-of-stability in the flow-aligning family at N = 10 is caused
by a one-dimensional director rotational instability pertinent to the existence of the
maximum allowable degree of orientation with respect to the flow-aligning major director,
5/6, and is coincident with the change-of-sign behavior of the first normal stress
difference and the smaller order parameter as well.
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