- Pressure oscillations and periodic extrudate
distortions of longchain branched polyolefins
- Jaap den Doelder, Rudy Koopmans, Marc Dees, and Marc Mangnus
- Steady state and transient rheological behavior of
mesophase pitch: Part I – Experimental
- Anthony D. Cato, Dan D. Edie, and Graham M. Harrison
- DNA configurations and concentration in shearing flow
near a glass surface in a microchannel
- Lin Fang, Hua Hu, and Ronald G. Larson
- Extensibility of rubber under different types of
deformation
- A. N. Gent
- Steady state and transient rheological behavior of
mesophase pitch: Part II – Theoretical
- Dana Grecov and Alejandro D. Rey
- Comparison of shear-induced crystallization
behavior of PB-1 samples with different molecular weight distribution
- C. Hadinata, C. Gabriel, M. Ruellmann, and H. M. Laun
- Glass transitions and shear thickening suspension
rheology
- C. B. Holmes, M. E. Cates, M. Fuchs, and P. Sollich
- The rheology of dilute solutions of flexible
polymers: Progress and problems
- Ronald G. Larson
- Response of concentrated suspensions under large
amplitude oscillatory shear flow
- Takatsune Narumi, Howard See, Atsushi Suzuki, and Tomiichi Hasegawa
- Extrusion of triblock and pentablock copolymers:
Evolution of bulk and surface morphology
- Alhad Phatak, Christopher W. Macosko, Frank S. Bates, and Stephen F.
Hahn
- Co-continuity in immiscible polymer blends: A gel
approach
- Mickael Castro, Frédéric Prochazka, and Christian Carrot
- Scaling behavior for gravity induced flow of a yield
stress material
- John E. Sader and Malcolm R. Davidson
- Basic rheological features of block polyurethane
solutions: Entanglements, crystallization and gelation
- Sonia Florez, María Eugenia Muñoz, and Anton Santamaría
- Stress dielectric response in liquid polymers
- Yiyan Peng, Yuri M Shkel, and GeunHyung Kim
- The flowability of ice suspensions
- Jason R. Stokes, Julia H Telford, and Ann-Marie Williamson
- A critical evaluation of step strain flows of
entangled linear polymer liquids
- David C. Venerus
- Theory of morphology evolution in mixtures of
viscoelastic immiscible components
- Wei Yu, Chixing Zhou, and Mosto Bousmina
Jaap den Doeldera) and Rudy Koopmans
Dow Benelux B.V., Core R&D
P.O. Box 48, 4530 AA, Terneuzen, The Netherlands
Marc Dees and Marc Mangnus
Dow Benelux B.V., Plastics R&D
P.O. Box 48, 4530 AA, Terneuzen, The Netherlands
Abstract
Capillary rheometry is a much used technique for measuring pressure –
flow rate behavior of polymer melts. The nature of such a “flow curve”
depends on polymer architecture, die geometry, die material composition,
and rheometer operating conditions. Typically, with increasing flow
rates, monotonic flow curves have been associated with extrudates that
transcend from smooth to being volume-distorted. Alternatively,
nonmonotonic
flow curves have been associated with a sequence of extrudate
appearances ranging from smooth via surface distortions and “spurt” to
volume distortions. New experiments however indicate that monotonic flow
curves can also be associated with “spurt-like” distorted extrudates.
For several long-chain branched polymers it is reported that while the
average pressure increases monotonically with increasing flow rate, the
extrudate distortions transition through an unanticipated regime where
the extrudate consists of alternating smooth and volume-distorted zones.
Its origin is conjectured related to the specific viscoelastic flow
properties of long-chain branched materials in the reservoir-die
contraction region. Using a fast-response pressure transducer in the
reservoir near the capillary die entry, the presence of small-amplitude
pressure oscillations corresponding to the distortion period is
confirmed. The critical conditions for the appearance of this phenomenon
depend strongly on molecular mass and branching distribution.
a) Author to whom all correspondence should
be addressed. E-mail:
cfdendoelder@dow.com
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Anthony D. Catoa),
Dan D. Edieb), and Graham M. Harrison
Center for Advanced Engineering
Fibers and Films and
Department of Chemical Engineering
127 Earle Hall, Clemson University
Clemson, SC 29634-0910, USA
Abstract
The rheology of a liquid crystalline mesophase pitch is reported. Over
the range of shear rates and temperatures investigated, the steady state
shear viscosity and the first normal stress difference display Region 1
and Region 2 flow behavior typical of many liquid crystalline systems. A
kink in the transition between Regions 1 and 2 is also observed. The
first normal stress difference is negative at low shear rates, but
transitions to positive values in the shear rate region of the kink in
the viscosity. These phenomena are explained by change in the molecular
orientation of the sample. The evolution of the shear stress in
transient startup and relaxation experiments is measured. There is a
distinct overshoot in the startup of shearing, and a rapid decay of
stress upon cessation of flow. As expected, the magnitude of the
overshoot depends on the rest time between shearing. The estimated
elastic constant is consistent with other work.
a) Current address: Chemical Technology Center,
Fluor Corporation, 100 Fluor Daniel Drive, Greenville, SC 29607-2770, USA
b) Corresponding author. E-mail address:
ddedie@clemson.edu
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Lin Fang, Hua Hu, and Ronald G. Larson
Department of Chemical Engineering
University of Michigan
Ann Arbor, Michigan 48109-2136
Abstract
We characterize the configurations and concentration of λ-phage DNA
molecules in shear flow near a glass surface in a microchannel through
epi-fluorescence microscopy. We observe that in Poiseuille flow, over a
region extending from a glass surface up to about one third of the
contour length of the DNA molecule, the average stretch of a λ-phage DNA
molecule is significantly lower than in the bulk, in agreement with
results obtained in a steady torsional shear flow by Li et al.
(2004). We also find that the concentration of DNA molecules in this
same region is notably lower than in the bulk, to a degree that
increases with increasing Weissenberg number. A simplified explanation
is proposed for the behavior of DNA molecules near the glass surface
based on wall influences on hydrodynamic interaction within the chain,
motivated by the recent theoretical work of Jendrejack et al.
(2003, 2004).
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A. N. Gent
The University of Akron
Akron OH 44325-3909
Abstract
The finite lengths of molecular strands in a crosslinked rubber network
impose a limit on the extensibility because some of the strands become
fully stretched. This feature must be taken into account in formulating
a strain energy function W to describe the elastic response of
rubber, especially for high strains. The question is: Are the maximum
strains the same for different types of deformation, or different?
Maximum strains are compared here for various types of homogeneous
deformation: simple extension; simple shear and pure shear (constrained
tension); and equi-biaxial extension. The rubber is assumed to consist
of a network of Gaussian strands that are randomly arranged in the
unstrained state and deform affinely until representative strands become
fully stretched, at a limiting value J1m of the
first strain invariant, J1. Dickie and Smith (1971)
showed that the extensibility in equi-biaxial stretching is only about
70% of that in simple extension, in accord with a limiting value of J1.
For other simple types of deformation the extensibilities are expected
to be nearly equal. Possible deficiencies in the model and in the
experiments are then considered. It is concluded that the general result
is likely to be valid, and that a model for rubber elasticity at large
strains should include a limiting value of the first strain invariant,
J1, rather than the second, J2.
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Dana Grecov and Alejandro D. Reya)
Department of Chemical Engineering
McGill University, 3610 University Street
Montreal, Quebec, Canada H3A 2B2
Abstract
We present a comprehensive nonlinear numerical analysis of the flow
modeling of mesophase pitches performed using a previously formulated
mesoscopic viscoelastic rheological theory (Singh and Rey (2000)) that
takes into account short-range order elasticity, long range elasticity
and flow-induced texture transformations. A complete extra stress tensor
equation is developed from first principles for liquid crystal materials
under non-homogeneous arbitrary flow. This mesoscopic viscoelastic model
has been adapted to describe the rheology of flow-aligning thermotropic
discotic nematic liquid crystals as models of mesophase pitches.
Predictions for simple shear flow (under non-homogeneous conditions) for
the shear viscosity, first normal stress differences and transient shear
stress are presented. The accuracy of the numerical results is
established by a thorough validation procedure based on (Cato et al.
(2004)), which is the companion paper, and permit to validate this
mesoscopic viscoelastic theory as model of liquid crystalline mesophase
pitch. Very good qualitatively agreement between experiments and
simulations is found for all rheological characterizations.
a) Corresponding author. E-mail address:
aleajandro.rey@mcgill.ca
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C. Hadinataa), C. Gabrielb),
M. Ruellmanna), and H. M. Launa)
a) Polymer Physics, BASF Aktiengesellschaft,
Polymer Physics
Ludwigshafen/Rhein 67056, Germany
b) Polymer Physics & Characterization, Basell
R&D
Frankfurt am Main, D-65926, Germany
Abstract
Shear-induced crystallization behavior of three grades of PB-1 having
different molecular weights and breadths of molecular weight
distribution was investigated by means of rotational rheometry covering
a shear rate range of 0.0001 up to 0.3 s-1 and temperatures
between 99°C and 107°C. The up-shoot in viscosity after a certain time
is used to define an onset time ton for both
quasi-quiescent and shear-induced crystallization. The plot of ton
vs. shear rate can be converted into a temperature-invariant curve by
dividing the y-axis by quiescent onset time ton,q
and multiplying x-axis by the square root of ton,q.
Possible reasons for this finding will be addressed. The shape and
location of the T-invariant curves for the three PB-1 samples are
compared with respect to their molecular parameters. An additional
normalization step by multiplying the abscissa by the square root of the
characteristic retardation time of the melt yields a dimensionless
representation of the T-invariant curve. Furthermore, by this
procedure the three curves are shifted into one region, where they have
the same threshold value indicating the onset of shear-induced
crystallization. A connection of this T-invariant curve to the
morphology of the crystallites formed will be addressed.
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C. B. Holmes and M. E. Catesa)
School of Physics, The University of Edinburgh, JCMB,
The King's Buildings, Edinburgh, EH9 VZ, UK
M. Fuchs
Fachbereich Physik, Universitat Konstanz, D-78457 Konstanz, Germany
P. Sollich
Department of Mathematics, King's College,
University of London, Strand, London, WC2R 2LS, UK
Abstract
We introduce a class of
simple models for shear thickening and/ or 'jamming' in colloidal
suspensions. These are based on schematic mode coupling theory (MCT) of
the glass transition, having a memory term that depends on a density
variable, and on both the shear stress and the shear rate. (Tensorial
aspects of the rheology, such as normal stresses, are ignored for
simplicity.) We calculate steady-state flow curves and correlation
functions. Depending on model parameters, we find a range of rheological
behaviours, including 'S-shaped' flow curves, indicating discontinuous
shear thickening, and stress-induced transitions from a fluid to a
nonergodic (jammed) state, showing zero flow rate in an interval of
applied stress. The shear thickening and jamming scenarios that we
explore appear broadly consistent with experiments on dense colloids
close to the glass transition, despite the fact that we ignore
hydrodynamic interactions. In particular, the jamming transition we
pro-pose is conceptually quite different from various hydrodynamic
mechanisms of shear thickening in the literature, although the latter
might remain pertinent at lower colloid densities. Our jammed state is a
stress-induced glass, but its nonergodicity transitions have an
analytical structure distinct from that of the conventional MCT glass
transition.
a) Author to whom
correspondence should be addressed. E-mail:
mec@ph.ed.ac.uk
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Ronald G. Larson
Department of Chemical Engineering
University of Michigan, Ann Arbor
Michigan 48109-2136
Abstract
Recent progress towards understanding the rheology of dilute solutions
of flexible polymers is reviewed, emphasizing experimental results from
flows of single DNA molecules and filament-stretching rheometry of
dilute polystyrene Boger fluids, as well as Brownian dynamics (BD)
simulations of these flows. The bead-spring and bead-rod models are
presented, the range of their applicability discussed, and methods
presented for inclusion of hydrodynamics interactions, excluded volume,
and other physical effects within BD simulations. After reviewing and
updating work in the linear viscoelastic regime, the primary focus
shifts to the more complex nonlinear regime. While Brownian dynamics
predictions of the conformations of 20-to-100-micron long DNA molecules
in strong shear and extensional flows has been in good to excellent
agreement with the corresponding experiments, predictions of the
polystyrene dilute solution rheometry data have been hit-or-miss, with
poorer results obtained for the higher molecular weights. This may in
part be due to the more important roles of hydrodynamic interactions and
excluded volume interactions in the more flexible, and therefore more
condensed, polystyrene coils. Inclusion of these effects in BD
simulations has led to improved predictions, but do not lead to accurate
prediction of the plateau Trouton viscosity for higher molecular weight
samples, nor the complete failure of simulations to predict measurements
of coil distortion by light scattering. Thus, despite enormous progress
in the past decade, some significant gaps in understanding remain.
Return to top.
Takatsune Narumia)
Department of Mechanical and Production Engineering, Niigata University,
8050 2-no-cho Ikarashi, Niigata 950-2181, Japan
Howard See
Department of Chemical Engineering, The University of Sydney,
NSW 2006, Sydney, Australia
Atsushi Suzuki and Tomiichi Hasegawa
Department of Mechanical and Production Engineering, Niigata University,
8050 2-no-cho Ikarashi, Niigata 950-2181, Japan
Abstract
Concentrated suspensions of non-Brownian spheres dispersed in a
Newtonian carrier liquid were placed under large amplitude oscillatory
shear flow. It was found that the response waveforms consisted of a
transient response after each reversal in the shearing direction,
followed by purely viscous behaviour. It was thought that rearrangements
in the particulate microstructure could account for this transient
response. Further, the characteristic strain for the microstructural
rearrangement was found to be essentially independent of the oscillation
frequency, and showed good agreement with the corresponding
characteristic strain obtained from measurements of the transient
response after shear reversal in continuous shear experiments. In
addition, the fluidity in the oscillatory flow after the transient
response was found to be higher than that in the steady flow case. This
increase in fluidity was found to depend on the particle size dispersity,
with the largest fluidity difference occurring with the mono-dispersed
systems.
a) Author to whom all correspondence should be
addressed. E-mail:
narumi@eng.niigata-u.ac.jp
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Alhad Phatak, Christopher W. Macosko, and Frank S. Batesa)
Department of Chemical Engineering and Materials Science
University of Minnesota
Minneapolis, Minnesota 55455
Stephen F. Hahn
The Dow Chemical Company
23-1 N. Brazosport Blvd, Building B-1470D
Freeport, Texas 77541
Abstract
We report studies on the extrusion of
nearly monodisperse triblock and pentablock copolymers composed of
poly(cyclohexylethylene) (C) and poly(ethylene) (E). Lamellae forming
CEC triblock and CECEC pentablock copolymers were extruded through a
slit die using a capillary rheometer at various processing speeds and
temperatures below the order-disorder transition temperatures. Extrudate
microstructure was characterized by small angle x-ray scattering (SAXS)
and the surface characteristics were investigated by optical microscopy
and profilometery. At low extrusion rates, the triblock and pentablock
copolymers display different bulk orientation behavior, leading to
relatively smooth surfaces in both cases. Above a characteristic wall
shear stress, associated with a slope change in the flow curve, both
polymers exhibit perpendicular lamellae alignment but dramatically
different surface properties. The CEC material contains relatively low
amplitude (ca. 1-3 mm) random roughness while
the CECEC surface is highly textured, with periodic ~50
mm undulations that resemble a sharkskin
morphology. These differences are attributed to the rheological
consequences of center C bridging in the pentablock copolymer.
c) Author to whom all correspondence should
be addressed. E-mail:
bates@cems.umn.edu
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Mickael Castro, Frédéric Prochazkaa), Christian
Carrot
Laboratoire de Rhéologie des Matières Plastiques, UMR 5156
Université Jean Monnet
23, rue du Dr Paul Michelon, 42023 Saint Etienne, France
Abstract
Rheological properties of PEO/PVdF-HFP immiscible polymer blends have
been studied in the low frequency domain. As a function of the blend
composition, two critical compositions have been determined by rheology.
These compositions exhibit a power law relaxation spectrum with a
critical exponent D. This observation leads
us to compare the evolution of the morphology in a binary blend to the
process of gelation. The supermolecular structure obtained at the limit
of the co-continuity zone is assimilated to the native network in the
chemical or physical gelation and discussed in term of self similar
superstructure and fractal dimension.
a) E-mail:
prochazk@univ-st-etienne.fr
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John E. Sadera) and Malcolm R. Davidsonb)
a) Department of Mathematics and Statistics
b) Department of Chemical and Biomolecular Engineering
The University of Melbourne
Victoria, 3010
Australia
Abstract
Deformation of a cylinder of yield stress material under gravitational
loading is investigated numerically, and found to obey a geometric
scaling law that is independent of both the magnitude of deformation and
yield stress. This scaling law provides a fundamental connection between
the initial and final dimensions of the body, and the critical aspect
ratio (radius / height) for the onset of flow. Importantly, this finding
is contrary to the standard model of [Murata, Mater. Constr. (Paris),
17, 117-129 (1984); Pashias et al. J. Rheol. 40,
1179-1189 (1996)], which is currently used in industrial processes to
measure the yield stress, and predicts that the deformation is
independent of radius. Consequently, the accuracy of this latter model
is assessed, and a new formalism for such yield stress measurements
proposed.
a) E-mail:
jsader@unimelb.edu.au
b) E-mail:
m.davidson@unimelb.edu.au
Return to top.
Sonia Floreza), María Eugenia Muñozb),
and Anton Santamaríab)
a) FUNDACIÓN INASMET
Paseo Mikeletegi, 2. 20009 San Sebastián, Spain
b) Polymer Science and Technology Department
POLYMAT Faculty of Chemistry
University of the Basque Country
20018 San Sebastián, Spain
Abstract
Three block polyurethane samples (differing
in hard (urethane) to soft (macroglycol) segments ratio) dissolved in
2-butanone, are investigated. Rheological results obtained in the range
10 to 25ºC led to the hypothesis of an order-disorder transition (ODT)
associated with H-bonds being discarded. The critical concentration and
the characteristic molecular weight for entanglements, Mc,
are estimated approximately from linear viscosity results. Mc
decreases as the percent of hard segments in the polyurethane increases,
a result which is correlated with short-distance chain parameters such
as length and molecular weight per bond and characteristic ratio.
Annealing clear solutions at temperatures around 0ºC causes haziness; on
heating, a clearing temperature is detected at Tc
» 15ºC. This transition coincides with a
maximum observed in complex viscosity h*
versus temperature curves. These results are probably due to incipient
crystallization of soft segments domains. This hypothesis is compatible
with DSC results. Opaque solutions give rise to thermoreversible gels:
we assume that the network branch points necessary for gelation involve
microcrystalline domains which result from crystallization of soft
segments from solution.
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Yiyan Peng, Yuri M Shkela), and GeunHyung Kim
Department of Mechanical Engineering
University of Wisconsin, Madison, WI 53706
Abstract
Deformation-induced dielectric response of dielectric materials, called
dielectrostriction, provides a newapproach to study properties and
structure of liquid polymers. The dielectrostriction effect resembles
the well-known birefringence phenomenon. While birefringence in liquid
polymers is described by the stressoptic relationship, a
stress-dielectric relationship applies to dielectrostriction. However,
dielectrostriction measurements can be performed on both transparent and
opaque materials, require a much simpler data acquisition technique, are
capable of local measuring stresses and can be implemented for in-line
monitoring of polymer processing. In this study, a planar capacitor
sensor technique has been developed to detect the dielectrostriction
effect in shear flow of liquid polymers. Experimental evidences of the
dielectrostriction effect and the stress-dielectric relationship in
liquid polymers are presented for both silicone elastomer and
Poly(ε-caprolactone). Mechanisms contributing to the similarity between
the stressdielectric and the stress-optic relationship are discussed.
a) Author to whom correspondence should be
addressed. E-mail:
yshkel@engr.wisc.edu
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Jason R. Stokesa), Julia H Telford, and
Ann-Marie Williamson
Unilever Corporate Research, Unilever R&D Colworth,
Sharnbrook,
Bedford MK44 1LQ, United Kingdom
Abstract
Ice slurries show great potential for use in low energy refrigeration
and cold storage systems but their transport properties and ice particle
agglomeration are not well understood. Determination of the rheology of
ice slurries has proved very difficult mainly due to the low viscosity
carrier fluids currently used. In this paper we accurately characterise
the rheology of a series of ice particle suspensions using a vane
geometry at -18°C. The ice slurries have the same high viscosity
continuous phase, so the effect of volume fraction of ice particles can
be examined, and no phase separation occurs. The flow curves across the
phase volume range of 9 % to 29 % were characterised by a large
zero-shear viscosity (h0 >
10,000 Pa-s), and a region where the viscosity shear thins dramatically.
The shear thinning occurs at a critical shear stress that is regarded
here as an apparent yield stress (sy).
Above the yield stress, the slurries flow according to a power law
relationship. The zero-shear viscosity and apparent yield stress scale
with the phase volume (f) according
h0 ~ f
5 and sy
~ f 3.5 respectively. The
large values of these exponents are in line with those found for
strongly flocculated particulate suspensions. This suggests that the
rheology at low stress is highly dependent on the interactions between
ice crystals, and the aggregation process that causes a network
structure to form.
a) E-mail:
Jason.Stokes@unilever.com
Return to top.
David C. Venerus
Department of Chemical Engineering and
Center of Excellence in Polymer Science and Engineering
Illinois Institute of Technology
Chicago, IL 60616
Abstract
A critical evaluation of step strain flow
experiments on entangled, linear polymer liquids is performed. Roughly
one-half of the published shear stress relaxation modulus data for these
systems are consistent with the predictions of the well-known tube
model. A model of step strain flow experiments is developed to determine
whether the remaining published data, which are qualitatively different
from tube model predictions, are simply artifacts caused by slip, an
imperfect strain step strain history, or transducer compliance. Modeling
results suggest that these factors are capable of producing the types of
behavior observed in experiments deemed anomalous . New criteria based
on the retraction time tR,
or longest Rouse relaxation time, for avoiding anomalies caused by
imperfect strain step strain history and transducer compliance are
proposed. These simple criteria are, in a majority of cases, found to be
capable of predicting the type of observed stress relaxation behavior
for 60 published step strain experiments on entangled, linear polymer
liquids.
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Wei Yua), Chixing Zhou
Department of Polymer Science and Engineering
Shanghai Jiao Tong University
Shanghai 200240, P. R. China
Mosto Bousmina
Canada Research Chair on Polymer Physics and Nanomaterials.
Department of Chemical Engineering, CREPEC
Laval University, Sainte-Foy, Quebec G1K 7P4, Canada
Abstract
An ellipsoidal model was constructed to describe the morphological
evolution and rheological properties of a mixture of two immiscible
viscoelastic components. The phenomenological parameters in the model
were determined by comparing the interfacial velocity gradient with the
viscoelastic theory for small deformation. The model was then applied to
various model blend systems to predict the steady deformation, transient
deformation and relaxation after cessation of step shear flow. The model
predictions were also compared with some available numerical
simulations. The predictions on droplet deformation both in steady and
transient regimes as well as the relaxation process were found to be in
good agreement with the experimental results in literatures. The
rheological properties predicted by present model were also found to
agree with experimental results.
a) Author to whom correspondence should be addressed. Email:
wyu@sjtu.edu.cn
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