- 1995 Bingham Medal Address: Oh, Thermorheological Simplicity,
Wherefore Art Thou?
- Donald J. Plazek
- Crossover Behavior in the Viscosity of Semiflexible Polymers:
Intermolecular Interactions as a Function of Concentration and Molecular Weight
- G. C. Berry
- Crossover Behavior in the Viscosity of Semiflexible Polymers:
Solutions of Sodium Hyaluronate as a Function of Concentration, Molecular Weight and
Temperature
- M. Milas, I. Roure, and G. C. Berry
- A Fifty Cent Rheometer for Yield Stress Measurement
- N. Pashias, D.V. Boger, J. Summers, and D.J. Glenister
- Brownian Electrorheological Fluids as a Model for Flocculated
Dispersions
- Yvette Baxter-Drayton and John F. Brady
- Nuclear Magnetic Resonance Imaging of Apparent Slip Effects
in Xanthan Solutions
- Craig J. Rofe, Lourdes de Vargas, José Pérez-González, Rodney K. Lambert, and Paul T.
Callaghan
- Quasi-Static Measurements on a Magnetorheological Fluid
- Xinlu Tang and Hans Conrad
- Tensile Stress Measurements of Dilute Polymer Solutions
Containing Traces of Salts and Dyes
- Jae K. Lee and Neil S. Berman
- Kinetics of Structure Development in Liquid-Liquid Dispersions
Under Simple Shear Flow. Theory
- S.A. Patlazhan and J.T. Lindt
- On the Effects of a Piezoviscous Lubricant on the Dynamics
of a Journal Bearing
- D. Rh. Gwynllyw, A. R. Davies, and T. N. Phillips
- Residual Normal Force after Cessation of Squeezing Flow of Liquid
Crystalline Polymers
- Alejandro D. Rey
- An Experimental Study of Particle Migration in Pipe Flow of
Viscoelastic Fluids
- M. A. Tehrani
- Influence of Molecular Weight Distribution on the Melt
Extrusion of High Density Polyethylene (HDPE) - Effects of Melt Relaxation Behavior on
Morphology andOrientation in EIDPE Extruded Tubular Films
- Ta-Hua Yu and Garth L. Wilkes
- Rheological Behavior of Highly Concentrated Aqueous Silica
Suspensions in the Presence of Sodium Nitrate and Polyethylene Oxide
- A. A. Zaman, B. M. Moudgil, A. L. Fricke, and H. El - Shall
- Rheology of Dense Suspensions of Plate-like Particles
- S. Jogun and C F. Zukoski
1995 Bingham Medal Address
Oh, Thermorheological Simplicity
Wherefore Art Thou?
Donald J. Plazek
Materials Science and Engineering
University of Pittsburgh
Pittsburgh, PA 15261
Abstract
Polyisobutylene PIB was the first polymer whose viscoelastic behavior was thoroughly
studied. The measurements made world wide on the PIB sample distributed from the National
Bureau of Standards were compiled and analyzed by Bob Marvin. The superposition of the
data substantiated the time-temperature reduction process, which was suggested by Herbert
Leaderman, first put into practice by Arthur Tobolsky and given a theoretical foundation
by John Ferry. Polymers that behaved in a like manner were called thermorheologically
simple by A.J. Staverman and F. Schwarzl. Subsequently the behavior of PIB has been found
to be the exception rather than the rule. The various deviations from this simplicity are
briefly reviewed and PIB is reexamined.
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Crossover Behavior in the Viscosity of
Semiflexible Polymers:
Intermolecular Interactions as a Function of Concentration and Molecular Weight
G. C. Berry
Department of Chemistry
Carnegie Mellon University
Pittsburgh, PA 15213
Abstract
A simple relation is presented for the viscosity of isotropic solutions of flexible,
semiflexible and rodlike chains over a range of concentration from dilute solutions to
undiluted polymer, chain contour length L and persistence length â. The
expression is designed to account for the separate effects of screening of thermodynamic
and hydrodynamic interactions, and the onset of intermolecular chain entanglements under
Flory theta solvent conditions, or in "good" solvents, for which intramolecular
excluded volume is important in dilute solutions. The relation includes a revised
(dimensionless) Fox parameter Xc that determines the onset of
intermolecular entanglements, where Xc = pi NA rho
Lc â / 3ML for semiflexible polymers with â
<< L, with rho the polymer density, ML the
mass per unit length of the chain, and Lc the value of L for
the onset of entanglement effects in undiluted polymer; Xc » 100 for
a number of systems, including rodlike chains.
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Crossover Behavior in the Viscosity of
Semiflexible Polymers:
Solutions of Sodium Hyaluronate as a Function of Concentration,
Molecular Weight and Temperature
M. Milas and I. Roure
Centre de Recherches sur les Macromolécules Végétales, CNRS
Affiliated with the Joseph Fourier University of Grenoble
BP 53, 38041 Grenoble cedex 9, France
G. C. Berry
Department of Chemistry
Carnegie Mellon University
Pittsburgh, PA, 15213, USA
Abstract
Viscometric data on moderately concentrated solutions of the semiflexible
macromolecule sodium hyaluronate over a range of molecular weight M and solute
concentration c in aqueous 0.1 M NaCl are analyzed using a generalized expression
for the viscosity of isotropic polymers and their solutions. Owing to its semiflexible
nature, the effects of excluded volume interactions are effectively screened for sodium
hyaluronate under the conditions studied, and intramolecular hydrodynamic interactions are
largely screened, even at infinite dilution. The consequences of this for scaling of the
viscosity relative of solutions of sodium hyaluronate with the parameters c[eta]
and cM is discussed. The dependence of the viscosity on cM is in accord
with the generalized relation, and leads to an estimate for the persistence length in
reasonable accord with that found by light scattering measurements on dilute solutions.
The temperature dependence of the viscosity suggests that the dependence of the
persistence length on temperature may be partially suppressed with increasing polymer
concentration.
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A Fifty Cent Rheometer for Yield Stress Measurement
N. Pashias, D.V. Boger
Department of Chemical Engineering
University of Melbourne
Parkville, Victoria 3052, Australia
J. Summers, D.J. Glenister
Residue Development Alcoa Australia
Booragoon, W.A. 6154, Australia
Abstract
The slump test, initially developed to determine the flow properties of fresh concrete,
has been adopted as a means of accurately measuring the yield stress of strongly
flocculated suspensions. The slump test offers a quick and easy way of measuring yield
stress without the need for sophisticated electronic equipment, thereby giving plant
operators an effective tool for determining yield stress. The model used to predict the
yield stress from the conical slump test was devised by Murata (1984) and corrected by
Christensen (1991). In the present case the theory has been adapted for a cylindrical
geometry. Yield stress measurements obtained with the vane for numerous mineral
suspensions under known surface chemistry conditions are compared to the slump
measurements and theoretical prediction. Good agreement is obtained.
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Brownian Electrorheological Fluids as a Model for
Flocculated Dispersions
Yvette Baxter-Drayton and John F. Brady
Division of Chemistry and Chemical Engineering
California Institute of Technology
Pasadena CA, 91125
Abstract
The rheological behavior of Brownian electrorheological (ER) fluids is studied as a
model for flocculated colloidal dispersions. The ER fluid has the advantages that the
interparticle potential energy can be varied by simply changing the applied field
strength, and the microstructure consists of essentially linear chains of particles
aligned with the field direction. Under simple shear flow, the suspension has a
high-shear-rate Newtonian viscosity and a shear thinning viscosity at lower shear rates.
For moderate attractive potential well depths, Umin/kT, the
suspension has a low-shear viscosity that scales as exp(Umin/kT).
Furthermore, the low shear limiting behavior is seen at shear rates that scale as
exp(– Umin/kT). A theory is proposed that makes use of
the time scale of diffusion for aggregated particles out of their mutual potential well, T
~ (a2/D) (kT/Umin) exp(Umin/kT),
much in the spirit of the Eyring theory. Here a is the particle radius and D
is the diffusivity of an isolated particle. When the shear rate is non-dimensionalized by
T, the reduced viscosity data for all field strengths collapse onto a single universal
curve. Although we use a relatively small monolayer suspension, our simulation results
compare well to the limited experimental and theoretical work on Brownian FlR suspensions.
The scaling relationship for the low-shear viscosity has also been evidenced in other
studies of flocculated dispersions.
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Nuclear Magnetic Resonance Imaging of Apparent
Slip Effects in Xanthan Solutions
Craig J. Rofe, Lourdes de Vargas†, José Pérez-González†,
Rodney K. Lambert, and Paul T. Callaghan
Department of Physics
Massey University
Palmerston North
New Zealand
†Departamento de Ciencia de Materiales, Escuela Superior de
Fisica y Matematicas, Instituto Politecnico Nacional, Mexico D.F., Mexico
Abstract
NMR imaging has been used to investigate the flow of 0.2% aqueous solutions of xanthan
gum. Apparent slip was observed in solutions made from the material supplied by UNAM but
not in that supplied by Aldrich or Kelco. The apparent slip velocity was a constant
fraction of the maximal velocity for a given contraction ratio. The apparent slip velocity
also appeared to be independent of L/D but was strongly influenced by the wall
stress, the observed apparent slip velocities being comparable with those determined using
the Mooney analysis on capillary flows. After exposure to the action of a syringe pump,
which reduced the mean molecular weight of the xanthan, the UNAM xanthan solution no
longer exhibited apparent slip. Slip appears to be a function of molecular weight,
possibly through sensitivity to the aspect ratio of the molecule.
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Quasi-Static Measurements on a Magnetorheological
Fluid
Xinlu Tang* and Hans Conrad
Material Science and Engineering Department
North Carolina State University
Raleigh, NC 27695-7907 U.S.A
*Visiting scholar, on leave from the Department of Mechanics and Mechanical Engineering
University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
Abstract
The shear stress tau shear strain gamma behavior of suspensions of
carbonyl iron particles in silicone oil was determined at a shear rate gamma-dot
= 0.042 s–1 as a function of applied magnetic induction B0
(0.5 - 6.0 kGauss), volume fraction of particles phi (0.05 - 0.30) and roughness
of the shearing surfaces. At low fields, the steady-state shear stress taus
was significantly higher for a roughened surface compared to a smooth surface, but became
only slightly dependent on roughness at high fields. In accord with theoretical
considerations, the ratio taus/phi was proportional to the
square of the calculated magnetic field H0 inside the suspension at
low fields, but its dependence on H0 became smaller as the field
increased. The smaller dependence may result from the magnetic saturation of the particles
or the slipping boundary condition.
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Tensile Stress Measurements of Dilute Polymer
Solutions
Containing Traces of Salts and Dyes
Jae K. Lee
Environmental Research Division, Korea Electric Power Research
Institute, Yusong, Taejon 305-380, Korea
Neil S. Berman
Department of Chemical, Bio and Materials Engineering
Arizona State University, Tempe, AZ 85287-6006
Abstract
Tensile stress studies were made on dilute solutions of poly(ethylene oxide)(PEO) and
polyacrylamide(PAM) using a fiber spinning apparatus to investigate the interaction of
polymer molecules with the flow field. The addition of dyes or metal ions to the solutions
has a considerable influence on the tensile stress. These ingredients normally cause
contraction of the polymer coils and stiffen the molecular chains. One additive, Congo
Red, markedly increased the tensile stress of poly(ethylene oxide) solutions.
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Kinetics of Structure Development in Liquid-Liquid
Dispersions
Under Simple Shear Flow. Theory
S.A. Patlazhan* and J.T. Lindt
Department of Materials Science and Engineering
University of Pittsburgh
848 Benedum Hall
Pittsburgh, Pennsylvania 15261, USA
*Permanent address: Institute of Chemical Physics, Russian Academy of Sciences,
Chernogolovka, Moscow Region, 142432 Russia
Abstract
The kinetics of structure development in a moderately concentrated liquid-liquid
dispersion under the hydrodynamic conditions of simple shear flow has been analyzed using
deferential population balance equations. The existing models of the breakup and
coalescence phenomena have been examined, modified and included in the population balances
to the extent necessary. It was found that in the present range of drop sizes and
viscosity ratios the temporal evolution of the average drop size is primarily determined
by drop breakup rather than by coalescence. It was further shown that the evolution of the
size distribution function as well as the average drop size are strong functions of the
viscosity ratio, exhibiting sharp changes at the critical capillary number. The role of
the initial drop size distribution on the time-dependent state of the dispersion was
examined, including the path leading to a bimodal distribution.
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On the Effects of a Piezoviscous Lubricant on
the Dynamics of a Journal Bearing
D. Rh. Gwynllyw, A. R. Davies, and T. N. Phillips
Department of Mathematics
University of Wales
Aberystwyth SY23 3BZ
United Kingdom
Abstract
A moving spectral element method is used to investigate the effects of non-Newtonian
lubricants on the dynamics of a journal bearing. It is well known that for a constant
viscosity full-film lubricant the journal eventually displays half-speed whirl which is
undesirable due to the accompanying fall in load bearing capacity and vibration. The
inclusion of a cavitation model into the scheme stabilises the motion of the journal in
some situations. In this paper it is demonstrated that piezoviscous lubricants can
stabilise the journal even without the incorporation of a cavitation model. The addition
of a cavitation model is shown to stabilise the motion of the journal further in the sense
that equilibrium points or limit cycles are reached more quickly. The effects of
shear-thinning and inertia on the motion of the journal are also considered.
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Residual Normal Force after Cessation of Squeezing
Flow of Liquid Crystalline Polymers
Alejandro D. Rey
Department of Chemical Engineering
McGill University
Montreal, Quebec H3A 2A7 Canada
Abstract
Classical liquid crystal theories are used to develop a model to compute the normal
forces and shear torques for liquid crystalline polymers. The model is applied to the
parallel disk geometry and the normal forces from three representative average molecular
orientations are computed. It is found that a positive normal force tending to separate
the parallel disks will always be present whenever the orientation is subjected to a
twisting deformation. For typical parameter values and geometries, the model predicts that
normal forces are six order of magnitude larger than shear torques. The model predictions
are validated with the experimental data presented by Langelaan and Gotsis (1996).
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An Experimental Study of Particle Migration in
Pipe Flow of Viscoelastic Fluids
M. A. Tehrani*
Schlumberger Cambridge Research
High Cross, Madingley Road
Cambridge CB3 0EL, England
*Present address: Schlumberger Dowell
Par Moor Road, Par, Cornwall PL24 2 SQ, England
Abstract
This paper reports experiments on particle migration in viscoelastic fluids used in
hydraulic fracturing. It is found that particle migration in such fluids is controlled by
the elastic properties of the suspending fluid and the shear rate gradient. In fluids with
low but measurable normal stresses and dominant shear-thinning properties, particles
migrate to regions of lower shear rate. Migration is fast initially but slows down rapidly
over a short distance. For these fluids the bulk migration velocity correlates with the
product of the Weissenberg number and the mean shear rate gradient. In contrast, highly
elastic fluids with relaxation times well above one second and shear-thickening properties
at low shear rates flow with a central plug region or slip at the wall, producing little
or no migration.
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Influence of Molecular Weight Distribution on the
Melt Extrusion
of High Density Polyethylene (HDPE) -
Effects of Melt Relaxation Behavior on Morphology and
Orientation in EIDPE Extruded Tubular Films
Ta-Hua Yu and Garth L. Wilkes
Department of Chemical Engineering
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061
Abstract
The influence of molecular weight distribution and extrusion processing variables on
the morphological features and orientation of HDPE uniaxially extruded tubular films was
investigated. In order to gain a better understanding of the orientation-crystallization
behavior occurring during extrusion processing, the melt flow properties of the two HDPE
resins with identical Mn (14,600) values but different molecular
weight distributions ( Mw / Mn =10.3, 15.1),
utilized in our previous study, were characterized by dynamic rheological experiments over
the temperature range from 150°C to 230°C within the angular frequency range from 0.1 to
100 rad/s. The experimental data were shifted to produce master flow curves. The flow
activation energy calculated from the shifting process was found to be 25.9 kJ/mol for
Resin 1 and 29.1 kJ/mol for Resin 2. The characteristic relaxation time at 190°C obtained
by use of a Carreau-Yasuda analysis for Resin 2 having the broader molecular weight
distribution was found to be 6.5 times greater than that of Resin 1. This observation
further supports our previous conjecture that the prominence of the fibril nuclei in Resin
2 is due to its longer melt relaxation time behavior. The extrusion processing variables
of melt temperature at the die exit, quench height (which is the distance from the exit of
the die to the cooling ring), flow rate of the air through the cooling ring, film line
speed, and die gap were varied to control the melt relaxation time of HDPE resins and the
processing time frame for cooling. The results show that a longer melt relaxation time and
a shorter cooling processing time can enhance the formation of fibril nuclei. The
importance of melt relaxation behavior in influencing the final morphological structure in
HDPE extruded films and their associated properties is clearly made evident in this paper.
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Rheological Behavior of Highly Concentrated Aqueous
Silica Suspensions
in the Presence of Sodium Nitrate and Polyethylene Oxide
A. A. Zaman*, B. M. Moudgil**, A. L. Fricke*, and H. El - Shall**
University of Florida
Gainesville
*Department of Chemical Engineering
**Department of Materials Science and Engineering
Abstract
The shear flow properties of aqueous silica suspensions at different solids loading in
the presence of PEO (polyethylene oxide) and added salt (NaNO3) have been
investigated. Particular attention is given to the evaluation of the role of electrolyte
concentration, pH, and polymer concentration in viscosity reduction. The variation of the
rheological properties with shear rate, solids loading, particle size, pH, electrolyte
concentration, PEO concentration and its molecular weight are discussed.
The viscosity of the silica suspension was determined to be a decreasing function of
the particle diameter and at 54% volume, the effect of particle size was scaled using
Peclet number and relative viscosity of the suspension (hard sphere scaling). The flow
properties of silica suspensions are highly affected by the pH of the suspending media and
concentration of the added salt. At a fixed electrolyte concentration, the viscosity
decreases by increasing pH, reaches a minimum and then increases with further increase in
pH. At a fixed pH level, the same behavior was observed for viscosity as a function of
electrolyte concentration. The effect of the electrolyte concentration is more significant
at lower shear rates. It is shown that the rheological properties of silica suspensions
are strongly affected by the concentration of the added polymer and its molecular weight.
For each sample, there is a critical amount of polymer that must be added before low
viscosities result. There is a nearly linear relation between the critical polymer
concentration and volume fraction of the particles. The results of this work provide
useful information for selection of a proper pH range, electrolyte concentration, and
optimum polymer concentration to control the viscosity behavior of highly concentrated
silica slurries.
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Rheology of Dense Suspensions of Plate-like
Particles
S. Jogun and C F. Zukoski
Department of Chemical Engineering and Beckman Institute
University of Illinois
Urbana, IL 61801
Abstract
The flow properties of dense kaolin suspensions are explored for volume fractions as
large as 0.43. The particles were suspended in phosphate buffers at pH's of 7 and 10 where
edge-face interactions are negligible. These platey particles have an aspect ratio of
approximately 12 and thus are likely to show alignment at volume fractions above a
critical volume fraction phi* = 0.10. As the concentration is increased from the
dilute region of Newtonian behavior, the suspensions develop a yielding type of response
near this critical volume fraction. The time dependence of the recoverable strain in some
dense suspensions is found to scale on gamma-dot0 t where t
is the time after the stress is released and gamma-dot0 is the steady
shear rate prior to release of the stress. Over the same time period the elastic modulus
remains constant. The magnitude of the modulus is, however, dependent on gamma-dot0
decreasing from a low shear rate plateau value of G'max to a high
shear rate plateau value of G'min. The shear rate halfway between G'max
and G'min is independent of volume fraction and lies near 0.39 D0rot
where D0rot is the free solution rotational diffusion
constant of the plates. This behavior is interpreted as indicating that the plates
experience a tumbling/shear aligning transition as the shear rate is raised. Further
evidence for alignment is found in shear induced changes in suspension conductivity.
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