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Nov 1999

Volume 43, Issue 6, pp. 1339-1710


Entry flow of a low-density-polyethylene melt into a slit die: An experimental study by laser-Doppler velocimetry

E. Wassner, M. Schmidt, and H. Münstedt

J. Rheol. 43, 1339 (1999); http://dx.doi.org/10.1122/1.551050 (15 pages) | Cited 3 times

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The flow behavior of a low-density-polyethylene melt in a 14:1 planar contraction was investigated by laser-Doppler velocimetry. The velocity field in the central plane of the flow channel is composed of the measurement of the velocity components in and perpendicular to the direction of extrusion. Two dies differing in their entrance angles are compared. In the case of the flat entry die large recirculating vortices are found in front of the die entry plane. Under stable flow conditions there is no material exchange between the vortices and the primary flow. It is shown that very small velocities within the vortices can be measured accurately. In the case of the oblique entry die no vortices are found. By the normalization of the velocity profiles with the average velocity in the die, calculated independently from the mass flow rate, an output-invariant presentation is found for the apparent shear rate range from 53 to 182 s−1. The velocity distribution along the centerline of the flow channel exhibits a pronounced velocity overshoot shortly after the die entry plane. The distance up to a fully developed velocity field within the die is about 15 times the height of the slit. Due to the acceleration of the melt in front of the die entry large elongational deformations occur. The resulting maximum elongation rates (20 s−1) are very high compared to those achievable by elongational rheometers. It is demonstrated by the comparison of the strain rate tensor components that the elongational deformation in the center plane of the flow channel is planar. © 1999 Society of Rheology.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
47.60.-i Flow phenomena in quasi-one-dimensional systems
83.50.-v Deformation and flow
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.50.-d Non-Newtonian fluid flows
06.30.Gv Velocity, acceleration, and rotation
81.10.Fq Growth from melts; zone melting and refining

Melt rheology of randomly branched polystyrenes

Dino Ferri and Paolo Lomellini

J. Rheol. 43, 1355 (1999); http://dx.doi.org/10.1122/1.551048 (18 pages) | Cited 4 times

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Melt rheological properties of different homologous series of linear polystyrenes (LPS) and randomly branched polystyrenes (RBPS) in both linear and nonlinear viscoelastic response regions are presented. In the linear regime, the master curves of the experimentally determined viscoelastic functions reveal that the temperature dependence of the shift factors aT for all the samples follow the Vogel–Tammann–Fulcher equation: aT∝exp[B/(T−T0)]. The value of the apparent activation energy B is found to increase slightly with an increasing degree of branching, reflecting a stronger temperature dependence of the viscosity of RBPS with respect to that of LPS. This difference is approached within the framework of both Ngai’s coupling model and free volume theory. In the nonlinear regime, the shear rate dependence of the steady state viscosity η(math), corrected for both non-Newtonian and entrance effects, was measured. A comparison with the angular frequency dependence of the dynamic complex viscosity ∣η∗(ω)∣ reveals interesting behavior concerning the Cox–Merz rule. In the non-Newtonian flow region, for LPS the relationship η(math) < ∣η∗(ω)∣ is found to hold. On the other hand, RBPS exhibit an unusual failure of the rule characterized by the relationship η(math) > ∣η∗(ω)∣. Elongational behavior of RBPS is also presented. Assuming a Wagner type single integral constitutive equation for the RBPS, a generalized time–temperature superposition principle in the field of nonlinear viscoelasticity is attempted: elongational stress curves measured at different temperatures are found to qualitatively match the same master curve if both the time and strain rate are reduced by an appropriate shift factor. © 1999 Society of Rheology.
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83.80.Sg Polymer melts
83.80.Rs Polymer solutions
83.60.Bc Linear viscoelasticity
66.20.-d Viscosity of liquids; diffusive momentum transport
47.50.-d Non-Newtonian fluid flows
36.20.Cw Molecular weights, dispersity

Classification of flow modes of viscoelastic fluids at a junction of two stratified laminar flow layers

Hiroshi Yamaguchi, Takeshi Yasumoto, and Hideaki Yamamoto

J. Rheol. 43, 1373 (1999); http://dx.doi.org/10.1122/1.551049 (18 pages)

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Experiments were conducted in order to obtain flow states occurring at a junction of two laminar flow layers. In the present study, various combinations of Newtonian and non-Newtonian fluids for two laminar layers were tested in a relatively high-speed stratification process where the inertia of flow has to be taken into account. From experimental results, flow states at a junction with two different junction angles were classified into 10 flow modes and these modes were arranged to establish a three-dimensional mode map using a generalized Reynolds number and a Deborah number. It was revealed that a mutual relationship among inertial, viscous, and elastic effects is essential for interfacial deformation and instability in the stratified flow. It was also shown that the junction angles are important factors in the determination of flow modes appearing in the region of the junction. © 1999 Society of Rheology.
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47.55.Hd Stratified flows
45.70.Mg Granular flow: mixing, segregation and stratification
83.60.Df Nonlinear viscoelasticity

In situ characterization by small angle light scattering of the shear-induced coalescence mechanisms in immiscible polymer blends

D. Rusu and E. Peuvrel-Disdier

J. Rheol. 43, 1391 (1999); http://dx.doi.org/10.1122/1.551051 (19 pages) | Cited 5 times

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This work presents an in situ experimental investigation of the shear-induced coalescence mechanism in low concentration polymer blends (1%–10%). An original sizing method based on small-angle light scattering and optical microscopy were used to determine the evolution of the drop size distributions as a function of time. In order to study the pure coalescence mechanisms, measurements were conducted according to a specific flow protocol. The influences of the shear rate, initial morphology, concentration of the polymer blend and phase inversion on the coalescence kinetics were investigated. The investigated blends are mixtures of polydimethylsiloxane and polyisobutene. The amount of strain, the step-down rate ratio and the concentration squared are identified as relevant parameters to describe the coalescence kinetics. The dependence of the steady state drop sizes on the applied shear rate is well described by a coalescence model considering partially mobile interfaces. © 1999 Society of Rheology.
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78.35.+c Brillouin and Rayleigh scattering; other light scattering
83.80.Tc Polymer blends
83.50.Ax Steady shear flows, viscometric flow
47.55.D- Drops and bubbles

Vanishing elasticity for wet foams: Equivalence with emulsions and role of polydispersity

A. Saint-Jalmes and D. J. Durian

J. Rheol. 43, 1411 (1999); http://dx.doi.org/10.1122/1.551052 (12 pages) | Cited 25 times

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We present an experimental study of the rheology of polydisperse aqueous foams of different gas volume fractions ϕ. With oscillatory deformation at fixed frequency, we determine the behavior of the maximum stress as a function of the strain amplitude. At low strain, the maximum stress increases linearly, defining a shear modulus G. At progressively higher strains, the response eventually becomes nonlinear, defining the yield strain and the yield stress. While ϕ decreases toward ϕc=0.635±0.01, G goes to zero, and the yield stress decreases by many orders of magnitude with a quadratic behavior. The yield strain, which can be extrapolated to 0.18±0.02 at ϕ=1, has a minimum value of 0.045±0.010 at ϕc. This behavior shows the occurrence of a melting transition located at ϕc, which can be correlated to the random close packing of spheres. We compare these results to similar ones obtained previously for monodisperse and polydisperse emulsions. Our new experiments clarify the rheological similarities between emulsions and foams, as well as the role of polydispersity. We find that as long as polydispersity is moderate, it does not play a crucial role in the elastic response of foams and emulsions. © 1999 Society of Rheology.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.60.La Viscoplasticity; yield stress
62.10.+s Mechanical properties of liquids
82.70.Rr Aerosols and foams
47.35.-i Hydrodynamic waves

Optical behavior of an associating polymer under shear flow

J.-F. Le Meins, J.-F. Tassin, and J.-M. Corpart

J. Rheol. 43, 1423 (1999); http://dx.doi.org/10.1122/1.551053 (14 pages) | Cited 2 times

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Flow birefringence and dichroism experiments are used to study the behavior of solutions of a hydrophobic ethoxylated urethane with a molecular weight of 35 000 g/mol and a C16 hydrophobic end cap in a concentration range around C∗. Relaxation experiments after step shear have shown the existence of two relaxation processes. The first relaxation process with a characteristic time, τshort≈0.1 s, independent of concentration, has been attributed to the lifetime of an end group in a micelle and subsequent relaxation through a Rouse process. The second relaxation process (τlong≈300 s), has been attributed to the relaxation of aggregates of polyoxyethylene chains. They induce a small dichroism in the solutions and damped oscillations in start-up shear flows at low-shear rates. Upon cessation of steady-shear flow, the two relaxations are still observed, the amplitude of the short time one increasing with shear rate. The origin of this long-time relaxation, which is not observed in classical rheological measurements, is attributed to the presence of organic impurities remaining from the chemical modification of the polymer. Extensive purification of the polymer leads to the disappearance of these impurities and consequently of the long relaxation process. © 1999 Society of Rheology.
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83.60.Df Nonlinear viscoelasticity
47.50.-d Non-Newtonian fluid flows
83.50.Ax Steady shear flows, viscometric flow
78.20.Fm Birefringence
83.80.Rs Polymer solutions
83.80.Sg Polymer melts

Prediction of the wax content of the incipient wax-oil gel in a pipeline: An application of the controlled-stress rheometer

Probjot Singh, H. Scott Fogler, and Nagi Nagarajan

J. Rheol. 43, 1437 (1999); http://dx.doi.org/10.1122/1.551054 (23 pages) | Cited 2 times

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High molecular weight paraffins are known to form gels of complex morphology at low temperatures due to the low solubility of these compounds in aromatic or naphthene-base oil solvents. The characteristics of these gels are strong functions of the shear and thermal histories of these samples. A model system of wax and oil was used to understand the gelation process of these mixtures. A significant depression in the gel point of a wax-oil sample was observed by either decreasing the cooling rate or increasing the steady shear stress. The wax-oil sample separates into two layers of different characteristics, a gel-like layer and a liquid-like layer, when sheared with a controlled-stress rheometer at high steady shear stresses and low cooling rates. The phase diagram of the model wax-oil system, obtained using a controlled-stress rheometer, was verified by analyzing the wax content of the incipient gel deposits formed on the wall of a flow loop. Based on the rheological measurements, a law has been suggested for the prediction of the wax content of the gel deposit on the laboratory flow loop walls. The wax content of the incipient gel formed on the wall of a field subsea pipeline was predicted to be much higher than that for the flow loop at similar operating conditions. This variation in the gel deposit characteristics is due to the significant differences in the cooling histories in the two cases. © 1999 Society of Rheology.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
82.70.Gg Gels and sols
64.75.-g Phase equilibria
83.50.Ax Steady shear flows, viscometric flow

A thermodynamically admissible reptation model for fast flows of entangled polymers

Hans Christian Öttinger

J. Rheol. 43, 1461 (1999); http://dx.doi.org/10.1122/1.551055 (33 pages) | Cited 17 times

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The primary purpose of this paper is to introduce the effect of chain stretching into a previously developed, thermodynamically admissible reptation model incorporating anisotropic tube cross sections, double reptation, and convective constraint release, while avoiding the independent alignment approximation. A second goal is the detailed illustration of the thermodynamic modeling approach. Two versions of the model with different stretching mechanisms are proposed, and the simpler one sheds new light on thermodynamically admissible reptation models without independent alignment. The stochastic reformulation of the new model, its simulation, its linear viscoelastic properties, its predictions for rapid double-step shear strains, and the model parameters are discussed in detail. © 1999 Society of Rheology.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.80.-k Material type
83.60.Bc Linear viscoelasticity
47.50.-d Non-Newtonian fluid flows
47.27.T- Turbulent transport processes
65.20.-w Thermal properties of liquids
65.40.gd Entropy
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.Ey Stochastic processes

Analysis of Palierne’s emulsion model in the case of viscoelastic interfacial properties

U. Jacobs, M. Fahrländer, J. Winterhalter, and Chr. Friedrich

J. Rheol. 43, 1495 (1999); http://dx.doi.org/10.1122/1.551056 (15 pages) | Cited 10 times

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The quantitative understanding of rheological experiments on compatibilized binary polymer blends requires the consideration of viscoelastic interfacial properties. The Palierne model offers these capabilities but a systematic analysis has not been performed yet. Starting from the Palierne model containing a Maxwell ansatz for complex interfacial shear or dilatational moduli and which considers a particle-size distribution function, we find that this model combines parameter and material functions in an ambiguous way. Consequently, a simplified version of the model—frequency-independent interfacial moduli and monomodal particle-size distribution—was introduced. Formulas have been derived for the relaxation times, the form relaxation time, and one additional still longer time which is associated with viscoelastic interfacial properties. We have found a good agreement between the predictions of the model and experimental data as well as the characteristic times in the relaxation time spectrum and the derived time constants for a PS/PMMA blend compatibilized with different amounts of a corresponding symmetric block copolymer. These results reveal that from the rheological point of view, the interface is of almost elastic nature, either shear or dilatational.© 1999 Society of Rheology.
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83.80.Tc Polymer blends
83.60.Df Nonlinear viscoelasticity
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.10.Gr Constitutive relations
82.70.Kj Emulsions and suspensions

Dynamic mechanical properties of linear and cross-linked polyurethane

Frederic Prochazka, Dominique Durand, and Taco Nicolai

J. Rheol. 43, 1511 (1999); http://dx.doi.org/10.1122/1.551057 (14 pages) | Cited 1 time

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Linear polyurethane melts were prepared by a polycondensation reaction of poly(oxypropylene) (POP) diol with a diisocyanate. Covalently cross-linked gels were obtained using three-armed star POP triol. The glass transition temperature and the viscoelastic properties were investigated as a function of the molar mass of the POP precursors. The variation of Tg is dominated by the density of urethane links. The loss peak of the shear modulus at high frequencies or low temperatures broadens with increasing density of urethane links. The gel modulus of end-linked POP triol decreases linearly with increasing molar mass of the precursors. The loss shear modulus of end-linked POP triol has a power law frequency dependence at low frequencies. The exponent of the power law dependence decreases with increasing molar mass of the precursors. Gels formed with POP triol with molar mass larger than 6 kg/mol show the effect of entanglements at intermediate frequencies. © 1999 Society of Rheology.
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83.80.Jx Reacting systems: thermosetting polymers, chemorheology, rheokinetics
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
64.70.P- Glass transitions of specific systems
64.70.Q- Theory and modeling of the glass transition
83.60.Bc Linear viscoelasticity
82.70.Gg Gels and sols
47.50.-d Non-Newtonian fluid flows

Secondary motions in straight and tapered channels: Experiments and three-dimensional finite element simulation with a multimode differential viscoelastic model

Benoît Debbaut and Joseph Dooley

J. Rheol. 43, 1525 (1999); http://dx.doi.org/10.1122/1.551058 (21 pages) | Cited 7 times

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The development of secondary motions due to the nonzero second normal stress difference is observed and analyzed by tracking the motion of the interface between two batches of the same low density polyethylene, each with a different pigmentation. In this article we focus on straight and tapered channels with a square cross section. Three-dimensional numerical simulations are also performed on the basis of a multimode differential viscoelastic fluid model. These calculations allow the investigation of the development of secondary motions in space. Predictions are compared with the experiments: good agreement is found between the experimental observations and their numerical counterparts. The magnitude and the relevance of secondary motions are also discussed. A numerical analysis is carried out on the sensitivity of secondary motions with respect to the nonlinear properties of the viscoelastic model. Finally, we make a brief attempt to explain the mechanism which drives the secondary motions. © 1999 Society of Rheology.
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83.80.Sg Polymer melts
83.60.Df Nonlinear viscoelasticity
83.80.Rs Polymer solutions
47.11.-j Computational methods in fluid dynamics
47.50.-d Non-Newtonian fluid flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
66.20.-d Viscosity of liquids; diffusive momentum transport

Rheological behavior of poly(methyl methacrylate) dispersions stabilized by a diblock copolymer: An anomalous viscosity–particle concentration dependence

Vladimír Pavlínek, Petr Sáha, Jaroslav Stejskal, and Otakar Quadrat

J. Rheol. 43, 1547 (1999); http://dx.doi.org/10.1122/1.551059 (8 pages) | Cited 1 time

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The rheological study of dispersions of poly(methyl methacrylate) particles stabilized in decane by a steric stabilizer, polystyrene-block-poly(ethylene-co-propylene) diblock copolymer, revealed an extremely high apparent viscosity at low shear rates or even the yield stress at a relatively low volume fraction of particles (∼0.1). This behavior is due to highly interacting stabilizer macromolecules anchored to the particle surface. As the concentration of poly(methyl methacrylate) is further increased, the volume fraction of particles also increases, the particle diameter grows, the number of particles is reduced and the viscosity of the dispersion falls. © 1999 Society of Rheology.
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83.80.Tc Polymer blends
83.60.La Viscoplasticity; yield stress
66.20.-d Viscosity of liquids; diffusive momentum transport
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
61.25.H- Macromolecular and polymers solutions; polymer melts
47.50.-d Non-Newtonian fluid flows
47.55.Kf Particle-laden flows
82.70.Kj Emulsions and suspensions

Separability criteria for entangled polymer liquids

Lynden A. Archer

J. Rheol. 43, 1555 (1999); http://dx.doi.org/10.1122/1.551060 (17 pages) | Cited 11 times

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Requirements for factorable nonlinear shear relaxation moduli were investigated using a series of entangled polystyrene/diethylphthalate solutions. Polymer solutions were formulated to maintain fixed entanglement spacing over a broad range of polymer molecular weights, 7 <N/Ne <90, 1.3×105 <ϕMw <1.6×106. For all polymers studied, a separability time λk was identified beyond which step shear relaxation moduli could be factorized into separate strain and time-dependent functions. In every case, λk exceeded the most optimistic estimates for the longest Rouse relaxation time τRouse, in some cases by as much as 2 orders of magnitude. λk was also found to scale nearly as strongly with polymer molecular weight as the terminal relaxation time and limiting shear viscosity. These results provide convincing evidence against a Rouse origin for the separability criterion in entangled polymer liquids, and could help explain previous experimental observations of “delayed” factorability and/or nonfactorable relaxation moduli in well entangled polymer liquids. The experimental findings are discussed in the context of a modified tube model that takes into account tube deformation in flow. © 1999 Society of Rheology.
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83.80.Sg Polymer melts
83.80.Rs Polymer solutions
83.60.Bc Linear viscoelasticity
47.50.-d Non-Newtonian fluid flows
68.03.-g Gas-liquid and vacuum-liquid interfaces
66.20.-d Viscosity of liquids; diffusive momentum transport

Nonhomogenous patterns with core defects in elongational flows of liquid crystal polymers

M. Gregory Forest, Qi Wang, and Hong Zhou

J. Rheol. 43, 1573 (1999); http://dx.doi.org/10.1122/1.551061 (10 pages) | Cited 2 times

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The interaction between flow and orientation of liquid crystalline polymers (LCPs) creates remarkable heterogeneous patterns in which defects, or singular solutions, serve to mediate a confluence of ordered nematic phases. The origin of defects remains a mystery. It is therefore valuable to have models for LCP flows that provide some evidence of defects, and of the corresponding physical competition between flow and LCP properties. In this direction, the flow-orientation moment-averaged Doi model is studied with an imposed elongational flow. Nonhomogeneous, biaxial nematic patterns are discovered in both axial and planar elongation. These exact solutions consist of spatially varying directors in the plane orthogonal to the flow axis, coupled with homogeneous biaxial order parameter equilibria fixed by the LCP concentration (N) and elongation rate (ν). For each (N,ν), the following patterns coexist all with identical order parameter values: the homogeneous patterns of [Macromol. Theory Simul. 4, 857872 (1995)]; radially symmetric director patterns; and finally, director patterns periodic in the cylindrical azimuthal angle. The nonhomogeneous structures are distinguished by the presence of core defects along the axis of flow symmetry, characterized by a logarithmic pressure singularity at the core. © 1999 Society of Rheology.
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83.80.Xz Liquid crystals: nematic, cholesteric, smectic, discotic, etc.
61.25.H- Macromolecular and polymers solutions; polymer melts
61.30.Eb Experimental determinations of smectic, nematic, cholesteric, and other structures

Rheology of a viscoelastic emulsion with a liquid crystalline polymer dispersed phase

Heon Sang Lee and Morton M. Denn

J. Rheol. 43, 1583 (1999); http://dx.doi.org/10.1122/1.551070 (16 pages) | Cited 2 times

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The steady-shear viscosity and first normal stress difference and the dynamic storage and loss moduli have been measured for a blend consisting of a thermotropic liquid crystalline polymer dispersed in a thermoplastic fluoropolymer matrix. The components are immiscible and nonreacting. Consistency with the Palierne emulsion theory for viscoelastic blends is possible if and only if the interfacial tension contribution is negligible for droplets that are comparable in size to a liquid crystalline domain or smaller, while retaining the effect for larger droplets. Steady shear results are approximately described by the scaling of the Doi–Ohta theory, but there is a significant reduction in the excess shear stress over a finite shear-rate range for the lowest concentration, which contains the smallest droplets. © 1999 Society of Rheology.
Show PACS
83.80.Sg Polymer melts
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.50.Ax Steady shear flows, viscometric flow
83.60.Bc Linear viscoelasticity
47.50.-d Non-Newtonian fluid flows
68.03.Cd Surface tension and related phenomena
68.03.-g Gas-liquid and vacuum-liquid interfaces
66.20.-d Viscosity of liquids; diffusive momentum transport

Polymeric and colloidal modes of relaxation in latex dispersions containing associative triblock copolymers

Q. T. Pham, W. B. Russel, J. C. Thibeault, and W. Lau

J. Rheol. 43, 1599 (1999); http://dx.doi.org/10.1122/1.551062 (17 pages) | Cited 1 time

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The viscoelasticity of latex dispersions containing triblock associative polymers exhibits multiple modes of relaxation. Here we confirm that the behavior at high frequency is imparted by the associated solution and characterized by a high frequency modulus and relaxation time comparable to the neat micellar solution at the same concentration. At low frequencies, diffusional modes of the particles generate a power law spectrum of relaxation times. Here the time scales and the volume fraction dependence of the contribution reflect the slower dynamics of particles incorporated into a percolating network via weak attractions between the adsorbed polymer layers. The viscoelasticity of the dispersions is correlated by superimposing the two modes. © 1999 Society of Rheology.
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83.80.Sg Polymer melts
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.60.Bc Linear viscoelasticity
66.20.-d Viscosity of liquids; diffusive momentum transport
62.10.+s Mechanical properties of liquids

Polymer disentanglement in steady-shear flow

Lynden A. Archer

J. Rheol. 43, 1617 (1999); http://dx.doi.org/10.1122/1.551063 (17 pages) | Cited 5 times

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A procedure is presented for investigating entanglement loss in polymer liquids during steady-shear flow. The method combines steady shearing with small-amplitude step strain measurements to determine the elastic modulus Ge of an entangled polymer network under steady-state flow conditions. In this study, superimposed step/steady-shear measurements are used to investigate entanglement loss in narrow molecular weight distribution polystyrene/diethyl phthalate solutions with variable entanglement density (9 < N/Ne < 58). For all materials studied, Ge decreases with increasing shear rate math over a wide range of rates. At high shear rates, an approximate scaling relation Ge(math)∼math−1/2 can be defined for all but the most weakly entangled polymer solution; for this material, a related scaling form Ge(math)∼math−1 correctly describes the experimental results. We also find that the ratio of limiting shear modulus Ge(0) to modulus at finite rate Ge(math) is related to a molecular stretching functional 〈∣E⋅u∣〉 by Ge(0)/Ge(math)≈〈∣E⋅u∣〉p, where p takes on values of 1 and 1/2, depending on whether contour length stretching is taken to be affine p=1, or nonaffine p=1/2. For the lowest molecular weight polymer investigated, the affine stretch result Ge(0)/Ge(math)≈〈∣E⋅u∣〉 fairly describes the experimental results over the entire range of shear rate investigated. Other materials manifest a transition from an initially affine to a square-root nonaffine response Ge(0)/Ge(γ)≈〈∣E⋅u∣〉1/2, as the rate is increased. Implications of these results on polymer contour length dynamics are discussed. © 1999 Society of Rheology.
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47.50.-d Non-Newtonian fluid flows
61.25.H- Macromolecular and polymers solutions; polymer melts
83.50.Ax Steady shear flows, viscometric flow
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
62.20.D- Elasticity
81.40.Jj Elasticity and anelasticity, stress-strain relations

Evolution equations for arbitrary moments of the orientation distribution of rigid-rod molecules

Davide A. Hill

J. Rheol. 43, 1635 (1999); http://dx.doi.org/10.1122/1.551064 (7 pages)

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The kinetic theory for rigid-rod molecules has been successful in describing a variety of experimental observations, from extremely dilute concentrations to the liquid crystalline limit. The theory is formulated in terms of an orientation distribution function, whose tensorial moments can be related to measurable properties. We introduce here a general relation from which evolution equations for moments of arbitrary order can easily be derived. The relation incorporates the effects of flow, magnetic and electric fields (permanent and induced dipoles), as well as “nematic” interactions necessary to describe liquid crystalline transitions. Relevant features of the equation(s) with regard to possible closure strategies are briefly discussed. © 1999 Society of Rheology.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
61.25.H- Macromolecular and polymers solutions; polymer melts
47.50.-d Non-Newtonian fluid flows
64.70.M- Transitions in liquid crystals
61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects on order

Steady-shear viscosity of stirred yogurts with varying ropiness

M. E. van Marle, D. van den Ende, C. G. de Kruif, and J. Mellema

J. Rheol. 43, 1643 (1999); http://dx.doi.org/10.1122/1.551065 (20 pages)

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Stirred yogurt was viewed as a concentrated dispersion of aggregates consisting of protein particles. The steady-shear behavior of three types of stirred yogurt with varying ropiness was investigated experimentally. To describe the shear-dependent viscosity, a microrheological model was used which was developed for weakly aggregating dispersions. This model was capable of successfully describing the steady-state viscosity as a function of shear rate of the stirred yogurts, the protein concentration of which ranged between 2.0% and 3.9%. The value of the fractal dimensionality df, following from the model for the aggregates is about 2.24, which was similar to the value of df found with other methods. Moreover, realistic values were found for the interaction forces (energies) describing interaction between the aggregates. The calculated size of the aggregates was close to the size found before by applying different experimental techniques. Using this model, the interpretation of the measured curves suggests that the exopolysaccharides, produced by the lactic acid bacteria in yogurt, play a significant role in the rheology of stirred yogurt. © 1999 Society of Rheology.
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66.20.-d Viscosity of liquids; diffusive momentum transport
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.80.Lz Physiological materials (e.g. blood, collagen, etc.)
82.70.-y Disperse systems; complex fluids
87.16.-b Subcellular structure and processes
87.14.E- Proteins

An analytical relation between relaxation time spectrum and molecular weight distribution

Wolfgang Thimm, Christian Friedrich, Michael Marth, and Josef Honerkamp

J. Rheol. 43, 1663 (1999); http://dx.doi.org/10.1122/1.551066 (10 pages) | Cited 7 times

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In this article it is shown that the relaxation time spectrum can be analytically related to the molecular weight distribution regarding a recently derived generalized mixing rule. This analytical relation greatly reduces the computational effort to determine the molecular weight distribution from the relaxation time spectrum. In this mixing rule a generalized mixing parameter β has been introduced. This parameter has been controversially discussed in the literature. The value of β has been determined theoretically by [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] as β=1 and [Europhys. Lett. 5, 437–442 (1988); 6, 475 (1988)] and [Polym. Prepr. (Am. Chem. Soc. Div. Polym. Chem.) 28, 185–186 (1987)] (β=2) and experimentally by [J. Rheol. 42, 1153–1173 (1998)] (β=3.84). In this article the influence of β on shape and position of peaks in bimodal molecular weight distributions is emphasized. © 1999 Society of Rheology.
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83.60.Df Nonlinear viscoelasticity
83.60.Bc Linear viscoelasticity
36.20.Cw Molecular weights, dispersity
62.40.+i Anelasticity, internal friction, stress relaxation, and mechanical resonances
81.40.Jj Elasticity and anelasticity, stress-strain relations
61.41.+e Polymers, elastomers, and plastics

A theoretical framework for granular suspensions in a steady simple shear flow

Christophe Ancey, Philippe Coussot, and Pierre Evesque

J. Rheol. 43, 1673 (1999); http://dx.doi.org/10.1122/1.551067 (27 pages) | Cited 15 times

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We focus our attention on granular suspensions made up of noncolloidal spherical particles within a Newtonian fluid. The main objective of this paper is to provide a general framework for the formulation of the bulk stress tensor. The bulk stress within granular suspensions is mainly generated at the particle level by strong interactions between particles, such as friction, collision, and lubricated contact. The existence of a few local mechanisms is a major cause of behavior complexity at the macroscopic scale. A direct consequence is that the constitutive equation is only known for some flow conditions and given types of mixture. Here we have used a microstructural approach, which consists of considering the mixture as an effective continuum at the macroscopic level and inferring the bulk stress tensor from averaging of local interactions and local stresses. The bulk stress tensor may be split into elementary contributions pertaining to particle interactions. A complementary equation standing for the bulk energy dissipation may be needed in some circumstances. The analytical computation of these contributions is generally not possible. We present the various physical or heuristic reasonings usually proposed to circumvent this difficulty. © 1999 Society of Rheology.
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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
47.55.Kf Particle-laden flows
83.80.Fg Granular solids

Letter to the Editor: On the thermorheological complexity and relaxation modes of asphalt cements

Didier Lesueur

J. Rheol. 43, 1701 (1999); http://dx.doi.org/10.1122/1.551068 (4 pages) | Cited 2 times

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83.80.-k Material type
83.10.Gr Constitutive relations
83.60.St Non-isothermal rheology
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
77.22.Ch Permittivity (dielectric function)
66.20.-d Viscosity of liquids; diffusive momentum transport

Response to “Letter to the Editor: ‘On the thermorheological complexity and relaxation modes of asphalt cements’ ” [J. Rheol. 43, 1701 (1999)]

J. Stastna and L. Zanzotto

J. Rheol. 43, 1705 (1999); http://dx.doi.org/10.1122/1.551069 (3 pages) | Cited 1 time

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Abstract Unavailable
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83.80.Nb Geological materials: Earth, magma, ice, rocks, etc.
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.60.St Non-isothermal rheology
77.22.Gm Dielectric loss and relaxation
62.10.+s Mechanical properties of liquids

Letter to the Editor: A note added to “Molecular constitutive equations for a class of branched polymers: The pom–pom polymer” [J. Rheol. 42, 81 (1998)]

P. Rubio and M. H. Wagner

J. Rheol. 43, 1709 (1999); http://dx.doi.org/10.1122/1.551071 (2 pages) | Cited 3 times

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Abstract Unavailable
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47.50.-d Non-Newtonian fluid flows
61.25.H- Macromolecular and polymers solutions; polymer melts
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
66.20.-d Viscosity of liquids; diffusive momentum transport
83.50.Ax Steady shear flows, viscometric flow
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