Contents

Experimental Study of Pure Bitumens in Tension, Compression and Shear

C. Y. Cheung and D. Cebon

Zeolite-Based Electro-Rheological Fluids: Testing, Modeling and Instrumental Artifacts

Mabel Jordan, Anita Schwendt, Davide A. Hill, Scott Burton, and Nicos Makris

Determination of the Molecular Weight Between Crosslinks of Waxy Maize Starches Using the Theory of Rubber Elasticity

J. B. Gluck-Hirsch and J. L. Kokini

Rheological and Rheo-optical Characterization of Shear-induced Structure Formation in a Nonionic Drag-Reducing Surfactant Solution

Yuntao Hu and Eric F. Matthys

The Effects of Viscoelasticity on the Transient Motion of a Sphere in a Shear-Thinning Fluid

Mark T. Arigo and Gareth H. McKinley

Melt Elongation and Recovery of Polymer Blends, Morphology, and Influence of Interfacial Tension

Hansjörg Gramespacher and Joachim Meissner

Scaling of Relative Viscosity of Emulsions

Rajinder Pal

Anomalous Viscosity-Temperature Behavior of Aqueous Carbopol Solutions

Noh A. Park and Thomas F. Irvine Jr.

Some Conditions for Rupture of Polymer Liquids in Extension

A. Ya. Malkin and C. J. S. Petrie

Conduit Flow of an Incompressible, Yield-Stress Fluid

Alexandra J. Taylor and Simon D. R. Wilson

Experimental Study of Pure Bitumens
in Tension, Compression and Shear

C. Y. Cheung and D. Cebon
University Engineering Department
Trumpington Street, Cambridge, CB2 1PZ, U.K.

Abstract

Two nominally identical pure bitumens, commonly employed for pavement construction in the U.K., were tested in uniaxial tension, compression and shear, over a wide range of temperatures, stresses and strain rates. The bitumens were found to exhibit linear viscous behaviour at low stress levels, and power-law creeping behaviour at higher stress levels. The temperature dependence was found to follow the Arrhenius relationship at temperatures immediately above the glass transition and the WLF equation at higher temperatures. Below the glass transition temperature, the Eyring plasticity model was found to hold. Constitutive models which reflect the physical mechanisms of steady state and transient deformation are proposed. The fracture properties of the bitumens are also discussed.

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Zeolite-Based Electro-Rheological Fluids:
Testing, Modeling and Instrumental Artifacts

Mabel Jordan, Anita Schwendt, Davide A. Hill*
Department of Chemical Engineering
and
Scott Burton and Nicos Makris†
Department of Civil Engineering and Geological Sciences

University of Notre Dame du Lac
Notre Dame, Indiana 46556

Abstract

We examine the rheological response of zeolite-based ER suspensions in silicone oil, mineral oil and N-(4-methoxybenzylidine)-4 butylaniline, a low molecular weight, nematic liquid crystal. The carriers were selected to explore the effects of fluid viscosity and dielectric permittivity on the ER properties of the suspensions. A particular form of the White-Metzner constitutive equation correctly reproduces the main, qualitative features of the experiments, with only three parameters. When used in conjunction with an equation describing rheometer dynamics, the rheological model satisfactorily captures artifacts caused by the coupling of inertia and elastic compliance of the instrument with the non linear material response.

* Corresponding author
* and † Principal Investigators
† Present address: Department of Civil and Environmental Engineering, University of California, Berkeley CA 94720-1710

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Determination of the Molecular Weight Between Crosslinks of
Waxy Maize Starches Using the Theory of Rubber Elasticity

J. B. Gluck-Hirsch and J. L. Kokini
Center for Advanced Food Technology
Department of Food Science
Rutgers-The State University of New Jersey
P.O. Box 231
New Brunswick, NJ 08903-0231

Abstract

The theory of elasticity for solvent swollen rubbers was used to calculate the average molecular weight of chain between crosslinks, M_c, of 5 waxy maize starches with different degrees of crosslinking. Above a critical starch concentration (%w/w), maximum packing of granules occurs, and the interior of the granules controls the rheological behavior of the starch suspensions. A rubbery plateau, characterized by a storage modulus, G', independent of frequency, is related to the average M_c by the equation: M_c = c ^1/3 rho ^2/3 R T / G'. M_c values determined (g/mol) for lightly crosslinked starch were 2.7×10⁶ and 2.6×10⁶; for moderately crosslinked, 2.5×10⁶; and, 1.2×10⁶ and 1.2×10⁶ for highly crosslinked starches. As expected, a lower degree of crosslinking results in a higher molecular weight between the covalent bonds.

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Rheological and Rheo-optical Characterization of Shear-induced
Structure Formation in a Nonionic Drag-Reducing Surfactant Solution

Yuntao Hu and Eric F. Matthys*
Material Research Laboratory and Department of Mechanical Engineering
University of California, Santa Barbara, CA 93106, USA

Abstract

We know of only a few rheological studies of nonionic surfactant solutions, and these did not show clear evidence of shear-induced structures (SIS) formation. This paper reports, however, some rheological and rheo-optical results for nonionic surfactant solutions at different concentrations and temperatures that do show clear evidence of such SIS formation. For example, in a 0.3% SPE 95285 solution at 5°C, the shear viscosity, N₁, and flow birefringence start from a low level and takes tens of seconds to grow to a high plateau region upon the application of a 100 s^-l shear. The re-application of the same shear after rest following a preshear indicates that the effect of the shear persists for a very long time (hundreds of seconds). These transient flow results resemble those exhibited by cationic surfactants or associating polymer solutions. The time for the viscosity and N₁ to reach plateau values generally decrease with increasing shear rate and temperature. At moderate shear rates, the N₁ and viscosity decreases monotonically with increasing temperature, whereas at low shear rate the viscosity increases with temperature up to the could point, and then decreases. The steady state N₁ and viscosity levels increase with the surfactant concentration. Both the transient and steady state behavior appear rather insensitive to the addition of chemicals.

* Corresponding author

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The Effects of Viscoelasticity on the Transient Motion
of a Sphere in a Shear-Thinning Fluid

Mark T. Arigo and Gareth H. McKinley
Division of Engineering and Applied Sciences
Harvard University, 29 Oxford Street
Cambridge, MA 02138 USA

Abstract

We present the first quantitative experimental measurements of the transient motion of a sphere as it accelerates from rest along the centerline of a tube containing a highly elastic, shear-thinning, aqueous polyacrylamide solution. For all shear-rate-dependent Deborah numbers (l.6 [ < over _ ] De(gamma-dot) [ < over _ ] 4.2) and sphere-to-tube ratios (0.089 [ < over _ ] a/R [ < over _ ] 0.387) investigated, transient oscillations in the velocity of the sphere are observed, often causing the sphere to "rebound," or reverse directions during the first oscillation. These measurements are in qualitative agreement with the analysis of King and Waters (1972) who presented an analytic solution for the transient motion of a sphere through an unbounded domain of fluid described by the linear Jeffreys model. We also show a similar response in one-dimensional creep experiments which are described quantitatively by a multimode formulation of the upper-convected Maxwell model including a solvent retardation term. Such experiments isolate the shear kinematics from the combined shear and extensional flow around a sphere and indicate that because of the slow quadratic growth of the elastic normal stresses in the fluid at short times and small fluid strains, the initial transient motion of the sphere is governed primarily by a balance of linear viscoelastic stresses and the inertia of the sphere.

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Melt Elongation and Recovery of Polymer Blends, Morphology,
and Influence of Interfacial Tension

Hansjörg Gramespacher* and Joachim Meissner
Swiss Federal Institute of Technology (ETHZ), Institute of Polymers
CH-8092 Zürich, Switzerland

Abstract

Blends of polystyrene (PS) and poly(methylmethacrylate) (PMMA) have been investigated in elongation at 170°C. The melts of the pure PS and PMMA have only a small difference in their viscosities. Consequently, with 8 - 12 - 16 - 20 weight % PS in PMMA, the elongational viscosities of the melts show only small differences and are similar to that of PMMA. However, when the maximum elongation of 3.5 Hencky units (corresponding to a stretch lambda = 33 and obtained at a strain rate of 0.1 s^-1) is followed by recovery, the recoverable strain strongly depends on the PS concentration and shows very large values with a maximum that corresponds to a recoverable stretch of lambda R = 14.5 (for the 20% PS blend). The morphology obtained by quenching the samples shows that the originally spherical PS droplets in the continuous PMMA are stretched into ellipsoids and finally into long needles. During recovery, the viscoelastic deformation (molecular orientation) recovers and the stretched needles change backwards into spheres. But these two procedures occur with different time scales. The driving force for the second procedure is the interfacial tension alpha. An analysis is given for the determination of alpha from the measured transient recovery. Conversely, the transient recovery can be predicted when alpha, the droplet size, and the equilibrium value lambda R are known. Resulting from the different blends the interfacial tension between the melts of PS and PMMA is between alpha = 1.5 and 2.2 mN/m. This range covers previously published results for the same blends measured by a very different method, viz., shear oscillations.

* Present address: RAYCHEM GmbH, D-85521 Ottobrunn, Germany

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Scaling of Relative Viscosity of Emulsions

Rajinder Pal
Department of Chemical Engineering
University of Waterloo
Waterloo, Ontario N2L 3G1
CANADA

Abstract

A scaling analysis of the relative viscosity of two-phase liquid-liquid emulsions is presented. According to the analysis, the relative viscosity of two oil-in-water emulsions at the same oil concentration and particle Reynolds number is the same, even if the emulsions differ greatly in droplet size. Experimental results are presented to confirm the validity of the proposed scaling relations.

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Anomalous Viscosity-Temperature Behavior of Aqueous Carbopol Solutions

Noh A. Park*
Stony Brook Scientific, Ltd., 914 Fillmore Road, Norristown, PA 19403 USA

Thomas F. Irvine Jr.
Department of Mechanical Engineering, State University of New York
Stony Brook, NY 11794 USA

Abstract

The viscosity measurements of four Carbopol solutions at various temperatures and concentrations show shear thinning effects. However, an unexpected viscosity temperature behavior according to the concentrations of Carbopol solutions has been found. The viscosities of 3500 and 5000 wppm of Carbopol solutions decreased with increasing temperature. However, the viscosities of the 7500 and 10000 wppm solutions increased with increasing temperature.

* Corresponding author

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Some Conditions for Rupture of Polymer Liquids in Extension

A. Ya. Malkin
Research Institute for Plastics, 35 Perovskii Proezd, Moscow, Russia 111 024

C. J. S. Petrie†
Department of Engineering Mathematics, University of Newcastle upon Tyne
Newcastle upon Tyne, NE1 7RU, UK

Abstract

Rupture is one of the least investigated and least understood features of the rheological behaviour of polymeric liquids. Some key experimental results on the rupture of polymer melts in uniaxial extension are discussed.

Three features of experimental results for narrow MWD polymers may be highlighted. Firstly, steady elongational flow becomes impossible and rupture of the liquid filament occurs when and if the stored elastic (Hencky) strain reaches 0.5 units. This can be interpreted in terms of a critical Weissenberg number. Secondly, at higher rates of strain (when the elastic strain becomes more than 0.5) the relationship between limiting stress and elastic strain (at the breaking point) is linear. In this case the limiting elastic strain can become at least as high as 2. Thirdly, the strength of a fluid polymer is not a constant but may be characterised by the life-time, or durability, t* of the filament.

This leads to empirical criterion for rupture M = (sigma³ t*/eta)^1/2 = 0.30 ± 0.05 MJ/m, where eta is the shear viscosity, sigma is the stress at rupture and M has the dimension of specific energy. This criterion also predicts conditions of rupture for various complicated deformation histories.

These results are compared with results for broad MWD polymers. Theoretical criteria based on the results are related to rheological ideas and hypotheses concerning rupture, highlighting areas where further work is required.

† Corresponding author

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Conduit Flow of an Incompressible, Yield-Stress Fluid

Alexandra J. Taylor and Simon D. R. Wilson
University of Manchester, Department of Mathematics
Manchester, U. K.

Abstract

The steady flow of an incompressible material of the Bingharn viscoplastic type along a rectangular duct is calculated. This flow has importance in a number of geophysical problems. A numerical solution to the problem is found using finite differencing of the partial differential equation governing the fluid motion. The flow is seen to consist of a plug in the centre of the duct with dead regions of "no-flow" at the corners, due to the rectangular cross-section. The variation of this flow-pattern as a function of two non-dimensional parameters, the yield-stress and the aspect ratio, is investigated.

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