- Shear Flow of Wormlike Micelles in Pipe and Cylindrical Couette
Geometries as Studied by NMR Microscopy
- R. W. Mair and P. T. Callaghan
- More on the Prediction of Molecular Weight Distributions of
Linear Polymers From Their Rheology
- C. Lavallée and A. Berker
- Bimodal Model of Suspension Viscoelasticity
- M.Z. Sengun and R.F. Probstein
- Experimental Characterization of Sharkskin in Polyethylenes
- C. Venet and B. Vergnes
- Quantitative Predictions of Suspension Rheologyby NEBD and
Hydrodynamic Preaveraging
- Sanjeev R. Rastogi and Norman J. Wagner
- l-D Isothermal Spinning Models for Liquid Crystalline Polymer
Fibers
- M. Gregory Forest, Qi Wang, and Stephen E. Bechtel
Shear Flow of Wormlike Micelles
in Pipe and Cylindrical Couette Geometries
as Studied by NMR Microscopy
R. W. Mair and P. T. Callaghan*
Department of Physics, Massey University
Palmerston North, New Zealand
*corresponding author
Abstract
The non-linear viscosity of the wormlike surfactant system cetyl pyridinium chloride/sodium
salicylate (60 mM/100 mM in water) has been investigated in both pipe and cylindrical
Couette geometries, using Nuclear Magnetic Resonance to image both velocity and diffusion.
In pipe flow we observe transitions from Newtonian to non-Newtonian viscosity, to spurt,
to unstable flow, and then to a regime where fluctuations are rapid on the time scale of a
few milliseconds. In the Couette cell we observe apparent slip at the inner wall as well
as a high shear rate band located away from the wall in the body of the fluid. The banding
phenomenon, which has its counterpart in the pipe flow, is consistent with double
valuedness in the stress vs. rate-of-strain relationship for this fluid.
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C. Lavallée
3M Canada, Inc., P.O. Box 5757, London, Ontario N6A 4T1
A. Berker
3M Co., 236-1B-21, 3M Center, St. Paul, MN 55144-1000
Abstract
We extend two methods (those due to Tuminello and to Shaw), among the several currently
available, for calculating the molecular weight distribution function W(M)
of linear polymers from their rheology data. An extension of Tuminello's method is
proposed by using the terminal Rouse relaxation time as a scaling factor. The 79th
percentile of the zero-shear viscosity normalized flow curve is used to evaluate the
terminal Rouse relaxation time. Using this technique, it is possible to convert frequency
to molecular weight, without the use of an external standard. An extension to Shaw's
numerical technique is also proposed which leads to an analytical expression for the
polydispersity ratio. For this purpose the Elbirli-Yasuda-Carreau viscosity model is used
to describe the flow curve. The development is carried out for both the logarithmic and
the power law mixing rules considered by Shaw.
Due to the approximate nature of both the original methods of Tuminello and Shaw that
we start out with and our subsequent approximations, the resulting distribution should
only serve as a first order approximation to the actual W(M) and the
calculated moments of W(M) may be off by as much as about 50% from their
true values. Since the more rigorous inverse problem techniques that are also currently
available can offer greater accuracy, justification for the use of the approximate methods
discussed in this work rests solely on their relative simplicity and ease of
implementation.
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Bimodal Model of Suspension Viscoelasticity
M.Z. Sengun* and R.F. Probstein
Department of Mechanical Engineering
Massachusettes Institute of Technology
Cambridge, MA 02139
*Present address; Xerox Corp., 800 Phillips Rd, Webster NY 14580
Abstract
In the bimodal model of the viscoelastic behavior of a bimodal suspension
with a colloidal size fine fraction and a non colloidal size coarse fraction, the two
fractions behave independently of each other when the particle size ratio is large. The
colloidal fraction is solely responsible for the non-Newtonian behavior while only
hydrodynamic interaction takes place between the coarse particles. Measurements performed
on a bimodal suspension and on a suspension of non-colloidal particles in a polymeric
liquid indicate that the non-Newtonian behavior originates from the colloidal fraction in
the former and from the polymeric liquid in the latter. The results support the validity
of the concepts behind the bimodal model.
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C. Veneta and B. Vergnesb
CEMEF, Ecole des Mines de Paris, URA CNRS 1374,
BP 207, 06904 Sophia-Antipolis, France
a Present address: Schneider Electric SA,Centre de Recherches de
Grenoble,38050 Grenoble Cedex 9, France
b To whom correspondence should be addressed
Abstract
The sharkskin defect appearing during the capillary extrusion of three low density
polyethylene resins with different molecular structures has been characterised. Using
complementary techniques - profilometry, optical microscopy and observation of cross
sections - the amplitude and the period of the defects have been measured accurately. The
influence of flow rate, temperature and die geometry has been quantified. The specific
behavior of the orifice die has been put in evidence. It shows that, if the role played by
the stress field is evident, the wall shear stress is not the unique determinant of the
sharkskin process. The influences of molecular structure and elongational behavior in
sharkskin are discussed. It appears that resins exhibiting long chain branching and strain
hardening are less sensitive to sharkskin.
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Quantitative Predictions of Suspension Rheology
by NEBD and Hydrodynamic Preaveraging
Sanjeev R. Rastogi* and Norman J.
Wagner†
Center for Molecular and Engineering Thermodynamics
Department of Chemical Engineering
University of Delaware, Newark DE 19716
*Current Address: Union Carbide, Bound Brook NJ 08805
†Author to whom correspondence should be sent. Current address:
Institute for Polymer Physics, ETH-Z ML H18, CH-8092 Zurich, Switzerland
Abstract
Nonequilibrium Brownian dynamics simulations are applied to model a highly-concentrated
dispersion of charged particles at high ionic strength. Through the
use of hydrodynamic preaveraging, as applied to the overdamped Langevin equation, and
correlations appropriate for hard spheres, good predictions are obtained for the
suspension shear viscosity at low to moderate shear rates. At higher shear rates, the
influence of near-field hydrodynamic interactions on the suspension microstructure
invalidates the preaveraging approach.
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M. Gregory Forest
Department of Mathematics
The University of North Carolina at Chapel Hill
Chapel Hill, NC 27599-3250
Qi Wang
Department of Mathematical Sciences
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202
Stephen E. Bechtel
Department of Aerospace Engineering, Applied Mechanics, and Aviation
The Ohio State University
Columbus, OH 43210
Abstract
A slender 1-D model for filaments of liquid crystalline polymers (LCPs) is applied to
simulate isothermal fiber spinning of materials with internal orientation. The focus is on
the hydrodynamic-orientation interactions in spinning flows, isolated from other
significant spinline effects of temperature, crystallization and phase changes. Spun fiber
orientation (in particular, birefringence) is deduced from first principles along with
fiber diameter and velocity. One result of our modeling and simulations is that, in
isothermal spinning, the microstructure (orientation tensor) is weakly radially dependent
and can be calculated from l-D models. Families of numerical steady state fiber spinning
solutions, together with their linearized stability, are presented. These calculations
reveal upper bounds on throughput in terms of the critical draw ratio, above which
the process is unstable. The effects on stability due to LCP parameter changes are
thoroughly investigated. We find enhancement of the effects of LCP kinetic energy or
relaxation can either stabilize or destabilize steady spinning solutions, whereas enhanced
anisotropic drag is always destabilizing. Evidence is given for a preferred degree of
upstream LCP alignment at which the critical draw ratio achieves a maximum, indicating an
important role played by near-spinneret conditions in increasing throughput.
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