- A theoretical framework for granular suspensions in a steady
simple shear flow
- Christophe Ancey, Philippe Coussot, and Pierre Evesque
- Polymer disentanglement in steady shear flow
- Lynden A. Archer
- Separability criteria for entangled polymer liquids
- Lynden A. Archer
- Secondary motions in straight and tapered channels:
Experiments and 3-D finite element simulation with a multi-mode differential viscoelastic
model
- Benoît Debbaut and Joseph Dooley
- Steady-shear viscosity of stirred yoghurts with varying
ropiness
- M. E. van Marle, D. van den Ende, C. G. de Kruif, and J. Mellema
- Rheology of a viscoelastic emulsion with a liquid crystalline
polymer dispersed phase
- Heon Sang Lee and Morton M. Denn
- Melt rheology of randomly branched polystyrenes
- Dino Ferri and Paolo Lomellini
- Prediction of the wax content of the incipient wax-oil gel in
a pipeline: An application of the controlled-stress rheometer
- Probjot Singh, H. Scott Fogler, and Nagi Nagarajan
- Nonhomogeneous patterns with core defects in elongational
flows of liquid crystal polymers
- M. Gregory Forest, Qi Wang, and Hong Zhou
- An analytical relation between relaxation time spectrum and
molecular weight distribution
- Wolfgang Thimm, Christian Friedrich, Michael Marth, and Josef Honerkamp
- Analysis of Palierne's emulsion model in the case of
viscoelastic interfacial properties
- U. Jacobs, M. Fahrländer, J. Winterhalter, and Chr. Friedrich
- Evolution equations for arbitrary moments of the orientation
distribution of rigid-rod molecules
- Davide A. Hill
- Entry flow of a PE-LD melt into a slit die: An experimental
study by laser-Doppler-velocimetry
- E. Wassner, M. Schmidt, H. Münstedt
- Dynamic mechanical properties of linear and cross-linked
polyurethane
- Frederic Prochazka, Dominique Durand, and Taco Nicolai
- A thermodynamically admissible reptation model for fast
flows of entangled polymers
- Hans Christian Öttinger
- In-situ characterization by small angle light
scattering of the shear-induced coalescence mechanisms in immiscible polymer blends
- D. Rusu and E. Peuvrel-Disdier
- Rheological behaviour of poly(methyl methacrylate)
dispersions stabilized by a diblock copolymer: An anomalous viscosity-particle
concentration dependence
- Vladimír Pavlíne, Petr Sáha, Jaroslav Stejskal, and Otakar Quadrat
- Polymeric and colloidal modes of relaxation in latex
dispersions containing associative triblock copolymers
- Q. T. Pham, W. B. Russel, J. C. Thibeault, and W. Lau
- Vanishing elasticity for wet foams: Equivalence with
emulsions and role of polydispersity
- A. Saint-Jalmes and D. J. Durian
- Optical behaviour of an associating polymer under shear flow
- J-F Le Meins, J-F Tassin, and J-M Corpart
- Classification of flow modes of viscoelastic fluids at a
junction of two stratified laminar flow layers
- Hiroshi Yamaguchi, Takeshi Yasumoto, and Hideaki Yamamoto
Christophe Ancey1, Philippe Coussot2, and Pierre
Evesque3
1 Cemagref - division ETNA, Domaine Universitaire BP 76
38402 Saint-Martin-d'Hčres Cedex, France
2 LMSGC, Cité Descartes, 2, allée Képler
77420 Champs-sur-Marne, France
3 École Centrale de Paris, Laboratoire MSSMAT
Allée des Vignes, 92295 Châtenay-Malabry Cedex, France
Abstract
We focus our attention on granular suspensions made
up of noncolloidal spherical particles within a Newtonian fluid. The main objective of
this paper is to provide a general framework for the formulation of the bulk stress
tensor. The bulk stress within granular suspensions is mainly generated at the particle
level by strong interactions between particles, such as friction, collision, and
lubricated contact. The existence of a few local mechanisms is a major cause of behavior
complexity at the macroscopic scale. A direct consequence is that the constitutive
equation is only known for some flow conditions and given types of mixture. Here we have
used a micro-structural approach, which consists in considering the mixture as an
effective continuum at the macroscopic level and inferring the bulk stress tensor from
averaging of local interactions and local stresses. The bulk stress tensor may be split
into elementary contributions pertaining to particle interactions. A complementary
equation standing for the bulk energy dissipation may be needed in some circumstances. The
analytical computation of these contributions is generally not possible. We present the
various physical or heuristic reasonings usually proposed to get round this difficulty.
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Lynden A. Archer
Department of Chemical Engineering
Texas A&M University
College Station, TX 77843 USA
Abstract
A procedure is presented for investigating entanglement loss in polymer liquids during
steady shear flow. The method combines steady shearing with small-amplitude step strain
measurements to determine the elastic modulus Ge of an entangled polymer
network under steady-state conditions. In this study, superimposed step/steady shear
measurements are used to investigate entanglement loss in narrow molecular weight
distribution polystyrene/diethyl phthalate solutions with variable entanglement density (9
< N/Ne < 58). For all materials studied, Ge
decreases with increasing shear rate g-dot over a wide range of
rates. At high shear rates, an approximate scaling relation Ge (g-dot) ~ g-dot -1/2 can be
defined for all but the most weakly entangled polymer solution; for this material, a
related scaling form Ge (g-dot) ~ g-dot -1 correctly describes the experimental results. We
also find that the ratio of limiting shear modulus, Ge(0), to modulus at
finite rate Ge(g-dot) is related to a
molecular stretching functional á˝E×u˝ń by Ge(0)/Ge(g-dot) » á˝E×u˝ńp, where
p takes on values of 1 and 1/2, depending on whether contour length stretching is
taken to be affine, p = 1, or non-affine, p = 1/2 . For the lowest molecular
weight polymer investigated, the affine stretch result Ge(0)/Ge(g-dot) » á˝E×u˝ń fairly describes the
experimental results over the entire range of shear rate investigated. Other materials
manifest a transition from an initially affine to a square-root non-affine
response, Ge(0)/Ge(g) » á˝E×u˝ń1/2, as rate is increased. Implications of
these results on polymer contour length dynamics are discussed.
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Lynden A. Archer
Department of Chemical Engineering
Texas A&M University
College Station, TX 77843 USA
Abstract
Requirements for factorable nonlinear shear relaxation moduli were investigated using a
series of entangled polystyrene/diethylphthalate solutions. Polymer solutions were
formulated to maintain fixed entanglement spacing over a broad range of polymer molecular
weights, 7 < N / Ne < 90, 1.3 × 105 < fMw < 1.6 × 106. For all polymers
studied, a separability time lk was
identified beyond which step shear relaxation moduli could be factorized into separate
strain and time-dependent functions. In every case, lk
exceeded the most optimistic estimates for the longest Rouse relaxation time tRouse, in some cases by as much as two orders
of magnitude. lk was also found to scale
nearly as strongly with polymer molecular weight as the terminal relaxation time and
limiting shear viscosity. These results provide convincing evidence against a Rouse origin
for the separability criterion in entangled polymer liquids and could help explain
previous experimental observations of "delayed" factorability and/or
non-factorable relaxation moduli in well entangled polymer liquids. The experimental
findings are discussed in the context of a modified tube model that takes into account
tube deformation in flow.
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Benoît Debbaut1* and Joseph Dooley2
1 Polyflow s.a., 16 Place de l'Université
B-1348 Louvain-la-Neuve, Belgium
2 The Dow Chemical Company
433 Building, Midland, MI 48667, USA
*Corresponding Author
Abstract
The development of secondary motions due to the non-zero second normal stress
difference is observed and analysed by tracking the motion of the interface between two
batches of the same low density polyethylene, each with a different pigmentation. In the
present paper we focus on straight and tapered channels with a square cross section.
Three-dimensional numerical simulations are also performed on the basis of a multi-mode
differential viscoelastic fluid model. Such calculations allow the investigation of the
development of secondary motions in space. Predictions are compared with the experiments:
good agreement is found between the experimental observations and their numerical
counterparts. The magnitude and the relevance of the secondary motions are also discussed.
A numerical analysis is also carried out on the sensitivity of the secondary motions with
respect to the nonlinear properties of the viscoelastic model. Finally, we make a brief
attempt in explaining the mechanism which drives the secondary motions.
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M. E. van Marle1, D. van den Ende2, C. G. de Kruif3*,
and J. Mellema2
1 NIZO food research, P.O. box 20
6710 BA Ede, The Netherlands
2 Twente University, P.O. box 217
7500 AE Enschede, The Netherlands
3 Van 't Hoff Laboratory for Physical and Colloid Chemistry
Debye Institute, Utrecht University
Padualaan 8, 3584 CH Utrecht, The Netherlands
* Corresponding Author
Abstract
Stirred yoghurt was viewed as a concentrated dispersion of aggregates consisting of
protein particles. The steady-shear behaviour of three types of stirred yoghurt with
varying ropiness was investigated experimentally. To describe the shear-dependent
viscosity a microrheological model was used which was developed for weakly aggregating
dispersions. This model was capable of successfully describing the steady-state viscosity
as a function of shear rate of the stirred yoghurts, the protein concentration of which
ranged between 2.0 and 3.9%. The value of the fractal dimensionality, df,
following from the model for the aggregates is about 2.24, which was similar to the value
of df found with other methods. Moreover, realistic values were found
for the interaction forces (energies) describing interaction between the aggregates. The
calculated size of the aggregates was close to the size found before by applying different
experimental techniques. Using this model, the interpretation of the measured curves
suggests that the exopolysaccharides, produced by the lactic acid bacteria in yoghurt,
play a significant role in the rheology of stirred yoghurt.
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Heon Sang Lee and Morton M. Denn*
Materials Sciences Division, Lawrence Berkeley National Laboratory, and
Department of Chemical Engineering, University of California at Berkeley
Berkeley, CA 94720-1462 USA
*Corresponding Author - Current address: The Levich Institute
City College of the City University of New York, 1-M Steinman Hall
Convent Avenue at 140th Street, New York, NY 10031 USA
Abstract
The steady-shear viscosity and first normal stress difference and the dynamic storage
and loss moduli have been measured for a blend consisting of a thermotropic liquid
crystalline polymer dispersed in a thermoplastic fluoropolymer matrix. The components are
immiscible and nonreacting. Consistency with the Palierne emulsion theory for viscoelastic
blends is possible if and only if the interfacial tension contribution is negligible for
droplets that are comparable in size to a liquid crystalline domain or smaller, while
retaining the effect for larger droplets. Steady shear results are approximately described
by the scaling of the Doi-Ohta theory, but there is a significant reduction in the excess
shear stress over a finite shear-rate range for the lowest concentration, which contains
the smallest droplets.
† The editorial process for this manuscript was carried out by
Editorial Board member Paula Moldenaers.
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Dino Ferri and Paolo Lomellini
ENICHEM Research Center
Via Taliercio 14, 46100 Mantova, Italy
Abstract
Melt rheological properties of different homologous series of linear polystyrenes (LPS)
and randomly branched polystyrenes (RBPS) in both linear and nonlinear viscoelastic
response regions are presented. In the linear regime, the master curves of the
experimentally determined viscoelastic functions reveal that the temperature dependence of
the shift factors aT for all the samples follow the Vogel-Tammann-Fulcher (VTF)
equation: aT µ exp[B / (T- T0)]. The
value of the apparent activation energy B is found to increase slightly with increasing
degree of branching, reflecting a stronger temperature dependence of the viscosity of RBPS
with respect to LPS. This difference is approached in the frame of both Ngai's coupling
model and free volume theory.
In the nonlinear regime, the shear rate dependence of the steady state viscosity h(g-dot), corrected for both non-Newtonian
and entrance effects, was measured. A comparison with the angular frequency dependence of
the dynamic complex viscosity |h * (w)|
reveals an interesting behavior concerning the Cox-Merz rule. In the non-Newtonian flow
region, for LPS the relationship h(g-dot)
< |h * (w)| is found to hold. On
the other hand, RBPS exhibit an unusual failure of the rule characterized by the
relationship h(g-dot) > |h * (w)|.
Elongational behavior of RBPS is also presented. Assuming a Wagner type single integral
constitutive equation for the RBPS, a generalized time-temperature superposition principle
(TTS) in the field of nonlinear viscosity is attempted: elongational stress curves
measured at different temperatures are found to match qualitatively the same master curve
if both time and strain rate are reduced with an appropriate shift factor.
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Prediction of the wax content of the incipient
wax-oil gel in a pipeline: An application of the controlled-stress rheometer
Probjot Singh and H. Scott Fogler
Department of Chemical Engineering
University of Michigan, Ann Arbor, MI 48109 USA
Nagi Nagarajan
Mobil Technology Company
13777 Midway Road, Dallas, TX 75244 USA
Abstract
High molecular weight paraffins are known to form gels of complex morphology at low
temperatures due to the low solubility of these compounds in aromatic or naphthene-base
oil solvents. The characteristics of these gels are strong functions of the shear and
thermal histories of these samples. A model system of wax and oil was used to understand
the gelation process of these mixtures. A significant depression in the gel point of a
wax-oil sample was observed by either decreasing the cooling rate or increasing the steady
shear stress. The wax-oil sample separates into two layers of different characteristics, a
gel-like layer and a liquid-like layer, when sheared with a controlled-stress rheometer at
high steady shear stresses and low cooling rates. The phase diagram of the model wax-oil
system, obtained using a controlled-stress rheometer, was verified by analyzing the wax
content of the incipient gel deposits formed on the wall of a flowloop. Based on the
rheological measurements, a law has been suggested for the prediction of the wax content
of the gel deposit on the laboratory flowloop walls. The wax content of the incipient gel
formed on the wall of a field sub-sea pipeline was predicted to be much higher than that
for the flowloop at similar operating conditions. This variation in the gel deposit
characteristics is due to the significant differences in the cooling histories in the two
cases.
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M. Gregory Forest, Qi Wang*, and Hong Zhou†
Department of Mathematics
The University of North Carolina
Chapel Hill, NC 27599-3250 USA
*Permanent Address: Department of Mathematical Sciences
Indiana University-Purdue University Indianapolis
Indianapolis, IN 46202 USA
† Current Address: Department of Mathematics
University of California, Santa Cruz, CA 95064
Abstract
The interaction between flow and orientation of liquid crystalline polymers (LCPs)
creates remarkable heterogeneous patterns in which defects, or singular solutions, serve
to mediate a confluence of ordered nematic phases. The origin of defects remains a
mystery. It is therefore valuable to have models for LCP flows that provide some evidence
of defects, and of the corresponding physical competition between flow and LCP properties.
In this direction, the flow-orientation moment-averaged Doi model is studied with an
imposed elongational flow. Nonhomogeneous, biaxial nematic patterns are discovered in both
axial and planar elongation. These exact solutions consist of spatially varying directors
in the plane orthogonal to the flow axis, coupled with homogeneous biaxial order parameter
equilibria fixed by the LCP concentration (N) and elongation rate (n). For each (N, n), the
following patterns co-exist all with identical order parameter values: the homogeneous
patterns of (Rey 1995); radially symmetric director patterns; finally, director patterns
periodic in the cylindrical azimuthal angle. The nonhomogeneous structures are
distinguished by the presence of core defects along the axis of flow symmetry,
characterized by a logarithmic pressure singularity at the core.
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Wolfgang Thimm1, Christian Friedrich1*, Michael
Marth1, and Josef Honerkamp1,2
1 Freiburger Materialforschungszentrum
Stefan-Meier-Straße 21
D-79104 Freiburg im Breisgau, Germany
2 Universität Freiburg, Fakultät für Physik,
Hermann-Herder-Straße 3
D-79104 Freiburg im Breisgau, Germany
*Corresponding Author. E-mail: chf@fmf.uni-freiburg.de
Abstract
In this article it is shown that the relaxation time spectrum can be analytically
related to the molecular weight distribution regarding a recently derived generalized
mixing rule. This analytical relation greatly reduces the computational effort to
determine the molecular weight distribution from the relaxation time spectrum. In this
mixing rule a generalized mixing parameter b has been
introduced. This parameter has been controversially discussed in the literature. The value
of b has been determined theoretically by Doi and
Edwards (1986) as b = 1 and Des Cloizeaux (1988) and
Tsenoglou (1987) (b = 2) and experimentally by Maier et
al. (1998) (b = 3.84). In this article the influence
of b on shape and position of peaks in bimodal molecular
weight distributions is emphasized.
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U. Jacobs, M. Fahrländer, J. Winterhalter, and Chr. Friedrich*
Freiburger Materialforschungszentrum
and Institut für Makromolekulare Chemie
Albert-Ludwigs-Universität, Stefan-Meier-Str. 21
D-79104 Freiburg im Breisgau, Germany
*Corresponding Author. E-mail: chf@fmf.uni-freiburg.de
Abstract
The quantitative understanding of rheological experiments on compatibilized binary
polymer blends requires the consideration of viscoelastic interfacial properties. The
Palierne model offers these capabilities but a systematic analysis has not been performed
yet.
Starting from the Palierne model containing a Maxwell-ansatz for complex interfacial
shear or dilatational moduli and which considers a particle size distribution function, we
find that this model combines parameter and material functions in an ambiguous way.
Consequently, a simplified version of the model - frequency independent interfacial moduli
and monomodal particle size distribution - was introduced. Formulas have been derived for
the relaxation times, the form relaxation time and one additional still longer time which
is associated with viscoelastic interfacial properties.
We have found a good agreement between the predictions of the model and experimental
data as well as the characteristic times in the relaxation time spectrum and the derived
time constants for a PS/PMMA blend compatibilized with different amounts of a
corresponding symmetric block copolymer. These results reveal that from the rheological
point of view, the interface is of almost elastic nature, either shear or dilatational.
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Davide A. Hill
Department of Chemical Engineering
University of Notre Dame du Lac
Notre Dame, IN 46556 USA
* This article is dedicated to Professor Morton M. Denn.
Abstract
The kinetic theory for rigid-rod molecules has been successful in describing a variety
of experimental observations, from extremely dilute concentrations to the liquid
crystalline limit. The theory is formulated in terms of an orientation distribution
function (ODF), whose tensorial moments can be related to measurable properties. We
introduce here a general relation from which evolution equations for moments of arbitrary
order can easily be derived. The relation incorporates the effects of flow, magnetic and
electric fields (permanent and induced dipoles) as well as "nematic"
interactions necessary to describe liquid crystalline transitions. Relevant features of
the equation(s) with regard to possible closure strategies are briefly discussed.
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E. Wassner1, M. Schmidt, H. Münstedt*
Institute of Polymer Materials, Department of Materials Science
University Erlangen-Nuremberg, Martenstr. 7
D-91058 Erlangen, Germany
1 Current Address: Polymer Research Division
BASF-AG, D-67056 Ludwigshafen, Germany
*Corresponding Author
Abstract
The flow behaviour of a PE-LD melt in a 14:1 planar contraction was investigated by
laser-Doppler-velocimetry. The velocity field in the central plane of the flow channel is
composed by the measurement of the velocity components in and perpendicular to the
direction of extrusion. Two dies differing in their entrance angles are compared. In the
case of the flat entry die large recirculating vortices are found in front of the die
entry plane. Under stable flow conditions there is no material exchange between the
vortices and the primary flow. It is shown that very small velocities within the vortices
can be measured accurately. In the case of the oblique entry die no vortices are found.
By the normalization of the velocity profiles with the average velocity in the die,
calculated independently from the mass flow rate, an output-invariant presentation is
found for the apparent shear rate range from 53 to 182 s-1.
The velocity distribution along the centerline of the flow channel exhibits a
pronounced velocity overshoot shortly after the die entry plane. The distance up to a
fully developed velocity field within the die is about 15 times the height of the slit.
Due to the acceleration of the melt in front of the die entry large elongational
deformations occur. The resulting maximum elongation rates (20 s-1) are
very high compared to those achievable by elongational rheometers. It is demonstrated by
the comparison of the strain rate tensor components that the elongational deformation in
the center plane of the flow channel is planar.
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Frederic Prochazka, Dominique Durand, and Taco Nicolai
Chimie et Physique des Matériaux Polymčres, UMR CNRS
Université du Maine, 72085 Le Mans Cedex 9, France
Abstract
Linear polyurethane melts were prepared by a
polycondensation reaction of poly(oxypropylene) (POP) diol with a diisocyanate. Covalently
cross-linked gels were obtained using 3-armed star POP triol. The glass transition
temperature and the viscoelastic properties were investigated as a function of the molar
mass of the POP precursors. The variation of Tg is dominated by the density of
urethane links. The loss peak of the shear modulus at high frequencies or low temperatures
broadens with increasing density of urethane links. The gel modulus of end-linked POP
triol decreases linearly with increasing molar mass of the precursors. The loss shear
modulus of end-linked POP triol has a power law frequency dependence at low frequencies.
The exponent of the power law dependence decreases with increasing molar mass of the
precursors. Gels formed with POP triol with molar mass larger than 6kg/mol show the effect
of entanglements at intermediate frequencies.
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Hans Christian Öttinger
ETH Zürich, Department of Materials, Institute of Polymers,
and Swiss F.I.T. Rheocenter, CH-8092 Zürich, Switzerland
Abstract
The primary purpose of this paper is to introduce the effect of chain stretching into a
previously developed, thermodynamically admissible reptation model incorporating
anisotropic tube cross sections, double reptation, and convective constraint release,
while avoiding the independent alignment approximation. A second goal is the detailed
illustration of the thermodynamic modeling approach. Two versions of the model with
different stretching mechanisms are proposed, and the simpler one sheds new light on
thermodynamically admissible reptation models without independent alignment. The
stochastic reformulation of the new model, its simulation, its linear viscoelastic
properties, its predictions for rapid double-step shear strains, and the model parameters
are discussed in detail.
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In-situ characterization by small angle
light scattering of the shear-induced coalescence mechanisms in immiscible polymer blends
D. Rusu1 and E. Peuvrel-Disdier*
École des Mines de Paris
Centre de Mise en Forme des Matériaux, UMR CNRS n° 7635
BP 207, 06904 Sophia-Antipolis Cedex, France
1 Permanent address: University of Medicine and Pharmacy
"Gr. T. Popa" Iasi
Faculty of Biomedical Engineering, Biomaterials Department, 6600 Iasi, Romania
*Corresponding Author. E-mail: edith.disdier@cemef.cma.fr
Abstract
This work presents an in-situ experimental investigation of the shear-induced
coalescence mechanism in low concentration polymer blends (1 to 10%). An original sizing
method based on small-angle light scattering and optical microscopy was used to determine
the evolution of the drop size distributions as a function of time. In order to study the
pure coalescence mechanisms, measurements were conducted according to a specific flow
protocol. The influences of the shear rate, initial morphology, concentration of the
polymer blend and phase inversion on the coalescence kinetics were investigated. The
investigated blends are mixtures of polydimethylsiloxane and polyisobutene.
The amount of strain, the step-down rate ratio and the concentration squared are
identified as relevant parameters to describe the coalescence kinetics. The dependence of
the steady state drop sizes on the applied shear rate is well described by a coalescence
model considering partially mobile interfaces.
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Vladimír Pavlínek and Petr Sáha
Faculty of Technology in Zlín
Technical University Brno
762 72 Zlín, Czech Republic
Jaroslav Stejskal and Otakar Quadrat*
Institute of Macromolecular Chemistry
Academy of Sciences of the Czech Republic
162 06 Prague 6, Czech Republic
*Corresponding Author. E-mail: quadrat@imc.cas.cz
Abstract
Rheological study of dispersions of poly(methyl methacrylate) particles stabilized in
decane by a steric stabilizer, polystyrene-block-poly(ethene-co-propene)
diblock copolymer, revealed an extremely high apparent viscosity at low shear rates or
even the yield stress at relatively low volume fraction of particles (~ 0.1). This
behaviour is due to highly interacting stabilizer macromolecules anchored to the particle
surface. As the concentration of poly(methyl methacrylate) is further increased, the
volume fraction of particles also increases, the particle diameter grows, the number of
particles is reduced and the viscosity of the dispersion falls down.
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Q. T. Pham*, W. B. Russel
Department of Chemical Engineering
Princeton University, Princeton, NJ 08544 USA
J. C. Thibeault, W. Lau
Research Laboratories, Rohm and Haas Company
Spring House, PA 19477 USA
* Current Address: Unilever Research, Edgewater, NJ, USA
Abstract
The viscoelasticity of latex dispersions containing triblock associative polymers
exhibits multiple modes of relaxation. Here we confirm that the behavior at high frequency
is imparted by the associated solution and characterized by a high frequency modulus and
relaxation time comparable to the neat micellar solution at the same concentration. At low
frequencies, diffusional modes of the particles generate a power law spectrum of
relaxation times. Here the time scales and the volume fraction dependence of the
contribution reflect the slower dynamics of particles incorporated into a percolating
network via weak attractions between the adsorbed polymer layers. The viscoelasticity of
the dispersions is correlated by superimposing the two modes.
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A. Saint-Jalmes and D. J. Durian
Department of Physics and Astronomy
University of California, Los Angeles, CA 90095-1547 USA
Abstract
We present an experimental study of the rheology of polydisperse aqueous foams of
different gas volume fractions, f. With oscillatory
deformation at fixed frequency, we determine the behavior of the maximum stress as a
function of the strain amplitude. At low strain, the maximum stress increases linearly,
defining a shear modulus G. At progressively higher strains, the response
eventually becomes nonlinear, defining the yield strain and the yield stress. While f decreases toward fc
= 0.635±0.01, G goes to zero, and the yield stress decreases by many orders of
magnitude with a quadratic behavior. The yield strain, which can be extrapolated to
0.18±0.02 at f = 1, has a minimum value of 0.045±0.010
at fc. This behavior shows the occurrence of
a melting transition located at fc, which can
be correlated to the random close packing of spheres. We compare these results to similar
ones obtained previously for monodisperse and polydisperse emulsions. Our new experiments
clarify the rheological similarities between emulsions and foams, as well as the role of
polydispersity. We find that as long as polydispersity is moderate, it does not play a
crucial role in the elastic response of foams and emulsions.
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J-F Le Meins, J-F Tassin*
Université du Maine, Chimie et Physique des Matériaux Polymčres
UMR CNRS 6515, Avenue Olivier Messiaen
72085 Le Mans Cedex 09, France
J-M Corpart
Elf Atochem S.A., Centre d 'applications de Levallois
95, rue Danton - B.P. 108, 92303 Levallois-Perret Cedex, France
*Corresponding Author
Abstract
Flow birefringence and dichroism experiments are used to study the behavior of
solutions of an Hydrophobic Ethoxylated Urethane (HEUR) with a molecular weight of
35000g/mol and a C16 hydrophobic end-cap in a concentration range around C*. Relaxation
experiments after step shear have shown the existence of two relaxation processes. The
first relaxation process with a characteristic time tshort»0.1s, independent on concentration, has been attributed to the
lifetime of an end group in a micelle and subsequent relaxation through a Rouse process.
The second relaxation process (tlong»300s), has been attributed to the relaxation of aggregates of POE
chains. They induce a small dichroism in the solutions and damped oscillations in start up
shear flows at low shear rates. Upon cessation of steady shear flow, the two relaxations
are still observed, the amplitude of the short time one increasing with shear rate. The
origin of this long time relaxation which is not observed in classical rheological
measurements is attributed to the presence of organic impurities remaining from the
chemical modification of the polymer. Extensive purification of the polymer leads to the
disappearance of these impurities and consequently of the long relaxation process.
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Hiroshi Yamaguchi, Takeshi Yasumoto, and Hideaki Yamamoto
Department of Mechanical Engineering
Doshisha University, Kyoto, 610-0321, Japan
Abstract
Experiments were conducted in order to obtain flow states occurring at a junction of
two laminar flow layers. In the present study, various combinations of Newtonian and
non-Newtonian fluids for two laminar layers were tested in a relatively high-speed
stratification process where the inertia of flow has to be taken into account. From
experimental results, flow states at a junction with two different junction angles were
classified into ten flow modes and these modes were arranged to establish a
three-dimensional mode map by using a generalized Reynolds number and Deborah number. It
was revealed that a mutual relationship among inertial, viscous and elastic effects is
essential for interfacial deformation and instability in the stratified flow. It was also
shown that the junction angles are important factors in the determination of flow modes
appearing in the region of the junction.
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