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Nov 1994

Volume 38, Issue 6, pp. 1641-1943


Rheo‐optics of liquid‐crystalline polymers in complex geometries

Jean‐Noël Baleo and Patrick Navard

J. Rheol. 38, 1641 (1994); http://dx.doi.org/10.1122/1.550564 (15 pages) | Cited 3 times

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The flow of isotropic and liquid‐crystalline hydroxypropylcellulose‐water solutions is studied in a transparent slit die with several geometries including divergent and convergent configurations. The flow is observed between crossed polars. In addition to the two different flow regimes that are known in shear (zones I and II), a new flow behavior is observed (zone III). Zone I is characterized by a large macroscopic orientation, as seen between crossed polars. It is localized where either shear rates or elongation rates are large. The extinction angle is a function of the position in the die. It is similar to the flow‐aligning regime observed at high shear rates. Zone II is much less oriented, due probably to a large density of defects. It is typical of the low shear rate region observed in simple shear. Zone III exhibits a peculiar behavior with long‐range orientation instabilities. It is always localized after a diverging zone. Flow around obstacles and colliding streams are also studied.
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83.80.Xz Liquid crystals: nematic, cholesteric, smectic, discotic, etc.
83.50.Ax Steady shear flows, viscometric flow
83.85.Ei Optical methods; rheo-optics
61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects on order

Molecular orientation and instability in plane Poiseuille flow of a liquid‐crystalline polymer

Bruce D. Bedford and Wesley R. Burghardt

J. Rheol. 38, 1657 (1994); http://dx.doi.org/10.1122/1.550565 (23 pages) | Cited 5 times

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A common rheological hypothesis, that the stress in a fluid element is only a function of its own deformation history, is rendered questionable in liquid‐crystalline polymers (LCPs) due to the presence of distortional elasticity, through which neighboring fluid elements may directly influence one another. However, the fine defect texture in LCPs has led to the suggestion that fluid properties may be averaged over a mesoscopic length scale, intermediate between the molecular and macroscopic, so that averaged measures of fluid structure and stress at this scale depend only on their own deformation history [R. G. Larson and M. Doi, J. Rheol. 35, 539 (1991)]. We describe an experimental test of this hypothesis. If true, it should be possible to use rheological and rheo‐optical data obtained in simple shear flow to predict the velocity and molecular orientation fields in a nonhomogeneous shear flow. Quantitative flow birefringence experiments are conducted on a liquid‐crystalline solution of poly(benzyl glutamate), in plane Poiseuille flow. At low flow rates, the data support the local response hypothesis. As flow rate is increased, however, a profound instability occurs that is unanticipated based on behavior reported in homogeneous simple shear flow. The instability is characterized by large wavelength disturbances in structure oriented perpendicular to the flow direction that are clearly visible to the naked eye. With increasing flow rate, these structures decrease in size and become increasingly chaotic. Despite the onset of the instability, time‐averaged measurements of average orientation may be qualitatively predicted based on simple shear flow data.
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83.80.Xz Liquid crystals: nematic, cholesteric, smectic, discotic, etc.
83.85.Cg Rheological measurements—rheometry
83.85.Ei Optical methods; rheo-optics
61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects on order

Rheological behavior of a hydrophobically associating water soluble polymer

T. Aubry and M. Moan

J. Rheol. 38, 1681 (1994); http://dx.doi.org/10.1122/1.550566 (12 pages) | Cited 2 times

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We have investigated experimentally the behavior of a water soluble associating polymer system, hydrophobically modified (hydroxypropyl)guar, with very few randomly distributed hydrophobic substituents along the chains. We focus mainly on the rheological effects due to the superposition of the reversible hydrophobic interaction network on the physical entanglement network in dense macromolecular systems of that kind. Both linear and nonlinear response to transient, steady, and oscillatory shear flow prove that, in the semidilute and moderately concentrated regime, the hydrophobically associating polymer behaves like a classical dense macromolecular system whose long‐time dynamics can be described using only one long relaxation time, identified as a retarded disengagement time, much larger than the association lifetime. The temporary hydrophobically associating network can be destroyed when applying a critical shear stress τc, which is studied as a function of polymer concentration.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.85.Jn Viscosity measurements
83.80.Jx Reacting systems: thermosetting polymers, chemorheology, rheokinetics

Reliability of dynamic mechanical thermal analyses (DMTA) for the study of frozen aqueous systems

G. Blond, K. Ivanova, and D. Simatos

J. Rheol. 38, 1693 (1994); http://dx.doi.org/10.1122/1.550567 (11 pages)

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Frozen aqueous solutions were studied using dynamic mechanical spectrometry. DMTA measurements required different devices because of the large evolution of the rheological behavior of the mixtures with temperature, particularly a strong decrease in rigidity during the melting of the ice. For stabilized frozen solutions in which the solutes were not able to crystallize, DMTA showed clearly that the beginning of softening was due to a glass transition of the amorphous fraction. The temperature range, where it is observed, corresponds well to the beginning of the two‐step thermal feature observed by differential scanning calorimetry before the ice melting. Compression tests have a better sensitivity at low temperatures but only shear tests allow one to make a full examination of the sample changes during the glass transition of the amorphous phase, and then the ice melting, during the heating process.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.80.Lz Physiological materials (e.g. blood, collagen, etc.)
05.70.Ce Thermodynamic functions and equations of state

Droplet deformation in polymer blends during uniaxial elongational flow: Influence of viscosity ratio for large capillary numbers

I. Delaby, B. Ernst, Y. Germain, and R. Muller

J. Rheol. 38, 1705 (1994); http://dx.doi.org/10.1122/1.550568 (16 pages) | Cited 11 times

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The deformation in uniaxial elongational flow of dispersed droplets in immiscible molten polymer blends was studied for viscosity ratios 0.005<p=η(drop)/η(matrix)<13 and negligible interfacial tension, with an original method based on quenching elongated specimens. Although drop deformations (drop major axis over initial diameter) were in the range 1≤λd≤5, good overall agreement was found with the small deformation Newtonian theory, which predicts that the drop versus matrix deformation ranges from 5/3 to 0 when p increases from 0 to infinity. The theoretical prediction that for p lower than 1, the droplet should deform more than the faraway surrounding matrix, with a limiting ratio of 5/3 at vanishing droplet viscosity, was verified both experimentally and numerically with a finite element simulation.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.50.Jf Extensional flow and combined shear and extension

Creep behavior of electrorheological fluids

Yasufumi Otsubo and Kazuya Edamura

J. Rheol. 38, 1721 (1994); http://dx.doi.org/10.1122/1.550601 (13 pages) | Cited 1 time

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Composite particles consisting of a polymer core and an inorganic shell were formed by suspension polymerization. For suspensions in a silicone oil, the steady‐shear viscosity and creep behavior were measured in electric fields up to 2.0 kV mm−1. Although the polymer core is not ER active, the suspensions of composite particles show a striking increase in the steady‐shear viscosity and the flow curve changes from Newtonian to Bingham profiles. The ER effects can be attributed to the shell layers on the polymer surfaces. The creep curves at low stresses are composed of instantaneous elastic, retarded elastic, and viscous regions. With increasing stress the retarded elastic and viscous components decrease. At some critical stress the strain almost instantaneously increases and reaches the equilibrium without viscous flow. After the removal of the critical stress, the suspensions show no elastic recovery. Therefore the creep and recovery behavior is purely plastic and the critical stress corresponds to the static yield value. The application of stresses above the static yield value causes the suspensions to flow. The development of yield stress (plateau value) in steady shear can be derived from the ideal chain model in which the particles all align into chains of single particle width and equal spacing. However, the model cannot predict the instantaneous deformation without recovery below the yield stress. The thick column formed by several chains may be responsible for purely plastic responses.
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83.80.Gv Electro- and magnetorheological fluids
83.60.La Viscoplasticity; yield stress
83.60.Np Effects of electric and magnetic fields

A stable ‘‘island’’ in the slip‐stick region of linear low‐density polyethylene

Stephanus Pudjijanto and Morton M. Denn

J. Rheol. 38, 1735 (1994); http://dx.doi.org/10.1122/1.550523 (10 pages) | Cited 5 times

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A stable ‘‘island’’ has been discovered in the slip‐stick region of a linear low‐density polyethylene. Within this region, which exists only in a narrow temperature range, pressure oscillations cease, the pressure drop falls by a substantial amount, and the extrudate becomes reasonably smooth. Unstable oscillating flow persists at throughputs on both sides of this island. The existence of this intermediate stable flow challenges all current theories of extrusion instabilities. The phenomenon resembles observations of a drop in extrusion pressure for which a mesophase transition has been suggested.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.-v Deformation and flow
83.60.Uv Wave propagation, fracture, and crack healing

Time‐dependent compressible extrudate‐swell problem with slip at the wall

Georgios C. Georgiou and Marcel J. Crochet

J. Rheol. 38, 1745 (1994); http://dx.doi.org/10.1122/1.550524 (11 pages) | Cited 4 times

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We solve the time‐dependent compressible Newtonian extrudate‐swell problem with slip at the wall, in an attempt to simulate the stick‐slip extrusion instability. An arbitrary nonlinear slip model relating the shear stress to the velocity at the wall is employed, such that the flow curve consists of two stable branches separated by an unstable negative‐slope branch. Finite elements are used for the space discretization and a standard fully implicit scheme for the time discretization. When the volumetric flow rate at the inlet is in the unstable regime and compressibility is taken into account, self‐sustained periodic oscillations of the pressure drop and of the mass flow rate at the exit are observed and the extrudate surface becomes wavy, as is the case in stick‐slip instability. Results are presented for different values of the compressibility number. As compressibility is reduced, the frequency of the oscillations becomes higher, the amplitude of the pressure drop oscillations decreases, and the amplitude of the mass flow‐rate oscillations decreases, whereas the amplitude and the wavelength of the free‐surface waves decrease.
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83.50.Lh Slip boundary effects (interfacial and free surface flows)
83.50.-v Deformation and flow
47.11.-j Computational methods in fluid dynamics

NMR flow imaging of aqueous polysaccharide solutions

S. J. Gibbs, D. Xing, T. A. Carpenter, L. D. Hall, S. Ablett, I. D. Evans, W. Frith, and D. E. Haycock

J. Rheol. 38, 1757 (1994); http://dx.doi.org/10.1122/1.550525 (11 pages) | Cited 5 times

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Nuclear‐magnetic‐resonance (NMR) flow imaging with spatial resolution of the order of 200 μm is used to measure the velocity fields in aqueous solutions of 0.2% and 1% xanthan gum and 1% guar gum for steady flow in a 1.2 cm internal diameter cylindrical polymethylmethacrylate pipe. The velocity fields show little evidence of apparent wall slip and are differentiated to obtain relationships between shear stress and shear rate which span over four decades in shear rate for the xanthan solutions and approximately three decades for the guar solution; these data agree well with those obtained by cone‐and‐plate viscometry. The behavior of the xanthan solutions is well described by a power‐law dependence of shear stress on shear rate, and the guar solution is better described by a Cross‐type relationship. The implications of these studies for future NMR flow imaging studies of more complex systems are discussed.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Lh Slip boundary effects (interfacial and free surface flows)
83.85.-c Techniques and apparatus
76.60.-k Nuclear magnetic resonance and relaxation

Numerical interconversion of linear viscoelastic material functions

D. W. Mead

J. Rheol. 38, 1769 (1994); http://dx.doi.org/10.1122/1.550526 (27 pages) | Cited 6 times

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Calculation of the relaxation modulus in a manner which addresses the ill‐posed nature of the problem specifically in the terminal and plateau regions is essential in order to subsequently determine a molecular weight distribution. A novel method to effect this result is demonstrated. The relaxation modulus is modeled as a discrete N element Maxwell (N≫1) line spectrum. The method incorporates additional independent rheological data into a constrained linear regression with regularization. Specifically, the zero shear viscosity and the steady‐state recoverable compliance are used to impose integral moment equality constraints on the calculated relaxation modulus. Moment constraints necessarily generate a self‐consistent conversion. All moduli are further constrained to be positive. The numerical method is robust and capable of extracting meaningful relaxation spectra from severely error infected and/or incomplete data sets. Imposing moment constraints dramatically reduces the error and dispersion of the calculated relaxation and retardation spectra in the terminal and plateau regions. Analytic conversion of the relaxation modulus to the compliance function is demonstrated through knowledge of the root sequence for a discrete Maxwell model.
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83.60.Bc Linear viscoelasticity
83.10.Gr Constitutive relations

Determination of molecular weight distributions of linear flexible polymers from linear viscoelastic material functions

D. W. Mead

J. Rheol. 38, 1797 (1994); http://dx.doi.org/10.1122/1.550527 (31 pages) | Cited 12 times

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Numerical and analytical methods are developed to invert the double reptation mixing rule to determine the molecular weight distribution (MWD). An analytic method involving Mellin transforms is developed for the case of a single exponential monodisperse relaxation function. A general analytic solution for the MWD is generated for a step‐function monodisperse relaxation function. Numerical methods are developed for more general multiple time constant monodisperse relaxation functions. Both analytical and numerical methods are simple, robust, and capable of appropriately handling error‐infected experimental data. The power‐law relaxation modulus associated with broad MWD commercial polymer is analytically inverted to generate the corresponding molecular weight distribution. MWDs calculated from rheological data for polybutadiene and polypropylene are in close agreement with the corresponding GPC data and are very sensitive to small amounts of high molecular weight material present. The fundamental origins of this sensitivity lie in the intrinsically nonlinear nature of the dependence of rheological properties on molecular weight. The quality of the results suggest that the ‘‘double reptation’’ mixing rule captures an essential feature of the physics of entangled polydisperse polymeric systems.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.60.Bc Linear viscoelasticity
83.10.Gr Constitutive relations
47.11.-j Computational methods in fluid dynamics

A numerical study of three‐dimensional Jeffery orbits in shear flow

M. S. Ingber and L. A. Mondy

J. Rheol. 38, 1829 (1994); http://dx.doi.org/10.1122/1.550604 (15 pages) | Cited 1 time

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We perform numerical simulations of rods and spheroids undergoing Jeffery orbits in a variety of shear flows. The numerical simulations are based on the boundary element method, which allows for the accurate modeling of the problem geometry. We compare the period of rotation for spheroids and rods, both far from walls and very close to walls. We find that the wall effects in three dimensions are minimal, even for flow in gaps not much larger than the longest dimension of the particle. We also show that two‐dimensional simulations grossly overpredict the wall effects seen in three dimensions. Results are similar for both linear and nonlinear shear flows. We also briefly look at the orbital motion of a particle in close proximity to another particle, and show that, again, there is very little effect on the period of rotation, although the resulting centroid trajectories are very different from that of an isolated particle.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.50.Ax Steady shear flows, viscometric flow
83.10.Pp Particle dynamics
47.11.-j Computational methods in fluid dynamics

Flow of colloidal aqueous silica dispersions

J. Persello, A. Magnin, J. Chang, J. M. Piau, and B. Cabane

J. Rheol. 38, 1845 (1994); http://dx.doi.org/10.1122/1.550528 (26 pages) | Cited 14 times

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Concentrated dispersions of colloidal silica particles in water behave as soft solids. Under low stresses they show viscoelastic behavior, i.e., elastic response at short times and viscous creep at long times. Visualization of the deformation field shows that in this case the shear is homogeneous throughout the sample. Under large stresses they yield and accommodate any rate of shear; the dynamic yield stress follows the osmotic pressure of the dispersion. Visualization of the flow field shows that in this case the shear localizes in internal slip layers. The mechanism for localization results from release of water into fractures which let the solid regions flow past each other. At rest the solid regions reabsorb this water and heal the fractures. In this sense the flow is self‐lubricating.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.50.Lh Slip boundary effects (interfacial and free surface flows)
83.60.La Viscoplasticity; yield stress
83.85.-c Techniques and apparatus

Effect of particulate solids on the rheology of a lyotropic gel medium

S. V. Shouche, D. K. Chokappa, V. M. Naik, and D. V. Khakhar

J. Rheol. 38, 1871 (1994); http://dx.doi.org/10.1122/1.550529 (14 pages)

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Experimental studies of the rheology of concentrated suspensions of particulate solids (marble) in a lyotropic gel phase (potassium palmitate with 40% water) were carried out. Such gels are viscoplastic and are characterized by strong colloidal interactions. Suspensions with lyotropic gels as a continuous phase serve as models for systems such as household detergent products, and processed foods. For comparison, experiments were also carried out on suspensions of the same solids in a viscous Newtonian medium (silicone oil). The steady shear experimental data for both the systems were fitted by the Bingham model. The entrance pressure drop for capillary flow of the gel–marble suspensions was interpreted in terms of an entrance yield stress. The latter when extrapolated to zero extrusion speeds was found to be nearly independent of die geometry, and was found to increase exponentially with solids volume fraction. The Bingham yield stress showed a similar behavior with volume fraction though its magnitude was found to be one to two orders smaller. For fixed volume fractions and shear rate, the apparent relative viscosity was found to be significantly larger for suspensions with the gel medium as compared to the Newtonian medium. The increase in the storage modulus of the gel suspensions with solids concentration showed a fundamentally different trend as compared to the Newtonian medium, increasing by two orders of magnitude on the addition of just 5% (v/v) of the particulate solids. Such behavior is typical of systems described by isostrain constitutive models, and might be a result of the formation of a sample‐spanning structure of particles bridged by the gel.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.60.La Viscoplasticity; yield stress
83.85.Cg Rheological measurements—rheometry
83.85.Jn Viscosity measurements

High frequency modulus of hard sphere colloids

R. A. Lionberger and W. B. Russel

J. Rheol. 38, 1885 (1994); http://dx.doi.org/10.1122/1.550530 (24 pages) | Cited 38 times

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The singular nature of the hard sphere potential combined with lubrication stresses near contact poses interesting issues with respect to the high frequency viscoelastic behavior. Dilute theories demonstrate clearly that soft potentials and/or lubrication stresses that reduce the relative mobility to zero at contact lead to a well defined plateau in G′ as ω→∞, whereas a hard sphere potential without hydrodynamic interaction produces G≊ω1/2 in this limit. The former follows from a small deformation of the equilibrium structure due solely to the oscillatory convection and the latter from a diffusional boundary layer near contact required to satisfy the no‐flux boundary condition. Two sets of data that delineate the high frequency response for colloidal hard spheres at high volume fraction appear to differ in this regime, suggesting different physics for the interactions at small separations. Here we apply our nonequilibrium theory to extend the existing treatments to high volume fractions to predict both limits quantitatively and provide a possible interpretation for the experimental results. The two experimental systems only differ in the surface modification of the particles and the high frequency modulus is the only rheological property sensitive to this difference. The predictions of our theory with varying extent of hydrodynamic interaction illustrate the link between the behavior of the high frequency modulus and the hydrodynamic properties very near the particle surface.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.10.Kn Reptation and tube theories
83.10.Mj Molecular dynamics, Brownian dynamics
83.60.Bc Linear viscoelasticity
83.10.Gr Constitutive relations

On consistency criteria for stress tensors in kinetic theory models

Jay D. Schieber and Hans Christian Öttinger

J. Rheol. 38, 1909 (1994); http://dx.doi.org/10.1122/1.550531 (16 pages) | Cited 3 times

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Two different consistency criteria are considered for the stress tensor expressions of two different kinetic theory models for dilute polymer solutions. The criteria are material objectivity and thermodynamic consistency. Two separate approaches for checking thermodynamic consistency are considered, the first proposed by Grmela [Phys. Lett. 111A, 41 (1985)] and the second by Jongschaap [Lecture Notes in Physics (Springer, Berlin, 1991)]. The two models considered are a Hookean dumbbell model with internal viscosity (no linearization or rotation matrix approximations), and an inertial, elastic bead‐spring chain. Both sets of criteria may be applied to these models without finding either a closed‐form expression for the stress tensor, or solving any of the equations. We find that the Giesekus form for the stress tensor expression for a Hookean dumbbell with internal viscosity is both thermodynamically consistent and objective, whereas the Kramers form is not thermodynamically consistent. The Kramers form for the stress tensor is found to be thermodynamically consistent for an inertial, elastic bead‐spring chain, but is not materially objective. We also find that the approaches of Grmela and Jongschaap are the same, although each requires a different ansatz for the relationship between thermodynamic quantities and polymer conformations.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.10.Gr Constitutive relations
83.10.Ff Continuum mechanics

Single‐point correction for parallel disks rheometry

M. S. Carvalho, M. Padmanabhan, and C. W. Macosko

J. Rheol. 38, 1925 (1994); http://dx.doi.org/10.1122/1.550532 (12 pages) | Cited 4 times

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The nonhomogeneous nature of the flow in the parallel disks rheometer necessitates the differentiation of the measured quantities (torque and normal force) with respect to the shear rate at the disk rim. Commercial instruments do not calculate true material functions online, rather they report apparent Newtonian values, i.e., ones obtained assuming the material functions are constants. In this work, we present a single‐point correction technique to obtain approximate values for material functions without numerical differentiation. The advantage of the single‐point correction method is that it gives more accurate results than the apparent Newtonian values and it takes less time than numerical differentiation. This can, therefore, be useful in quality control laboratories and for process‐line measurements where reasonably accurate data are needed in a short time. A single‐point correction is applied to the parallel disks device for the shear viscosity and a new correction method for the normal stress coefficients is also developed. The accuracy of these approximate methods is tested with experimental results for a polymer melt and a polymer solution. The correction for both shear viscosity η and normal stress coefficient Ψ≡Ψ1−Ψ2 avoids the numerical differentiation of the data and can be easily implemented in software that provide online material functions.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.85.Jn Viscosity measurements
83.85.Lq Normal stress difference measurements

Note: The work‐hardening behavior of aggregated TiO2 suspensions

T. Aubry and M. Moan

J. Rheol. 38, 1937 (1994); http://dx.doi.org/10.1122/1.550533 (4 pages)

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This note presents a nonclassical nonlinear rheological behavior experimentally observed with TiO2 aggregated suspensions above some volume fraction. It is characterized by a sinusoidal response to oscillatory shear flow with G′≫G″ but differs from purely elastic response because it is history‐dependent and G′ increases with increasing imposed shear stress below an apparent yield stress. This work‐hardening behavior is discussed in terms of the structure of the aggregates present in the suspension.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.60.La Viscoplasticity; yield stress
83.10.Gr Constitutive relations
83.85.Cg Rheological measurements—rheometry

Letter to the Editor: Which Is More Critical— The Stress Or The Strain?

David Holland

J. Rheol. 38, 1941 (1994); http://dx.doi.org/10.1122/1.550534 (3 pages) | Cited 1 time

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Abstract Unavailable
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83.85.Cg Rheological measurements—rheometry
83.60.Bc Linear viscoelasticity
83.10.Gr Constitutive relations
83.80.Lz Physiological materials (e.g. blood, collagen, etc.)
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